%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG132+1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 : Sat Jun 21 04:58:21 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.43s
% Output : Proof 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG132+1 : TPTP v9.0.0. Released v2.7.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 10:49:04 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 tff(e1_type, type, (
% 0.19/0.43 e1: $i)).
% 0.19/0.43 tff(op_type, type, (
% 0.19/0.43 op: ( $i * $i ) > $i)).
% 0.19/0.43 tff(e3_type, type, (
% 0.19/0.43 e3: $i)).
% 0.19/0.43 tff(e2_type, type, (
% 0.19/0.43 e2: $i)).
% 0.19/0.43 tff(e0_type, type, (
% 0.19/0.43 e0: $i)).
% 0.19/0.43 tff(1,assumption,(~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))), introduced(assumption)).
% 0.19/0.43 tff(2,plain,
% 0.19/0.43 (((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))) | (op(e3, op(e0, e3)) = e3)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(3,plain,
% 0.19/0.43 (op(e3, op(e0, e3)) = e3),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.19/0.43 tff(4,plain,
% 0.19/0.43 (((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))) | (op(e1, op(e0, e1)) = e1)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(5,plain,
% 0.19/0.43 (op(e1, op(e0, e1)) = e1),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.19/0.43 tff(6,plain,
% 0.19/0.43 (((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))) | (op(e0, op(e0, e0)) = e0)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(7,plain,
% 0.19/0.43 (op(e0, op(e0, e0)) = e0),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[6, 1])).
% 0.19/0.43 tff(8,plain,
% 0.19/0.43 (((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))) | (op(e2, op(e0, e2)) = e2)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(9,plain,
% 0.19/0.43 (op(e2, op(e0, e2)) = e2),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[8, 1])).
% 0.19/0.43 tff(10,assumption,(~(op(e2, e1) = e2)), introduced(assumption)).
% 0.19/0.43 tff(11,plain,
% 0.19/0.43 ((e0 = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 0.19/0.43 inference(commutativity,[status(thm)],[])).
% 0.19/0.43 tff(12,assumption,(~(op(e1, e1) = e2)), introduced(assumption)).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 ((e2 = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 0.19/0.43 inference(commutativity,[status(thm)],[])).
% 0.19/0.43 tff(14,assumption,(op(e0, e1) = e2), introduced(assumption)).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 ((op(e0, e1) = op(e2, e1)) <=> (e2 = op(e2, e1))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[14])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 0.19/0.43 inference(transitivity,[status(thm)],[15, 13])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[16])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = op(e2, e1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(19,axiom,((((((((((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))) & (~(op(e2, e1) = op(e2, e3)))) & (~(op(e2, e2) = op(e2, e3)))) & (~(op(e3, e0) = op(e3, e1)))) & (~(op(e3, e0) = op(e3, e2)))) & (~(op(e3, e0) = op(e3, e3)))) & (~(op(e3, e1) = op(e3, e2)))) & (~(op(e3, e1) = op(e3, e3)))) & (~(op(e3, e2) = op(e3, e3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax3')).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (((((((((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))) & (~(op(e2, e1) = op(e2, e3)))) & (~(op(e2, e2) = op(e2, e3)))) & (~(op(e3, e0) = op(e3, e1)))) & (~(op(e3, e0) = op(e3, e2)))) & (~(op(e3, e0) = op(e3, e3)))) & (~(op(e3, e1) = op(e3, e2)))) & (~(op(e3, e1) = op(e3, e3)))),
% 0.19/0.43 inference(and_elim,[status(thm)],[19])).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 ((((((((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))) & (~(op(e2, e1) = op(e2, e3)))) & (~(op(e2, e2) = op(e2, e3)))) & (~(op(e3, e0) = op(e3, e1)))) & (~(op(e3, e0) = op(e3, e2)))) & (~(op(e3, e0) = op(e3, e3)))) & (~(op(e3, e1) = op(e3, e2)))),
% 0.19/0.43 inference(and_elim,[status(thm)],[20])).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 (((((((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))) & (~(op(e2, e1) = op(e2, e3)))) & (~(op(e2, e2) = op(e2, e3)))) & (~(op(e3, e0) = op(e3, e1)))) & (~(op(e3, e0) = op(e3, e2)))) & (~(op(e3, e0) = op(e3, e3)))),
% 0.19/0.44 inference(and_elim,[status(thm)],[21])).
% 0.19/0.44 tff(23,plain,
% 0.19/0.44 ((((((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))) & (~(op(e2, e1) = op(e2, e3)))) & (~(op(e2, e2) = op(e2, e3)))) & (~(op(e3, e0) = op(e3, e1)))) & (~(op(e3, e0) = op(e3, e2)))),
% 0.19/0.44 inference(and_elim,[status(thm)],[22])).
% 0.19/0.44 tff(24,plain,
% 0.19/0.44 (((((((((((((((((((((((((((((((((((((((((((~(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)))),
% 0.19/0.44 inference(and_elim,[status(thm)],[23])).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 ((((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))) & (~(op(e2, e1) = op(e2, e3)))) & (~(op(e2, e2) = op(e2, e3)))),
% 0.19/0.45 inference(and_elim,[status(thm)],[24])).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 (((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))) & (~(op(e2, e1) = op(e2, e3)))),
% 0.19/0.45 inference(and_elim,[status(thm)],[25])).
% 0.19/0.45 tff(27,plain,
% 0.19/0.45 ((((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))) & (~(op(e2, e1) = op(e2, e2)))),
% 0.19/0.45 inference(and_elim,[status(thm)],[26])).
% 0.19/0.45 tff(28,plain,
% 0.19/0.45 (((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))) & (~(op(e2, e0) = op(e2, e3)))),
% 0.19/0.46 inference(and_elim,[status(thm)],[27])).
% 0.19/0.46 tff(29,plain,
% 0.19/0.46 ((((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))) & (~(op(e2, e0) = op(e2, e2)))),
% 0.19/0.46 inference(and_elim,[status(thm)],[28])).
% 0.19/0.46 tff(30,plain,
% 0.19/0.46 (((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))) & (~(op(e2, e0) = op(e2, e1)))),
% 0.19/0.46 inference(and_elim,[status(thm)],[29])).
% 0.19/0.46 tff(31,plain,
% 0.19/0.46 ((((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))) & (~(op(e1, e2) = op(e1, e3)))),
% 0.19/0.46 inference(and_elim,[status(thm)],[30])).
% 0.19/0.46 tff(32,plain,
% 0.19/0.46 (((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))) & (~(op(e1, e1) = op(e1, e3)))),
% 0.19/0.46 inference(and_elim,[status(thm)],[31])).
% 0.19/0.46 tff(33,plain,
% 0.19/0.46 ((((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))) & (~(op(e1, e1) = op(e1, e2)))),
% 0.19/0.46 inference(and_elim,[status(thm)],[32])).
% 0.19/0.46 tff(34,plain,
% 0.19/0.46 (((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))) & (~(op(e1, e0) = op(e1, e3)))),
% 0.19/0.47 inference(and_elim,[status(thm)],[33])).
% 0.19/0.47 tff(35,plain,
% 0.19/0.47 ((((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))) & (~(op(e1, e0) = op(e1, e2)))),
% 0.19/0.47 inference(and_elim,[status(thm)],[34])).
% 0.19/0.47 tff(36,plain,
% 0.19/0.47 (((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))) & (~(op(e1, e0) = op(e1, e1)))),
% 0.19/0.47 inference(and_elim,[status(thm)],[35])).
% 0.19/0.47 tff(37,plain,
% 0.19/0.47 ((((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))) & (~(op(e0, e2) = op(e0, e3)))),
% 0.19/0.47 inference(and_elim,[status(thm)],[36])).
% 0.19/0.47 tff(38,plain,
% 0.19/0.47 (((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))) & (~(op(e0, e1) = op(e0, e3)))),
% 0.19/0.47 inference(and_elim,[status(thm)],[37])).
% 0.19/0.47 tff(39,plain,
% 0.19/0.47 ((((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))) & (~(op(e0, e1) = op(e0, e2)))),
% 0.19/0.47 inference(and_elim,[status(thm)],[38])).
% 0.19/0.47 tff(40,plain,
% 0.19/0.47 (((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))) & (~(op(e0, e0) = op(e0, e3)))),
% 0.19/0.47 inference(and_elim,[status(thm)],[39])).
% 0.19/0.47 tff(41,plain,
% 0.19/0.47 ((((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))) & (~(op(e0, e0) = op(e0, e2)))),
% 0.19/0.47 inference(and_elim,[status(thm)],[40])).
% 0.19/0.47 tff(42,plain,
% 0.19/0.47 (((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))) & (~(op(e0, e0) = op(e0, e1)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[41])).
% 0.19/0.48 tff(43,plain,
% 0.19/0.48 ((((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))) & (~(op(e2, e3) = op(e3, e3)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[42])).
% 0.19/0.48 tff(44,plain,
% 0.19/0.48 (((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))) & (~(op(e1, e3) = op(e3, e3)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[43])).
% 0.19/0.48 tff(45,plain,
% 0.19/0.48 ((((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))) & (~(op(e1, e3) = op(e2, e3)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[44])).
% 0.19/0.48 tff(46,plain,
% 0.19/0.48 (((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))) & (~(op(e0, e3) = op(e3, e3)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[45])).
% 0.19/0.48 tff(47,plain,
% 0.19/0.48 ((((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))) & (~(op(e0, e3) = op(e2, e3)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[46])).
% 0.19/0.48 tff(48,plain,
% 0.19/0.48 (((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))) & (~(op(e0, e3) = op(e1, e3)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[47])).
% 0.19/0.48 tff(49,plain,
% 0.19/0.48 ((((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))) & (~(op(e2, e2) = op(e3, e2)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[48])).
% 0.19/0.48 tff(50,plain,
% 0.19/0.48 (((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))) & (~(op(e1, e2) = op(e3, e2)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[49])).
% 0.19/0.48 tff(51,plain,
% 0.19/0.48 ((((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))) & (~(op(e1, e2) = op(e2, e2)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[50])).
% 0.19/0.48 tff(52,plain,
% 0.19/0.48 (((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))) & (~(op(e0, e2) = op(e3, e2)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[51])).
% 0.19/0.48 tff(53,plain,
% 0.19/0.48 ((((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))) & (~(op(e0, e2) = op(e2, e2)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[52])).
% 0.19/0.48 tff(54,plain,
% 0.19/0.48 (((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))) & (~(op(e0, e2) = op(e1, e2)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[53])).
% 0.19/0.48 tff(55,plain,
% 0.19/0.48 ((((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))) & (~(op(e2, e1) = op(e3, e1)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[54])).
% 0.19/0.48 tff(56,plain,
% 0.19/0.48 (((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))) & (~(op(e1, e1) = op(e3, e1)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[55])).
% 0.19/0.48 tff(57,plain,
% 0.19/0.48 ((((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))) & (~(op(e1, e1) = op(e2, e1)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[56])).
% 0.19/0.48 tff(58,plain,
% 0.19/0.48 (((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))) & (~(op(e0, e1) = op(e3, e1)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[57])).
% 0.19/0.48 tff(59,plain,
% 0.19/0.48 ((((((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))) & (~(op(e1, e0) = op(e3, e0)))) & (~(op(e2, e0) = op(e3, e0)))) & (~(op(e0, e1) = op(e1, e1)))) & (~(op(e0, e1) = op(e2, e1)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[58])).
% 0.19/0.48 tff(60,plain,
% 0.19/0.48 (~(op(e0, e1) = op(e2, e1))),
% 0.19/0.48 inference(and_elim,[status(thm)],[59])).
% 0.19/0.48 tff(61,plain,
% 0.19/0.48 (~(op(e0, e1) = op(e2, e1))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[60, 18])).
% 0.19/0.48 tff(62,plain,
% 0.19/0.48 (~(op(e2, e1) = e2)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[61, 17])).
% 0.19/0.48 tff(63,assumption,(~(op(e3, e3) = e0)), introduced(assumption)).
% 0.19/0.48 tff(64,plain,
% 0.19/0.48 ((e2 = op(e0, e2)) <=> (op(e0, e2) = e2)),
% 0.19/0.48 inference(commutativity,[status(thm)],[])).
% 0.19/0.48 tff(65,plain,
% 0.19/0.48 ((op(e0, e1) = op(e0, e2)) <=> (e2 = op(e0, e2))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[14])).
% 0.19/0.48 tff(66,plain,
% 0.19/0.48 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e2)),
% 0.19/0.48 inference(transitivity,[status(thm)],[65, 64])).
% 0.19/0.48 tff(67,plain,
% 0.19/0.48 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e2))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.48 tff(68,plain,
% 0.19/0.48 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = op(e0, e2)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(69,plain,
% 0.19/0.48 (~(op(e0, e1) = op(e0, e2))),
% 0.19/0.48 inference(and_elim,[status(thm)],[39])).
% 0.19/0.48 tff(70,plain,
% 0.19/0.48 (~(op(e0, e1) = op(e0, e2))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.48 tff(71,plain,
% 0.19/0.48 (~(op(e0, e2) = e2)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[70, 67])).
% 0.19/0.48 tff(72,plain,
% 0.19/0.48 ((e2 = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.19/0.48 inference(commutativity,[status(thm)],[])).
% 0.19/0.48 tff(73,plain,
% 0.19/0.48 ((e1 = op(e2, e3)) <=> (op(e2, e3) = e1)),
% 0.19/0.48 inference(commutativity,[status(thm)],[])).
% 0.19/0.48 tff(74,assumption,(~(op(e2, e0) = e2)), introduced(assumption)).
% 0.19/0.48 tff(75,assumption,(~(op(e3, e3) = e2)), introduced(assumption)).
% 0.19/0.48 tff(76,plain,
% 0.19/0.48 ((e1 = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 0.19/0.48 inference(commutativity,[status(thm)],[])).
% 0.19/0.48 tff(77,plain,
% 0.19/0.48 ((op(e3, e3) = e1) <=> (e1 = op(e3, e3))),
% 0.19/0.48 inference(symmetry,[status(thm)],[76])).
% 0.19/0.48 tff(78,plain,
% 0.19/0.48 ((e3 = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.19/0.48 inference(commutativity,[status(thm)],[])).
% 0.19/0.48 tff(79,assumption,(~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))), introduced(assumption)).
% 0.19/0.48 tff(80,plain,
% 0.19/0.48 (((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))) | (op(e3, op(e1, e3)) = e3)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(81,plain,
% 0.19/0.49 (op(e3, op(e1, e3)) = e3),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.19/0.49 tff(82,plain,
% 0.19/0.49 ((e0 = op(e0, e3)) <=> (op(e0, e3) = e0)),
% 0.19/0.49 inference(commutativity,[status(thm)],[])).
% 0.19/0.49 tff(83,plain,
% 0.19/0.49 (((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))) | (op(e0, op(e1, e0)) = e0)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(84,plain,
% 0.19/0.49 (op(e0, op(e1, e0)) = e0),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[83, 79])).
% 0.19/0.49 tff(85,plain,
% 0.19/0.49 ((e2 = op(e0, e3)) <=> (op(e0, e3) = e2)),
% 0.19/0.49 inference(commutativity,[status(thm)],[])).
% 0.19/0.49 tff(86,plain,
% 0.19/0.49 ((op(e0, e1) = op(e0, e3)) <=> (e2 = op(e0, e3))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[14])).
% 0.19/0.49 tff(87,plain,
% 0.19/0.49 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e3) = e2)),
% 0.19/0.49 inference(transitivity,[status(thm)],[86, 85])).
% 0.19/0.49 tff(88,plain,
% 0.19/0.49 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e3) = e2))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[87])).
% 0.19/0.49 tff(89,plain,
% 0.19/0.49 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e1) = op(e0, e3)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(90,plain,
% 0.19/0.49 (~(op(e0, e1) = op(e0, e3))),
% 0.19/0.49 inference(and_elim,[status(thm)],[38])).
% 0.19/0.49 tff(91,plain,
% 0.19/0.49 (~(op(e0, e1) = op(e0, e3))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.49 tff(92,plain,
% 0.19/0.49 (~(op(e0, e3) = e2)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[91, 88])).
% 0.19/0.49 tff(93,plain,
% 0.19/0.49 ((e2 = op(e1, e1)) <=> (op(e1, e1) = e2)),
% 0.19/0.49 inference(commutativity,[status(thm)],[])).
% 0.19/0.49 tff(94,plain,
% 0.19/0.49 ((op(e0, e1) = op(e1, e1)) <=> (e2 = op(e1, e1))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[14])).
% 0.19/0.49 tff(95,plain,
% 0.19/0.49 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e2)),
% 0.19/0.49 inference(transitivity,[status(thm)],[94, 93])).
% 0.19/0.49 tff(96,plain,
% 0.19/0.49 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e2))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.49 tff(97,plain,
% 0.19/0.49 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e0, e1) = op(e1, e1)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(98,plain,
% 0.19/0.49 (((((((~(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)))),
% 0.19/0.49 inference(and_elim,[status(thm)],[59])).
% 0.19/0.49 tff(99,plain,
% 0.19/0.49 (~(op(e0, e1) = op(e1, e1))),
% 0.19/0.49 inference(and_elim,[status(thm)],[98])).
% 0.19/0.49 tff(100,plain,
% 0.19/0.49 (~(op(e0, e1) = op(e1, e1))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[99, 97])).
% 0.19/0.49 tff(101,plain,
% 0.19/0.49 (~(op(e1, e1) = e2)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.19/0.49 tff(102,plain,
% 0.19/0.49 (((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))) | (op(e2, op(e1, e2)) = e2)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(103,plain,
% 0.19/0.49 (op(e2, op(e1, e2)) = e2),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[102, 79])).
% 0.19/0.49 tff(104,assumption,(~(op(e0, e3) = e2)), introduced(assumption)).
% 0.19/0.49 tff(105,assumption,(~(op(e1, e0) = e2)), introduced(assumption)).
% 0.19/0.49 tff(106,assumption,(op(e2, op(e1, e2)) = e2), introduced(assumption)).
% 0.19/0.49 tff(107,assumption,(~(op(e1, e3) = e2)), introduced(assumption)).
% 0.19/0.49 tff(108,plain,
% 0.19/0.49 (((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))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(109,plain,
% 0.19/0.49 ((((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))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(110,plain,
% 0.19/0.49 ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) <=> ((op(e1, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e2))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(111,plain,
% 0.19/0.49 (((((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))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[110])).
% 0.19/0.49 tff(112,plain,
% 0.19/0.49 (((((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))),
% 0.19/0.49 inference(transitivity,[status(thm)],[111, 109])).
% 0.19/0.49 tff(113,axiom,(((((((((((((((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))) & ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))) & ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2))) & ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2))) & ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3))) & ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) | (op(e3, e2) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0))) & ((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) | (op(e3, e3) = e0))) & ((((op(e3, e0) = e1) | (op(e3, e1) = e1)) | (op(e3, e2) = e1)) | (op(e3, e3) = e1))) & ((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) | (op(e3, e3) = e1))) & ((((op(e3, e0) = e2) | (op(e3, e1) = e2)) | (op(e3, e2) = e2)) | (op(e3, e3) = e2))) & ((((op(e0, e3) = e2) | (op(e1, e3) = e2)) | (op(e2, e3) = e2)) | (op(e3, e3) = e2))) & ((((op(e3, e0) = e3) | (op(e3, e1) = e3)) | (op(e3, e2) = e3)) | (op(e3, e3) = e3))) & ((((op(e0, e3) = e3) | (op(e1, e3) = e3)) | (op(e2, e3) = e3)) | (op(e3, e3) = e3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax2')).
% 0.19/0.49 tff(114,plain,
% 0.19/0.49 ((((((((((((((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))) & ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))) & ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2))) & ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2))) & ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3))) & ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) | (op(e3, e2) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0))) & ((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) | (op(e3, e3) = e0))) & ((((op(e3, e0) = e1) | (op(e3, e1) = e1)) | (op(e3, e2) = e1)) | (op(e3, e3) = e1))) & ((((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))),
% 0.19/0.50 inference(and_elim,[status(thm)],[113])).
% 0.19/0.50 tff(115,plain,
% 0.19/0.50 (((((((((((((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, 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))),
% 0.19/0.50 inference(and_elim,[status(thm)],[114])).
% 0.19/0.50 tff(116,plain,
% 0.19/0.50 ((((((((((((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, 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))),
% 0.19/0.50 inference(and_elim,[status(thm)],[115])).
% 0.19/0.50 tff(117,plain,
% 0.19/0.50 (((((((((((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, 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))),
% 0.19/0.51 inference(and_elim,[status(thm)],[116])).
% 0.19/0.51 tff(118,plain,
% 0.19/0.51 ((((((((((((((((((((((((((((((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))),
% 0.19/0.51 inference(and_elim,[status(thm)],[117])).
% 0.19/0.51 tff(119,plain,
% 0.19/0.51 (((((((((((((((((((((((((((((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))),
% 0.19/0.51 inference(and_elim,[status(thm)],[118])).
% 0.19/0.51 tff(120,plain,
% 0.19/0.51 ((((((((((((((((((((((((((((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))),
% 0.19/0.52 inference(and_elim,[status(thm)],[119])).
% 0.19/0.52 tff(121,plain,
% 0.19/0.52 (((((((((((((((((((((((((((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))),
% 0.19/0.52 inference(and_elim,[status(thm)],[120])).
% 0.19/0.52 tff(122,plain,
% 0.19/0.52 ((((((((((((((((((((((((((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))),
% 0.19/0.52 inference(and_elim,[status(thm)],[121])).
% 0.19/0.52 tff(123,plain,
% 0.19/0.52 (((((((((((((((((((((((((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))),
% 0.19/0.52 inference(and_elim,[status(thm)],[122])).
% 0.19/0.52 tff(124,plain,
% 0.19/0.52 ((((((((((((((((((((((((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))),
% 0.19/0.53 inference(and_elim,[status(thm)],[123])).
% 0.19/0.53 tff(125,plain,
% 0.19/0.53 (((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))) & ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))),
% 0.19/0.53 inference(and_elim,[status(thm)],[124])).
% 0.19/0.53 tff(126,plain,
% 0.19/0.53 ((((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))) & ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1))),
% 0.19/0.53 inference(and_elim,[status(thm)],[125])).
% 0.19/0.53 tff(127,plain,
% 0.19/0.53 (((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))) & ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0))),
% 0.19/0.53 inference(and_elim,[status(thm)],[126])).
% 0.19/0.53 tff(128,plain,
% 0.19/0.53 ((((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0))),
% 0.19/0.53 inference(and_elim,[status(thm)],[127])).
% 0.19/0.53 tff(129,plain,
% 0.19/0.53 (((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))) & ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3))),
% 0.19/0.54 inference(and_elim,[status(thm)],[128])).
% 0.19/0.54 tff(130,plain,
% 0.19/0.54 ((((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))) & ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3))),
% 0.19/0.54 inference(and_elim,[status(thm)],[129])).
% 0.19/0.54 tff(131,plain,
% 0.19/0.54 (((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))) & ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2))),
% 0.19/0.54 inference(and_elim,[status(thm)],[130])).
% 0.19/0.54 tff(132,plain,
% 0.19/0.54 ((((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))) & ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2))),
% 0.19/0.54 inference(and_elim,[status(thm)],[131])).
% 0.19/0.54 tff(133,plain,
% 0.19/0.54 ((((op(e1, e0) = e2) | (op(e1, e1) = e2)) | (op(e1, e2) = e2)) | (op(e1, e3) = e2)),
% 0.19/0.54 inference(and_elim,[status(thm)],[132])).
% 0.19/0.54 tff(134,plain,
% 0.19/0.54 ((op(e1, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e2) | (op(e1, e3) = e2)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[133, 112])).
% 0.19/0.54 tff(135,plain,
% 0.19/0.54 ((op(e1, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e2) = e2) | (op(e1, e3) = e2)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[134, 108])).
% 0.19/0.54 tff(136,plain,
% 0.19/0.54 (op(e1, e2) = e2),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[135, 107, 12, 105])).
% 0.19/0.54 tff(137,plain,
% 0.19/0.54 (e2 = op(e1, e2)),
% 0.19/0.54 inference(symmetry,[status(thm)],[136])).
% 0.19/0.54 tff(138,plain,
% 0.19/0.54 (op(e2, e2) = op(e2, op(e1, e2))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[137])).
% 0.19/0.54 tff(139,plain,
% 0.19/0.54 (op(e2, e2) = e2),
% 0.19/0.54 inference(transitivity,[status(thm)],[138, 106])).
% 0.19/0.54 tff(140,plain,
% 0.19/0.54 (((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))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(141,plain,
% 0.19/0.54 ((((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))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(142,plain,
% 0.19/0.54 ((((op(e0, e3) = e2) | (op(e1, e3) = e2)) | (op(e2, e3) = e2)) <=> ((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(143,plain,
% 0.19/0.54 (((((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))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[142])).
% 0.19/0.54 tff(144,plain,
% 0.19/0.54 (((((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))),
% 0.19/0.54 inference(transitivity,[status(thm)],[143, 141])).
% 0.19/0.54 tff(145,plain,
% 0.19/0.54 ((((op(e0, e3) = e2) | (op(e1, e3) = e2)) | (op(e2, e3) = e2)) | (op(e3, e3) = e2)),
% 0.19/0.54 inference(and_elim,[status(thm)],[115])).
% 0.19/0.54 tff(146,plain,
% 0.19/0.54 ((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2) | (op(e3, e3) = e2)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.19/0.54 tff(147,plain,
% 0.19/0.54 ((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e2, e3) = e2) | (op(e3, e3) = e2)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[146, 140])).
% 0.19/0.54 tff(148,plain,
% 0.19/0.54 (op(e2, e3) = e2),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[147, 107, 75, 104])).
% 0.19/0.54 tff(149,plain,
% 0.19/0.54 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e2)),
% 0.19/0.54 inference(monotonicity,[status(thm)],[148])).
% 0.19/0.54 tff(150,plain,
% 0.19/0.54 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e2))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[149])).
% 0.19/0.54 tff(151,plain,
% 0.19/0.54 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = op(e2, e3)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(152,plain,
% 0.19/0.54 (~(op(e2, e2) = op(e2, e3))),
% 0.19/0.54 inference(and_elim,[status(thm)],[25])).
% 0.19/0.54 tff(153,plain,
% 0.19/0.54 (~(op(e2, e2) = op(e2, e3))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.19/0.54 tff(154,plain,
% 0.19/0.54 (~(op(e2, e2) = e2)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[153, 150])).
% 0.19/0.54 tff(155,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[154, 139])).
% 0.19/0.54 tff(156,plain,((op(e1, e3) = e2) | (~(op(e2, op(e1, e2)) = e2)) | (op(e1, e1) = e2) | (op(e1, e0) = e2) | (op(e3, e3) = e2) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(157,plain,
% 0.19/0.54 (op(e1, e3) = e2),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[156, 103, 12, 105, 75, 104])).
% 0.19/0.54 tff(158,plain,
% 0.19/0.54 (e2 = op(e1, e3)),
% 0.19/0.54 inference(symmetry,[status(thm)],[157])).
% 0.19/0.54 tff(159,plain,
% 0.19/0.54 (op(e3, e2) = op(e3, op(e1, e3))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[158])).
% 0.19/0.54 tff(160,plain,
% 0.19/0.54 (op(e3, e2) = e3),
% 0.19/0.54 inference(transitivity,[status(thm)],[159, 81])).
% 0.19/0.54 tff(161,plain,
% 0.19/0.54 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e3)),
% 0.19/0.54 inference(monotonicity,[status(thm)],[160])).
% 0.19/0.54 tff(162,plain,
% 0.19/0.54 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e3))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[161])).
% 0.19/0.54 tff(163,plain,
% 0.19/0.54 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = op(e3, e2)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(164,plain,
% 0.19/0.54 (~(op(e1, e2) = op(e3, e2))),
% 0.19/0.54 inference(and_elim,[status(thm)],[50])).
% 0.19/0.54 tff(165,plain,
% 0.19/0.54 (~(op(e1, e2) = op(e3, e2))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.19/0.54 tff(166,plain,
% 0.19/0.54 (~(op(e1, e2) = e3)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[165, 162])).
% 0.19/0.54 tff(167,assumption,(~(op(e1, e2) = e3)), introduced(assumption)).
% 0.19/0.54 tff(168,assumption,(~(op(e1, e2) = e1)), introduced(assumption)).
% 0.19/0.54 tff(169,plain,
% 0.19/0.54 (op(e1, e3) = e2),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[156, 106, 12, 105, 75, 104])).
% 0.19/0.54 tff(170,plain,
% 0.19/0.54 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e2) = e2)),
% 0.19/0.54 inference(monotonicity,[status(thm)],[169])).
% 0.19/0.54 tff(171,plain,
% 0.19/0.54 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = e2))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[170])).
% 0.19/0.54 tff(172,plain,
% 0.19/0.54 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e2) = op(e1, e3)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(173,plain,
% 0.19/0.54 (~(op(e1, e2) = op(e1, e3))),
% 0.19/0.54 inference(and_elim,[status(thm)],[31])).
% 0.19/0.54 tff(174,plain,
% 0.19/0.54 (~(op(e1, e2) = op(e1, e3))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.19/0.54 tff(175,plain,
% 0.19/0.54 (~(op(e1, e2) = e2)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[174, 171])).
% 0.19/0.54 tff(176,plain,
% 0.19/0.54 (((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))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(177,plain,
% 0.19/0.54 ((((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))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(178,plain,
% 0.19/0.54 ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) <=> ((op(e1, e2) = e0) | (op(e1, e2) = e1) | (op(e1, e2) = e2))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(179,plain,
% 0.19/0.54 (((((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))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[178])).
% 0.19/0.54 tff(180,plain,
% 0.19/0.54 (((((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))),
% 0.19/0.54 inference(transitivity,[status(thm)],[179, 177])).
% 0.19/0.54 tff(181,axiom,(((((((((((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))) & ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3))) & ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3))) & ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3))) & ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) | (op(e3, e0) = e3))) & ((((op(e3, e1) = e0) | (op(e3, e1) = e1)) | (op(e3, e1) = e2)) | (op(e3, e1) = e3))) & ((((op(e3, e2) = e0) | (op(e3, e2) = e1)) | (op(e3, e2) = e2)) | (op(e3, e2) = e3))) & ((((op(e3, e3) = e0) | (op(e3, e3) = e1)) | (op(e3, e3) = e2)) | (op(e3, e3) = e3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax1')).
% 0.19/0.55 tff(182,plain,
% 0.19/0.55 ((((((((((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))) & ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3))) & ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3))) & ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3))) & ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) | (op(e3, e0) = e3))) & ((((op(e3, e1) = e0) | (op(e3, e1) = e1)) | (op(e3, e1) = e2)) | (op(e3, e1) = e3))) & ((((op(e3, e2) = e0) | (op(e3, e2) = e1)) | (op(e3, e2) = e2)) | (op(e3, e2) = e3))),
% 0.19/0.55 inference(and_elim,[status(thm)],[181])).
% 0.19/0.55 tff(183,plain,
% 0.19/0.55 (((((((((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))) & ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3))) & ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3))) & ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3))) & ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) | (op(e3, e0) = e3))) & ((((op(e3, e1) = e0) | (op(e3, e1) = e1)) | (op(e3, e1) = e2)) | (op(e3, e1) = e3))),
% 0.19/0.55 inference(and_elim,[status(thm)],[182])).
% 0.19/0.55 tff(184,plain,
% 0.19/0.55 ((((((((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))) & ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3))) & ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3))) & ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3))) & ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3))) & ((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) | (op(e3, e0) = e3))),
% 0.19/0.55 inference(and_elim,[status(thm)],[183])).
% 0.19/0.55 tff(185,plain,
% 0.19/0.55 (((((((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))) & ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3))) & ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3))) & ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3))) & ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3))),
% 0.19/0.55 inference(and_elim,[status(thm)],[184])).
% 0.19/0.55 tff(186,plain,
% 0.19/0.55 ((((((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))) & ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3))) & ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3))) & ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3))),
% 0.19/0.55 inference(and_elim,[status(thm)],[185])).
% 0.19/0.55 tff(187,plain,
% 0.19/0.55 (((((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))) & ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3))) & ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3))),
% 0.19/0.55 inference(and_elim,[status(thm)],[186])).
% 0.19/0.55 tff(188,plain,
% 0.19/0.55 ((((((((((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)) & ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3))) & ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3))) & ((((op(e0, e3) = e0) | (op(e0, e3) = e1)) | (op(e0, e3) = e2)) | (op(e0, e3) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e0) = e1)) | (op(e1, e0) = e2)) | (op(e1, e0) = e3))) & ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3))) & ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3))) & ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3))) & ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3))),
% 0.19/0.55 inference(and_elim,[status(thm)],[187])).
% 0.19/0.55 tff(189,plain,
% 0.19/0.55 (((((((((((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))),
% 0.19/0.56 inference(and_elim,[status(thm)],[188])).
% 0.19/0.56 tff(190,plain,
% 0.19/0.56 ((((((((((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))),
% 0.19/0.56 inference(and_elim,[status(thm)],[189])).
% 0.19/0.56 tff(191,plain,
% 0.19/0.56 ((((op(e1, e2) = e0) | (op(e1, e2) = e1)) | (op(e1, e2) = e2)) | (op(e1, e2) = e3)),
% 0.19/0.56 inference(and_elim,[status(thm)],[190])).
% 0.19/0.56 tff(192,plain,
% 0.19/0.56 ((op(e1, e2) = e0) | (op(e1, e2) = e1) | (op(e1, e2) = e2) | (op(e1, e2) = e3)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[191, 180])).
% 0.19/0.56 tff(193,plain,
% 0.19/0.56 ((op(e1, e2) = e0) | (op(e1, e2) = e1) | (op(e1, e2) = e2) | (op(e1, e2) = e3)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[192, 176])).
% 0.19/0.56 tff(194,plain,
% 0.19/0.56 (op(e1, e2) = e0),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[193, 175, 168, 167])).
% 0.19/0.56 tff(195,plain,
% 0.19/0.56 (e0 = op(e1, e2)),
% 0.19/0.56 inference(symmetry,[status(thm)],[194])).
% 0.19/0.56 tff(196,plain,
% 0.19/0.56 (op(e2, e0) = op(e2, op(e1, e2))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[195])).
% 0.19/0.56 tff(197,plain,
% 0.19/0.56 (op(e2, e0) = e2),
% 0.19/0.56 inference(transitivity,[status(thm)],[196, 106])).
% 0.19/0.56 tff(198,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[74, 197])).
% 0.19/0.56 tff(199,plain,((~(op(e2, op(e1, e2)) = e2)) | (op(e2, e0) = e2) | (op(e1, e2) = e1) | (op(e1, e2) = e3) | (op(e1, e1) = e2) | (op(e1, e0) = e2) | (op(e3, e3) = e2) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(200,plain,
% 0.19/0.56 (op(e1, e2) = e1),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[199, 166, 74, 103, 12, 105, 75, 104])).
% 0.19/0.56 tff(201,plain,
% 0.19/0.56 (e1 = op(e1, e2)),
% 0.19/0.56 inference(symmetry,[status(thm)],[200])).
% 0.19/0.56 tff(202,plain,
% 0.19/0.56 (op(e2, e1) = op(e2, op(e1, e2))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[201])).
% 0.19/0.56 tff(203,plain,
% 0.19/0.56 (op(e2, e1) = e2),
% 0.19/0.56 inference(transitivity,[status(thm)],[202, 103])).
% 0.19/0.56 tff(204,plain,
% 0.19/0.56 ($false),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[10, 203])).
% 0.19/0.56 tff(205,plain,(((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))) | (op(e2, e1) = e2) | (op(e2, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e0) = e2) | (op(e3, e3) = e2) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.56 tff(206,plain,
% 0.19/0.56 (op(e1, e0) = e2),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[205, 79, 62, 101, 74, 75, 92])).
% 0.19/0.56 tff(207,plain,
% 0.19/0.56 (e2 = op(e1, e0)),
% 0.19/0.56 inference(symmetry,[status(thm)],[206])).
% 0.19/0.56 tff(208,plain,
% 0.19/0.56 (op(e0, e2) = op(e0, op(e1, e0))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[207])).
% 0.19/0.56 tff(209,plain,
% 0.19/0.56 (op(e0, e2) = e0),
% 0.19/0.56 inference(transitivity,[status(thm)],[208, 84])).
% 0.19/0.56 tff(210,plain,
% 0.19/0.56 ((op(e0, e2) = op(e0, e3)) <=> (e0 = op(e0, e3))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[209])).
% 0.19/0.56 tff(211,plain,
% 0.19/0.56 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e3) = e0)),
% 0.19/0.56 inference(transitivity,[status(thm)],[210, 82])).
% 0.19/0.56 tff(212,plain,
% 0.19/0.56 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e3) = e0))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[211])).
% 0.19/0.56 tff(213,plain,
% 0.19/0.56 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = op(e0, e3)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(214,plain,
% 0.19/0.56 (~(op(e0, e2) = op(e0, e3))),
% 0.19/0.56 inference(and_elim,[status(thm)],[37])).
% 0.19/0.56 tff(215,plain,
% 0.19/0.56 (~(op(e0, e2) = op(e0, e3))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.19/0.56 tff(216,plain,
% 0.19/0.56 (~(op(e0, e3) = e0)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[215, 212])).
% 0.19/0.56 tff(217,plain,
% 0.19/0.56 ((e2 = e0) <=> (e0 = e2)),
% 0.19/0.56 inference(commutativity,[status(thm)],[])).
% 0.19/0.56 tff(218,plain,
% 0.19/0.56 ((e2 = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.19/0.56 inference(commutativity,[status(thm)],[])).
% 0.19/0.56 tff(219,plain,
% 0.19/0.56 ((op(e1, e0) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[206])).
% 0.19/0.56 tff(220,plain,
% 0.19/0.56 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.19/0.56 inference(transitivity,[status(thm)],[219, 218])).
% 0.19/0.56 tff(221,plain,
% 0.19/0.56 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[220])).
% 0.19/0.56 tff(222,plain,
% 0.19/0.56 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = op(e1, e3)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(223,plain,
% 0.19/0.56 (~(op(e1, e0) = op(e1, e3))),
% 0.19/0.56 inference(and_elim,[status(thm)],[34])).
% 0.19/0.56 tff(224,plain,
% 0.19/0.56 (~(op(e1, e0) = op(e1, e3))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.19/0.56 tff(225,plain,
% 0.19/0.56 (~(op(e1, e3) = e2)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[224, 221])).
% 0.19/0.56 tff(226,plain,
% 0.19/0.56 (op(e2, e3) = e2),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[147, 225, 92, 75])).
% 0.19/0.56 tff(227,plain,
% 0.19/0.56 ((op(e2, e3) = e0) <=> (e2 = e0)),
% 0.19/0.56 inference(monotonicity,[status(thm)],[226])).
% 0.19/0.56 tff(228,plain,
% 0.19/0.56 ((op(e2, e3) = e0) <=> (e0 = e2)),
% 0.19/0.56 inference(transitivity,[status(thm)],[227, 217])).
% 0.19/0.56 tff(229,plain,
% 0.19/0.56 ((e0 = e2) <=> (op(e2, e3) = e0)),
% 0.19/0.56 inference(symmetry,[status(thm)],[228])).
% 0.19/0.56 tff(230,plain,
% 0.19/0.56 ((~(e0 = e2)) <=> (~(op(e2, e3) = e0))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[229])).
% 0.19/0.56 tff(231,plain,
% 0.19/0.56 ((~(e0 = e2)) <=> (~(e0 = e2))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(232,axiom,((((((~(e0 = e1)) & (~(e0 = e2))) & (~(e0 = e3))) & (~(e1 = e2))) & (~(e1 = e3))) & (~(e2 = e3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax4')).
% 0.19/0.56 tff(233,plain,
% 0.19/0.56 (((((~(e0 = e1)) & (~(e0 = e2))) & (~(e0 = e3))) & (~(e1 = e2))) & (~(e1 = e3))),
% 0.19/0.56 inference(and_elim,[status(thm)],[232])).
% 0.19/0.56 tff(234,plain,
% 0.19/0.56 ((((~(e0 = e1)) & (~(e0 = e2))) & (~(e0 = e3))) & (~(e1 = e2))),
% 0.19/0.56 inference(and_elim,[status(thm)],[233])).
% 0.19/0.56 tff(235,plain,
% 0.19/0.56 (((~(e0 = e1)) & (~(e0 = e2))) & (~(e0 = e3))),
% 0.19/0.56 inference(and_elim,[status(thm)],[234])).
% 0.19/0.56 tff(236,plain,
% 0.19/0.56 ((~(e0 = e1)) & (~(e0 = e2))),
% 0.19/0.56 inference(and_elim,[status(thm)],[235])).
% 0.19/0.56 tff(237,plain,
% 0.19/0.56 (~(e0 = e2)),
% 0.19/0.56 inference(and_elim,[status(thm)],[236])).
% 0.19/0.56 tff(238,plain,
% 0.19/0.56 (~(e0 = e2)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[237, 231])).
% 0.19/0.56 tff(239,plain,
% 0.19/0.56 (~(op(e2, e3) = e0)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[238, 230])).
% 0.19/0.56 tff(240,plain,
% 0.19/0.56 (((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))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(241,plain,
% 0.19/0.56 ((((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))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(242,plain,
% 0.19/0.56 ((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) <=> ((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e0))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(243,plain,
% 0.19/0.56 (((((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))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[242])).
% 0.19/0.56 tff(244,plain,
% 0.19/0.56 (((((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))),
% 0.19/0.56 inference(transitivity,[status(thm)],[243, 241])).
% 0.19/0.56 tff(245,plain,
% 0.19/0.56 ((((op(e0, e3) = e0) | (op(e1, e3) = e0)) | (op(e2, e3) = e0)) | (op(e3, e3) = e0)),
% 0.19/0.56 inference(and_elim,[status(thm)],[119])).
% 0.19/0.56 tff(246,plain,
% 0.19/0.56 ((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e0) | (op(e3, e3) = e0)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.19/0.56 tff(247,plain,
% 0.19/0.56 ((op(e0, e3) = e0) | (op(e1, e3) = e0) | (op(e2, e3) = e0) | (op(e3, e3) = e0)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[246, 240])).
% 0.19/0.56 tff(248,plain,
% 0.19/0.56 (op(e1, e3) = e0),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[247, 239, 216, 63])).
% 0.19/0.56 tff(249,plain,
% 0.19/0.56 (e0 = op(e1, e3)),
% 0.19/0.56 inference(symmetry,[status(thm)],[248])).
% 0.19/0.56 tff(250,plain,
% 0.19/0.56 (op(e3, e0) = op(e3, op(e1, e3))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[249])).
% 0.19/0.56 tff(251,plain,
% 0.19/0.56 (op(e3, e0) = e3),
% 0.19/0.56 inference(transitivity,[status(thm)],[250, 81])).
% 0.19/0.56 tff(252,plain,
% 0.19/0.56 ((op(e3, e0) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[251])).
% 0.19/0.56 tff(253,plain,
% 0.19/0.56 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.19/0.56 inference(transitivity,[status(thm)],[252, 78])).
% 0.19/0.56 tff(254,plain,
% 0.19/0.56 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[253])).
% 0.19/0.56 tff(255,plain,
% 0.19/0.56 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = op(e3, e3)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(256,plain,
% 0.19/0.56 (~(op(e3, e0) = op(e3, e3))),
% 0.19/0.56 inference(and_elim,[status(thm)],[22])).
% 0.19/0.56 tff(257,plain,
% 0.19/0.56 (~(op(e3, e0) = op(e3, e3))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.19/0.56 tff(258,plain,
% 0.19/0.56 (~(op(e3, e3) = e3)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[257, 254])).
% 0.19/0.56 tff(259,plain,
% 0.19/0.56 (((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))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(260,plain,
% 0.19/0.56 ((((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))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(261,plain,
% 0.19/0.56 ((((op(e3, e3) = e0) | (op(e3, e3) = e1)) | (op(e3, e3) = e2)) <=> ((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e2))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(262,plain,
% 0.19/0.56 (((((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))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[261])).
% 0.19/0.56 tff(263,plain,
% 0.19/0.56 (((((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))),
% 0.19/0.56 inference(transitivity,[status(thm)],[262, 260])).
% 0.19/0.56 tff(264,plain,
% 0.19/0.56 ((((op(e3, e3) = e0) | (op(e3, e3) = e1)) | (op(e3, e3) = e2)) | (op(e3, e3) = e3)),
% 0.19/0.56 inference(and_elim,[status(thm)],[181])).
% 0.19/0.56 tff(265,plain,
% 0.19/0.56 ((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e2) | (op(e3, e3) = e3)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.19/0.56 tff(266,plain,
% 0.19/0.56 ((op(e3, e3) = e0) | (op(e3, e3) = e1) | (op(e3, e3) = e2) | (op(e3, e3) = e3)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[265, 259])).
% 0.19/0.56 tff(267,plain,
% 0.19/0.56 (op(e3, e3) = e1),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[266, 258, 63, 75])).
% 0.19/0.56 tff(268,plain,
% 0.19/0.56 (e1 = op(e3, e3)),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[267, 77])).
% 0.19/0.56 tff(269,plain,
% 0.19/0.56 (op(e3, op(e3, e3)) = op(e3, e1)),
% 0.19/0.56 inference(monotonicity,[status(thm)],[267])).
% 0.19/0.56 tff(270,plain,
% 0.19/0.56 (op(e3, e1) = op(e3, op(e3, e3))),
% 0.19/0.56 inference(symmetry,[status(thm)],[269])).
% 0.19/0.56 tff(271,plain,
% 0.19/0.56 ((e0 = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 0.19/0.56 inference(commutativity,[status(thm)],[])).
% 0.19/0.56 tff(272,plain,
% 0.19/0.56 ((op(e0, e2) = op(e3, e2)) <=> (e0 = op(e3, e2))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[209])).
% 0.19/0.56 tff(273,plain,
% 0.19/0.56 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 0.19/0.56 inference(transitivity,[status(thm)],[272, 271])).
% 0.19/0.56 tff(274,plain,
% 0.19/0.56 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[273])).
% 0.19/0.56 tff(275,plain,
% 0.19/0.56 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e0, e2) = op(e3, e2)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(276,plain,
% 0.41/0.57 (~(op(e0, e2) = op(e3, e2))),
% 0.41/0.57 inference(and_elim,[status(thm)],[52])).
% 0.41/0.57 tff(277,plain,
% 0.41/0.57 (~(op(e0, e2) = op(e3, e2))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.41/0.57 tff(278,plain,
% 0.41/0.57 (~(op(e3, e2) = e0)),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[277, 274])).
% 0.41/0.57 tff(279,plain,
% 0.41/0.57 ((e3 = e0) <=> (e0 = e3)),
% 0.41/0.57 inference(commutativity,[status(thm)],[])).
% 0.41/0.57 tff(280,plain,
% 0.41/0.57 ((op(e3, e0) = e0) <=> (e3 = e0)),
% 0.41/0.57 inference(monotonicity,[status(thm)],[251])).
% 0.41/0.57 tff(281,plain,
% 0.41/0.57 ((op(e3, e0) = e0) <=> (e0 = e3)),
% 0.41/0.57 inference(transitivity,[status(thm)],[280, 279])).
% 0.41/0.57 tff(282,plain,
% 0.41/0.57 ((e0 = e3) <=> (op(e3, e0) = e0)),
% 0.41/0.57 inference(symmetry,[status(thm)],[281])).
% 0.41/0.57 tff(283,plain,
% 0.41/0.57 ((~(e0 = e3)) <=> (~(op(e3, e0) = e0))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[282])).
% 0.41/0.57 tff(284,plain,
% 0.41/0.57 ((~(e0 = e3)) <=> (~(e0 = e3))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(285,plain,
% 0.41/0.57 (~(e0 = e3)),
% 0.41/0.57 inference(and_elim,[status(thm)],[235])).
% 0.41/0.57 tff(286,plain,
% 0.41/0.57 (~(e0 = e3)),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.41/0.57 tff(287,plain,
% 0.41/0.57 (~(op(e3, e0) = e0)),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[286, 283])).
% 0.41/0.57 tff(288,plain,
% 0.41/0.57 (((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0) | (op(e3, e3) = e0)) <=> ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0) | (op(e3, e3) = e0))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(289,plain,
% 0.41/0.57 ((((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0)) | (op(e3, e3) = e0)) <=> ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0) | (op(e3, e3) = e0))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(290,plain,
% 0.41/0.57 ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) <=> ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(291,plain,
% 0.41/0.57 (((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0)) <=> (((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0)) | (op(e3, e3) = e0))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[290])).
% 0.41/0.57 tff(292,plain,
% 0.41/0.57 (((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0)) <=> ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0) | (op(e3, e3) = e0))),
% 0.41/0.57 inference(transitivity,[status(thm)],[291, 289])).
% 0.41/0.57 tff(293,plain,
% 0.41/0.57 ((((op(e3, e0) = e0) | (op(e3, e1) = e0)) | (op(e3, e2) = e0)) | (op(e3, e3) = e0)),
% 0.41/0.57 inference(and_elim,[status(thm)],[120])).
% 0.41/0.57 tff(294,plain,
% 0.41/0.57 ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0) | (op(e3, e3) = e0)),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.41/0.57 tff(295,plain,
% 0.41/0.57 ((op(e3, e0) = e0) | (op(e3, e1) = e0) | (op(e3, e2) = e0) | (op(e3, e3) = e0)),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[294, 288])).
% 0.41/0.57 tff(296,plain,
% 0.41/0.57 (op(e3, e1) = e0),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[295, 287, 278, 63])).
% 0.41/0.57 tff(297,plain,
% 0.41/0.57 (e0 = op(e3, e1)),
% 0.41/0.57 inference(symmetry,[status(thm)],[296])).
% 0.41/0.57 tff(298,plain,
% 0.41/0.57 (e0 = op(e3, op(e3, e3))),
% 0.41/0.57 inference(transitivity,[status(thm)],[297, 270])).
% 0.41/0.57 tff(299,plain,
% 0.41/0.57 (op(e3, op(e3, e3)) = e0),
% 0.41/0.57 inference(transitivity,[status(thm)],[269, 296])).
% 0.41/0.57 tff(300,plain,
% 0.41/0.57 (op(op(e3, op(e3, e3)), op(e3, e3)) = op(e0, e1)),
% 0.41/0.57 inference(monotonicity,[status(thm)],[299, 267])).
% 0.41/0.57 tff(301,plain,
% 0.41/0.57 (op(e0, e1) = op(op(e3, op(e3, e3)), op(e3, e3))),
% 0.41/0.57 inference(symmetry,[status(thm)],[300])).
% 0.41/0.57 tff(302,plain,
% 0.41/0.57 (e2 = op(e0, e1)),
% 0.41/0.57 inference(symmetry,[status(thm)],[14])).
% 0.41/0.57 tff(303,plain,
% 0.41/0.57 (e2 = op(op(e3, op(e3, e3)), op(e3, e3))),
% 0.41/0.57 inference(transitivity,[status(thm)],[302, 301])).
% 0.41/0.57 tff(304,plain,
% 0.41/0.57 ((~(~((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(e3, e3)))) | (~(e2 = op(op(e3, op(e3, e3)), op(e3, e3))))))) <=> ((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(e3, e3)))) | (~(e2 = op(op(e3, op(e3, e3)), op(e3, e3)))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(305,plain,
% 0.41/0.57 (((e1 = op(e3, e3)) & (e0 = op(e3, op(e3, e3))) & (e2 = op(op(e3, op(e3, e3)), op(e3, e3)))) <=> (~((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(e3, e3)))) | (~(e2 = op(op(e3, op(e3, e3)), op(e3, e3))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(306,plain,
% 0.41/0.57 ((~((e1 = op(e3, e3)) & (e0 = op(e3, op(e3, e3))) & (e2 = op(op(e3, op(e3, e3)), op(e3, e3))))) <=> (~(~((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(e3, e3)))) | (~(e2 = op(op(e3, op(e3, e3)), op(e3, e3)))))))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[305])).
% 0.41/0.57 tff(307,plain,
% 0.41/0.57 ((~((e1 = op(e3, e3)) & (e0 = op(e3, op(e3, e3))) & (e2 = op(op(e3, op(e3, e3)), op(e3, e3))))) <=> ((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(e3, e3)))) | (~(e2 = op(op(e3, op(e3, e3)), op(e3, e3)))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[306, 304])).
% 0.41/0.57 tff(308,plain,
% 0.41/0.57 ((~((e1 = op(e3, e3)) & (e0 = op(e3, op(e3, e3))) & (e2 = op(op(e3, op(e3, e3)), op(e3, e3))))) <=> (~((e1 = op(e3, e3)) & (e0 = op(e3, op(e3, e3))) & (e2 = op(op(e3, op(e3, e3)), op(e3, e3)))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(309,plain,
% 0.41/0.57 ((~(((e1 = op(e3, e3)) & (e0 = op(e3, op(e3, e3)))) & (e2 = op(op(e3, op(e3, e3)), op(e3, e3))))) <=> (~((e1 = op(e3, e3)) & (e0 = op(e3, op(e3, e3))) & (e2 = op(op(e3, op(e3, e3)), op(e3, e3)))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(310,axiom,(~(((e1 = op(e3, e3)) & (e0 = op(e3, op(e3, e3)))) & (e2 = op(op(e3, op(e3, e3)), op(e3, e3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax13')).
% 0.41/0.57 tff(311,plain,
% 0.41/0.57 (~((e1 = op(e3, e3)) & (e0 = op(e3, op(e3, e3))) & (e2 = op(op(e3, op(e3, e3)), op(e3, e3))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.41/0.57 tff(312,plain,
% 0.41/0.57 (~((e1 = op(e3, e3)) & (e0 = op(e3, op(e3, e3))) & (e2 = op(op(e3, op(e3, e3)), op(e3, e3))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[311, 308])).
% 0.41/0.57 tff(313,plain,
% 0.41/0.57 ((~(e1 = op(e3, e3))) | (~(e0 = op(e3, op(e3, e3)))) | (~(e2 = op(op(e3, op(e3, e3)), op(e3, e3))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[312, 307])).
% 0.41/0.57 tff(314,plain,
% 0.41/0.57 ($false),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[313, 303, 298, 268])).
% 0.41/0.57 tff(315,plain,(((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))) | (~(op(e0, e1) = e2)) | (op(e3, e3) = e0) | (op(e3, e3) = e2) | (op(e2, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.41/0.57 tff(316,plain,
% 0.41/0.57 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[315, 75, 63, 14, 74])).
% 0.41/0.57 tff(317,plain,
% 0.41/0.57 ((e2 = e1) <=> (e1 = e2)),
% 0.41/0.57 inference(commutativity,[status(thm)],[])).
% 0.41/0.57 tff(318,plain,
% 0.41/0.57 ((op(e0, e1) = e1) <=> (e2 = e1)),
% 0.41/0.57 inference(monotonicity,[status(thm)],[14])).
% 0.41/0.57 tff(319,plain,
% 0.41/0.57 ((op(e0, e1) = e1) <=> (e1 = e2)),
% 0.41/0.57 inference(transitivity,[status(thm)],[318, 317])).
% 0.41/0.57 tff(320,plain,
% 0.41/0.57 ((e1 = e2) <=> (op(e0, e1) = e1)),
% 0.41/0.57 inference(symmetry,[status(thm)],[319])).
% 0.41/0.57 tff(321,plain,
% 0.41/0.57 ((~(e1 = e2)) <=> (~(op(e0, e1) = e1))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[320])).
% 0.41/0.57 tff(322,plain,
% 0.41/0.57 ((~(e1 = e2)) <=> (~(e1 = e2))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(323,plain,
% 0.41/0.57 (~(e1 = e2)),
% 0.41/0.57 inference(and_elim,[status(thm)],[234])).
% 0.41/0.57 tff(324,plain,
% 0.41/0.57 (~(e1 = e2)),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.41/0.57 tff(325,plain,
% 0.41/0.57 (~(op(e0, e1) = e1)),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[324, 321])).
% 0.41/0.57 tff(326,plain,
% 0.41/0.57 ((e2 = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 0.41/0.57 inference(commutativity,[status(thm)],[])).
% 0.41/0.57 tff(327,plain,
% 0.41/0.57 ((op(e0, e1) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[14])).
% 0.41/0.57 tff(328,plain,
% 0.41/0.57 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 0.41/0.57 inference(transitivity,[status(thm)],[327, 326])).
% 0.41/0.57 tff(329,plain,
% 0.41/0.57 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[328])).
% 0.41/0.57 tff(330,plain,
% 0.41/0.57 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = op(e3, e1)))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(331,plain,
% 0.41/0.57 (~(op(e0, e1) = op(e3, e1))),
% 0.41/0.57 inference(and_elim,[status(thm)],[58])).
% 0.41/0.57 tff(332,plain,
% 0.41/0.57 (~(op(e0, e1) = op(e3, e1))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.41/0.57 tff(333,plain,
% 0.41/0.57 (~(op(e3, e1) = e2)),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[332, 329])).
% 0.41/0.57 tff(334,assumption,(~((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3)))), introduced(assumption)).
% 0.41/0.57 tff(335,plain,
% 0.41/0.57 (((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (op(e2, op(e3, e2)) = e2)),
% 0.41/0.57 inference(tautology,[status(thm)],[])).
% 0.41/0.57 tff(336,plain,
% 0.41/0.57 (op(e2, op(e3, e2)) = e2),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[335, 334])).
% 0.41/0.57 tff(337,plain,
% 0.41/0.57 (((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (op(e1, op(e3, e1)) = e1)),
% 0.41/0.57 inference(tautology,[status(thm)],[])).
% 0.41/0.57 tff(338,plain,
% 0.41/0.57 (op(e1, op(e3, e1)) = e1),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[337, 334])).
% 0.41/0.57 tff(339,assumption,(op(e1, op(e3, e1)) = e1), introduced(assumption)).
% 0.41/0.57 tff(340,assumption,(op(e3, e1) = e1), introduced(assumption)).
% 0.41/0.57 tff(341,plain,
% 0.41/0.57 (e1 = op(e3, e1)),
% 0.41/0.57 inference(symmetry,[status(thm)],[340])).
% 0.41/0.57 tff(342,plain,
% 0.41/0.57 (op(e1, e1) = op(e1, op(e3, e1))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[341])).
% 0.41/0.57 tff(343,plain,
% 0.41/0.57 (op(e1, e1) = e1),
% 0.41/0.57 inference(transitivity,[status(thm)],[342, 339])).
% 0.41/0.57 tff(344,plain,
% 0.41/0.57 ((op(e1, e1) = op(e3, e1)) <=> (op(e1, e1) = e1)),
% 0.41/0.57 inference(monotonicity,[status(thm)],[340])).
% 0.41/0.57 tff(345,plain,
% 0.41/0.57 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = e1))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[344])).
% 0.41/0.57 tff(346,plain,
% 0.41/0.57 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e1, e1) = op(e3, e1)))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(347,plain,
% 0.41/0.57 (~(op(e1, e1) = op(e3, e1))),
% 0.41/0.57 inference(and_elim,[status(thm)],[56])).
% 0.41/0.57 tff(348,plain,
% 0.41/0.57 (~(op(e1, e1) = op(e3, e1))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.41/0.57 tff(349,plain,
% 0.41/0.57 (~(op(e1, e1) = e1)),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[348, 345])).
% 0.41/0.57 tff(350,plain,
% 0.41/0.57 ($false),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[349, 343])).
% 0.41/0.57 tff(351,plain,((~(op(e3, e1) = e1)) | (~(op(e1, op(e3, e1)) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.57 tff(352,plain,
% 0.41/0.57 (~(op(e3, e1) = e1)),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[351, 338])).
% 0.41/0.57 tff(353,plain,
% 0.41/0.57 (((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (op(e3, op(e3, e3)) = e3)),
% 0.41/0.57 inference(tautology,[status(thm)],[])).
% 0.41/0.57 tff(354,plain,
% 0.41/0.57 (op(e3, op(e3, e3)) = e3),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[353, 334])).
% 0.41/0.57 tff(355,assumption,(op(e3, e3) = e1), introduced(assumption)).
% 0.41/0.57 tff(356,plain,
% 0.41/0.57 (e1 = op(e3, e3)),
% 0.41/0.57 inference(symmetry,[status(thm)],[355])).
% 0.41/0.57 tff(357,plain,
% 0.41/0.57 (op(e3, e1) = op(e3, op(e3, e3))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[356])).
% 0.41/0.57 tff(358,plain,
% 0.41/0.57 (op(e3, op(e3, e3)) = op(e3, e1)),
% 0.41/0.57 inference(symmetry,[status(thm)],[357])).
% 0.41/0.57 tff(359,assumption,(op(e3, op(e3, e3)) = e3), introduced(assumption)).
% 0.41/0.57 tff(360,plain,
% 0.41/0.57 (e3 = op(e3, op(e3, e3))),
% 0.41/0.57 inference(symmetry,[status(thm)],[359])).
% 0.41/0.57 tff(361,plain,
% 0.41/0.57 (e3 = op(e3, e1)),
% 0.41/0.57 inference(transitivity,[status(thm)],[360, 358])).
% 0.41/0.57 tff(362,plain,
% 0.41/0.57 (op(e1, e3) = op(e1, op(e3, e1))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[361])).
% 0.41/0.57 tff(363,plain,
% 0.41/0.57 (op(e1, e3) = e1),
% 0.41/0.57 inference(transitivity,[status(thm)],[362, 339])).
% 0.41/0.57 tff(364,plain,
% 0.41/0.57 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e1)),
% 0.41/0.57 inference(monotonicity,[status(thm)],[355])).
% 0.41/0.57 tff(365,plain,
% 0.41/0.57 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e1))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[364])).
% 0.41/0.57 tff(366,plain,
% 0.41/0.57 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = op(e3, e3)))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(367,plain,
% 0.41/0.57 (~(op(e1, e3) = op(e3, e3))),
% 0.41/0.57 inference(and_elim,[status(thm)],[44])).
% 0.41/0.57 tff(368,plain,
% 0.41/0.57 (~(op(e1, e3) = op(e3, e3))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[367, 366])).
% 0.41/0.57 tff(369,plain,
% 0.41/0.57 (~(op(e1, e3) = e1)),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[368, 365])).
% 0.41/0.57 tff(370,plain,
% 0.41/0.57 ($false),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[369, 363])).
% 0.41/0.57 tff(371,plain,((~(op(e3, e3) = e1)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e3, op(e3, e3)) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.57 tff(372,plain,
% 0.41/0.57 (~(op(e3, e3) = e1)),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[371, 354, 338])).
% 0.41/0.57 tff(373,plain,
% 0.41/0.57 ((e1 = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 0.41/0.57 inference(commutativity,[status(thm)],[])).
% 0.41/0.57 tff(374,assumption,(~(op(e3, e1) = e2)), introduced(assumption)).
% 0.41/0.57 tff(375,assumption,(op(e3, e3) = e2), introduced(assumption)).
% 0.41/0.57 tff(376,assumption,(op(e2, op(e3, e2)) = e2), introduced(assumption)).
% 0.41/0.57 tff(377,plain,
% 0.41/0.57 (e2 = op(e3, e3)),
% 0.41/0.57 inference(symmetry,[status(thm)],[375])).
% 0.41/0.57 tff(378,plain,
% 0.41/0.57 (op(e3, e2) = op(e3, op(e3, e3))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[377])).
% 0.41/0.57 tff(379,plain,
% 0.41/0.57 (op(e3, op(e3, e3)) = op(e3, e2)),
% 0.41/0.57 inference(symmetry,[status(thm)],[378])).
% 0.41/0.57 tff(380,plain,
% 0.41/0.57 (e3 = op(e3, e2)),
% 0.41/0.57 inference(transitivity,[status(thm)],[360, 379])).
% 0.41/0.57 tff(381,plain,
% 0.41/0.57 (op(e2, e3) = op(e2, op(e3, e2))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[380])).
% 0.41/0.57 tff(382,plain,
% 0.41/0.57 (op(e2, e3) = e2),
% 0.41/0.57 inference(transitivity,[status(thm)],[381, 376])).
% 0.41/0.57 tff(383,plain,
% 0.41/0.57 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e2)),
% 0.41/0.57 inference(monotonicity,[status(thm)],[375])).
% 0.41/0.57 tff(384,plain,
% 0.41/0.57 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e2))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[383])).
% 0.41/0.57 tff(385,plain,
% 0.41/0.57 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = op(e3, e3)))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(386,plain,
% 0.41/0.57 (~(op(e2, e3) = op(e3, e3))),
% 0.41/0.57 inference(and_elim,[status(thm)],[43])).
% 0.41/0.57 tff(387,plain,
% 0.41/0.57 (~(op(e2, e3) = op(e3, e3))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.41/0.57 tff(388,plain,
% 0.41/0.57 (~(op(e2, e3) = e2)),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[387, 384])).
% 0.41/0.57 tff(389,plain,
% 0.41/0.57 ($false),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[388, 382])).
% 0.41/0.57 tff(390,plain,((~(op(e3, e3) = e2)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.57 tff(391,plain,
% 0.41/0.57 ($false),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[390, 354, 336, 375])).
% 0.41/0.57 tff(392,plain,(((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (~(op(e3, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.57 tff(393,plain,
% 0.41/0.57 (~(op(e3, e3) = e2)),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[392, 334])).
% 0.41/0.57 tff(394,plain,
% 0.41/0.57 (op(e3, e3) = e3),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[266, 372, 63, 393])).
% 0.41/0.57 tff(395,plain,
% 0.41/0.57 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e3)),
% 0.41/0.57 inference(monotonicity,[status(thm)],[394])).
% 0.41/0.57 tff(396,plain,
% 0.41/0.57 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e3))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[395])).
% 0.41/0.57 tff(397,plain,
% 0.41/0.57 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = op(e3, e3)))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(398,plain,
% 0.41/0.57 (~(op(e3, e1) = op(e3, e3))),
% 0.41/0.57 inference(and_elim,[status(thm)],[20])).
% 0.41/0.57 tff(399,plain,
% 0.41/0.57 (~(op(e3, e1) = op(e3, e3))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.41/0.57 tff(400,plain,
% 0.41/0.57 (~(op(e3, e1) = e3)),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[399, 396])).
% 0.41/0.57 tff(401,plain,
% 0.41/0.57 (((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))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(402,plain,
% 0.41/0.57 ((((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))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(403,plain,
% 0.41/0.57 ((((op(e3, e1) = e0) | (op(e3, e1) = e1)) | (op(e3, e1) = e2)) <=> ((op(e3, e1) = e0) | (op(e3, e1) = e1) | (op(e3, e1) = e2))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(404,plain,
% 0.41/0.57 (((((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))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[403])).
% 0.41/0.58 tff(405,plain,
% 0.41/0.58 (((((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))),
% 0.41/0.58 inference(transitivity,[status(thm)],[404, 402])).
% 0.41/0.58 tff(406,plain,
% 0.41/0.58 ((((op(e3, e1) = e0) | (op(e3, e1) = e1)) | (op(e3, e1) = e2)) | (op(e3, e1) = e3)),
% 0.41/0.58 inference(and_elim,[status(thm)],[183])).
% 0.41/0.58 tff(407,plain,
% 0.41/0.58 ((op(e3, e1) = e0) | (op(e3, e1) = e1) | (op(e3, e1) = e2) | (op(e3, e1) = e3)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[406, 405])).
% 0.41/0.58 tff(408,plain,
% 0.41/0.58 ((op(e3, e1) = e0) | (op(e3, e1) = e1) | (op(e3, e1) = e2) | (op(e3, e1) = e3)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[407, 401])).
% 0.41/0.58 tff(409,plain,
% 0.41/0.58 (op(e3, e1) = e0),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[408, 400, 374, 352])).
% 0.41/0.58 tff(410,plain,
% 0.41/0.58 (e0 = op(e3, e1)),
% 0.41/0.58 inference(symmetry,[status(thm)],[409])).
% 0.41/0.58 tff(411,plain,
% 0.41/0.58 (op(e1, e0) = op(e1, op(e3, e1))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[410])).
% 0.41/0.58 tff(412,plain,
% 0.41/0.58 (op(e1, e0) = e1),
% 0.41/0.58 inference(transitivity,[status(thm)],[411, 338])).
% 0.41/0.58 tff(413,plain,
% 0.41/0.58 ((op(e1, e0) = op(e3, e0)) <=> (e1 = op(e3, e0))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[412])).
% 0.41/0.58 tff(414,plain,
% 0.41/0.58 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 0.41/0.58 inference(transitivity,[status(thm)],[413, 373])).
% 0.41/0.58 tff(415,plain,
% 0.41/0.58 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e1))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[414])).
% 0.41/0.58 tff(416,plain,
% 0.41/0.58 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = op(e3, e0)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(417,plain,
% 0.41/0.58 ((((((~(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)))),
% 0.41/0.58 inference(and_elim,[status(thm)],[98])).
% 0.41/0.58 tff(418,plain,
% 0.41/0.58 (((((~(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)))),
% 0.41/0.58 inference(and_elim,[status(thm)],[417])).
% 0.41/0.58 tff(419,plain,
% 0.41/0.58 (~(op(e1, e0) = op(e3, e0))),
% 0.41/0.58 inference(and_elim,[status(thm)],[418])).
% 0.41/0.58 tff(420,plain,
% 0.41/0.58 (~(op(e1, e0) = op(e3, e0))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[419, 416])).
% 0.41/0.58 tff(421,plain,
% 0.41/0.58 (~(op(e3, e0) = e1)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[420, 415])).
% 0.41/0.58 tff(422,plain,
% 0.41/0.58 (((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))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(423,plain,
% 0.41/0.58 ((((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))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(424,plain,
% 0.41/0.58 ((((op(e3, e0) = e1) | (op(e3, e1) = e1)) | (op(e3, e2) = e1)) <=> ((op(e3, e0) = e1) | (op(e3, e1) = e1) | (op(e3, e2) = e1))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(425,plain,
% 0.41/0.58 (((((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))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[424])).
% 0.41/0.58 tff(426,plain,
% 0.41/0.58 (((((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))),
% 0.41/0.58 inference(transitivity,[status(thm)],[425, 423])).
% 0.41/0.58 tff(427,plain,
% 0.41/0.58 ((((op(e3, e0) = e1) | (op(e3, e1) = e1)) | (op(e3, e2) = e1)) | (op(e3, e3) = e1)),
% 0.41/0.58 inference(and_elim,[status(thm)],[118])).
% 0.41/0.58 tff(428,plain,
% 0.41/0.58 ((op(e3, e0) = e1) | (op(e3, e1) = e1) | (op(e3, e2) = e1) | (op(e3, e3) = e1)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.41/0.58 tff(429,plain,
% 0.41/0.58 ((op(e3, e0) = e1) | (op(e3, e1) = e1) | (op(e3, e2) = e1) | (op(e3, e3) = e1)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[428, 422])).
% 0.41/0.58 tff(430,plain,
% 0.41/0.58 (op(e3, e2) = e1),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[429, 421, 372, 352])).
% 0.41/0.58 tff(431,plain,
% 0.41/0.58 (op(e2, op(e3, e2)) = op(e2, e1)),
% 0.41/0.58 inference(monotonicity,[status(thm)],[430])).
% 0.41/0.58 tff(432,plain,
% 0.41/0.58 (op(e2, e1) = op(e2, op(e3, e2))),
% 0.41/0.58 inference(symmetry,[status(thm)],[431])).
% 0.41/0.58 tff(433,assumption,(~(op(e0, e1) = e1)), introduced(assumption)).
% 0.41/0.58 tff(434,plain,
% 0.41/0.58 ((e1 = op(e1, e1)) <=> (op(e1, e1) = e1)),
% 0.41/0.58 inference(commutativity,[status(thm)],[])).
% 0.41/0.58 tff(435,plain,
% 0.41/0.58 ((op(e1, e0) = op(e1, e1)) <=> (e1 = op(e1, e1))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[412])).
% 0.41/0.58 tff(436,plain,
% 0.41/0.58 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e1) = e1)),
% 0.41/0.58 inference(transitivity,[status(thm)],[435, 434])).
% 0.41/0.58 tff(437,plain,
% 0.41/0.58 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e1) = e1))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[436])).
% 0.41/0.58 tff(438,plain,
% 0.41/0.58 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = op(e1, e1)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(439,plain,
% 0.41/0.58 (~(op(e1, e0) = op(e1, e1))),
% 0.41/0.58 inference(and_elim,[status(thm)],[36])).
% 0.41/0.58 tff(440,plain,
% 0.41/0.58 (~(op(e1, e0) = op(e1, e1))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[439, 438])).
% 0.41/0.58 tff(441,plain,
% 0.41/0.58 (~(op(e1, e1) = e1)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[440, 437])).
% 0.41/0.58 tff(442,plain,
% 0.41/0.58 (((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))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(443,plain,
% 0.41/0.58 ((((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))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(444,plain,
% 0.41/0.58 ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) <=> ((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e1) = e1))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(445,plain,
% 0.41/0.58 (((((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))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[444])).
% 0.41/0.58 tff(446,plain,
% 0.41/0.58 (((((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))),
% 0.41/0.58 inference(transitivity,[status(thm)],[445, 443])).
% 0.41/0.58 tff(447,plain,
% 0.41/0.58 (((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))) & ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1))),
% 0.41/0.58 inference(and_elim,[status(thm)],[132])).
% 0.41/0.58 tff(448,plain,
% 0.41/0.58 ((((op(e0, e1) = e1) | (op(e1, e1) = e1)) | (op(e2, e1) = e1)) | (op(e3, e1) = e1)),
% 0.41/0.58 inference(and_elim,[status(thm)],[447])).
% 0.41/0.58 tff(449,plain,
% 0.41/0.58 ((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e1) = e1) | (op(e3, e1) = e1)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[448, 446])).
% 0.41/0.58 tff(450,plain,
% 0.41/0.58 ((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e2, e1) = e1) | (op(e3, e1) = e1)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[449, 442])).
% 0.41/0.58 tff(451,plain,
% 0.41/0.58 (op(e2, e1) = e1),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[450, 441, 433, 352])).
% 0.41/0.58 tff(452,plain,
% 0.41/0.58 (e1 = op(e2, e1)),
% 0.41/0.58 inference(symmetry,[status(thm)],[451])).
% 0.41/0.58 tff(453,plain,
% 0.41/0.58 (e1 = e2),
% 0.43/0.58 inference(transitivity,[status(thm)],[452, 432, 336])).
% 0.43/0.58 tff(454,plain,
% 0.43/0.58 ($false),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[324, 453])).
% 0.43/0.58 tff(455,plain,(((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (op(e0, e1) = e1) | (op(e3, e1) = e2) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.58 tff(456,plain,
% 0.43/0.58 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[455, 63, 333, 325])).
% 0.43/0.58 tff(457,plain,
% 0.43/0.58 ((op(e0, e1) = e3) <=> (e2 = e3)),
% 0.43/0.58 inference(monotonicity,[status(thm)],[14])).
% 0.43/0.58 tff(458,plain,
% 0.43/0.58 ((e2 = e3) <=> (op(e0, e1) = e3)),
% 0.43/0.58 inference(symmetry,[status(thm)],[457])).
% 0.43/0.58 tff(459,plain,
% 0.43/0.58 ((~(e2 = e3)) <=> (~(op(e0, e1) = e3))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[458])).
% 0.43/0.58 tff(460,plain,
% 0.43/0.58 ((~(e2 = e3)) <=> (~(e2 = e3))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(461,plain,
% 0.43/0.58 (~(e2 = e3)),
% 0.43/0.58 inference(and_elim,[status(thm)],[232])).
% 0.43/0.58 tff(462,plain,
% 0.43/0.58 (~(e2 = e3)),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[461, 460])).
% 0.43/0.58 tff(463,plain,
% 0.43/0.58 (~(op(e0, e1) = e3)),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[462, 459])).
% 0.43/0.58 tff(464,plain,
% 0.43/0.58 ((op(e0, e1) = e0) <=> (e2 = e0)),
% 0.43/0.58 inference(monotonicity,[status(thm)],[14])).
% 0.43/0.58 tff(465,plain,
% 0.43/0.58 ((op(e0, e1) = e0) <=> (e0 = e2)),
% 0.43/0.58 inference(transitivity,[status(thm)],[464, 217])).
% 0.43/0.58 tff(466,plain,
% 0.43/0.58 ((e0 = e2) <=> (op(e0, e1) = e0)),
% 0.43/0.58 inference(symmetry,[status(thm)],[465])).
% 0.43/0.58 tff(467,plain,
% 0.43/0.58 ((~(e0 = e2)) <=> (~(op(e0, e1) = e0))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[466])).
% 0.43/0.58 tff(468,plain,
% 0.43/0.58 (~(op(e0, e1) = e0)),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[238, 467])).
% 0.43/0.58 tff(469,plain,
% 0.43/0.58 ((e2 = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.43/0.58 inference(commutativity,[status(thm)],[])).
% 0.43/0.58 tff(470,assumption,(~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))), introduced(assumption)).
% 0.43/0.58 tff(471,plain,
% 0.43/0.58 (((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))) | (op(e3, op(e2, e3)) = e3)),
% 0.43/0.58 inference(tautology,[status(thm)],[])).
% 0.43/0.58 tff(472,plain,
% 0.43/0.58 (op(e3, op(e2, e3)) = e3),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[471, 470])).
% 0.43/0.58 tff(473,plain,
% 0.43/0.58 (((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))) | (op(e2, op(e2, e2)) = e2)),
% 0.43/0.58 inference(tautology,[status(thm)],[])).
% 0.43/0.58 tff(474,plain,
% 0.43/0.58 (op(e2, op(e2, e2)) = e2),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[473, 470])).
% 0.43/0.58 tff(475,assumption,(op(e2, op(e2, e2)) = e2), introduced(assumption)).
% 0.43/0.58 tff(476,assumption,(op(e2, e2) = e0), introduced(assumption)).
% 0.43/0.58 tff(477,plain,
% 0.43/0.58 (e0 = op(e2, e2)),
% 0.43/0.58 inference(symmetry,[status(thm)],[476])).
% 0.43/0.58 tff(478,plain,
% 0.43/0.58 (op(e2, e0) = op(e2, op(e2, e2))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[477])).
% 0.43/0.58 tff(479,plain,
% 0.43/0.58 (op(e2, e0) = e2),
% 0.43/0.58 inference(transitivity,[status(thm)],[478, 475])).
% 0.43/0.58 tff(480,plain,
% 0.43/0.58 ($false),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[74, 479])).
% 0.43/0.58 tff(481,plain,((~(op(e2, e2) = e0)) | (op(e2, e0) = e2) | (~(op(e2, op(e2, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.43/0.58 tff(482,plain,
% 0.43/0.58 (~(op(e2, e2) = e0)),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[481, 474, 74])).
% 0.43/0.58 tff(483,assumption,(op(e2, e2) = e1), introduced(assumption)).
% 0.43/0.58 tff(484,plain,
% 0.43/0.58 (e1 = op(e2, e2)),
% 0.43/0.58 inference(symmetry,[status(thm)],[483])).
% 0.43/0.58 tff(485,plain,
% 0.43/0.58 (op(e2, e1) = op(e2, op(e2, e2))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[484])).
% 0.43/0.58 tff(486,plain,
% 0.43/0.58 (op(e2, e1) = e2),
% 0.43/0.58 inference(transitivity,[status(thm)],[485, 475])).
% 0.43/0.58 tff(487,plain,
% 0.43/0.58 ($false),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[10, 486])).
% 0.43/0.58 tff(488,plain,((~(op(e2, e2) = e1)) | (op(e2, e1) = e2) | (~(op(e2, op(e2, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.43/0.58 tff(489,plain,
% 0.43/0.58 (~(op(e2, e2) = e1)),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[488, 474, 10])).
% 0.43/0.59 tff(490,assumption,(~(op(e2, e2) = e1)), introduced(assumption)).
% 0.43/0.59 tff(491,assumption,(~(op(e2, e2) = e0)), introduced(assumption)).
% 0.43/0.59 tff(492,assumption,(op(e2, e3) = e2), introduced(assumption)).
% 0.43/0.59 tff(493,plain,
% 0.43/0.59 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e2)),
% 0.43/0.59 inference(monotonicity,[status(thm)],[492])).
% 0.43/0.59 tff(494,plain,
% 0.43/0.59 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e2))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[493])).
% 0.43/0.59 tff(495,plain,
% 0.43/0.59 (~(op(e2, e2) = e2)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[153, 494])).
% 0.43/0.59 tff(496,assumption,(op(e3, op(e2, e3)) = e3), introduced(assumption)).
% 0.43/0.59 tff(497,plain,
% 0.43/0.59 (e2 = op(e2, e3)),
% 0.43/0.59 inference(symmetry,[status(thm)],[492])).
% 0.43/0.59 tff(498,plain,
% 0.43/0.59 (op(e3, e2) = op(e3, op(e2, e3))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[497])).
% 0.43/0.59 tff(499,plain,
% 0.43/0.59 (op(e3, e2) = e3),
% 0.43/0.59 inference(transitivity,[status(thm)],[498, 496])).
% 0.43/0.59 tff(500,plain,
% 0.43/0.59 ((op(e2, e2) = op(e3, e2)) <=> (op(e2, e2) = e3)),
% 0.43/0.59 inference(monotonicity,[status(thm)],[499])).
% 0.43/0.59 tff(501,plain,
% 0.43/0.59 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = e3))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[500])).
% 0.43/0.59 tff(502,plain,
% 0.43/0.59 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e2, e2) = op(e3, e2)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(503,plain,
% 0.43/0.59 (~(op(e2, e2) = op(e3, e2))),
% 0.43/0.59 inference(and_elim,[status(thm)],[49])).
% 0.43/0.59 tff(504,plain,
% 0.43/0.59 (~(op(e2, e2) = op(e3, e2))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[503, 502])).
% 0.43/0.59 tff(505,plain,
% 0.43/0.59 (~(op(e2, e2) = e3)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[504, 501])).
% 0.43/0.59 tff(506,plain,
% 0.43/0.59 (((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))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(507,plain,
% 0.43/0.59 ((((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))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(508,plain,
% 0.43/0.59 ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) <=> ((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e2))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(509,plain,
% 0.43/0.59 (((((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))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[508])).
% 0.43/0.59 tff(510,plain,
% 0.43/0.59 (((((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))),
% 0.43/0.59 inference(transitivity,[status(thm)],[509, 507])).
% 0.43/0.59 tff(511,plain,
% 0.43/0.59 ((((op(e2, e2) = e0) | (op(e2, e2) = e1)) | (op(e2, e2) = e2)) | (op(e2, e2) = e3)),
% 0.43/0.59 inference(and_elim,[status(thm)],[186])).
% 0.43/0.59 tff(512,plain,
% 0.43/0.59 ((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e2) | (op(e2, e2) = e3)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.43/0.59 tff(513,plain,
% 0.43/0.59 ((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e2) | (op(e2, e2) = e3)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[512, 506])).
% 0.43/0.59 tff(514,plain,
% 0.43/0.59 ($false),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[513, 505, 495, 491, 490])).
% 0.43/0.59 tff(515,plain,((~(op(e2, e3) = e2)) | (op(e2, e2) = e0) | (op(e2, e2) = e1) | (~(op(e3, op(e2, e3)) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.43/0.59 tff(516,plain,
% 0.43/0.59 (~(op(e2, e3) = e2)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[515, 489, 482, 472])).
% 0.43/0.59 tff(517,plain,
% 0.43/0.59 (((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))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(518,plain,
% 0.43/0.59 ((((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))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(519,plain,
% 0.43/0.59 ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) <=> ((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(520,plain,
% 0.43/0.59 (((((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))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[519])).
% 0.43/0.59 tff(521,plain,
% 0.43/0.59 (((((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))),
% 0.43/0.59 inference(transitivity,[status(thm)],[520, 518])).
% 0.43/0.59 tff(522,plain,
% 0.43/0.59 ((((op(e2, e0) = e2) | (op(e2, e1) = e2)) | (op(e2, e2) = e2)) | (op(e2, e3) = e2)),
% 0.43/0.59 inference(and_elim,[status(thm)],[124])).
% 0.43/0.59 tff(523,plain,
% 0.43/0.59 ((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2) | (op(e2, e3) = e2)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[522, 521])).
% 0.43/0.59 tff(524,plain,
% 0.43/0.59 ((op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e2, e2) = e2) | (op(e2, e3) = e2)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[523, 517])).
% 0.43/0.59 tff(525,plain,
% 0.43/0.59 (op(e2, e2) = e2),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[524, 516, 10, 74])).
% 0.43/0.59 tff(526,plain,
% 0.43/0.59 ((op(e2, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[525])).
% 0.43/0.59 tff(527,plain,
% 0.43/0.59 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.43/0.59 inference(transitivity,[status(thm)],[526, 469])).
% 0.43/0.59 tff(528,plain,
% 0.43/0.59 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[527])).
% 0.43/0.59 tff(529,plain,
% 0.43/0.59 (~(op(e3, e2) = e2)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[504, 528])).
% 0.43/0.59 tff(530,plain,
% 0.43/0.59 (((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))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(531,plain,
% 0.43/0.59 ((((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))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(532,plain,
% 0.43/0.59 ((((op(e3, e0) = e2) | (op(e3, e1) = e2)) | (op(e3, e2) = e2)) <=> ((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(533,plain,
% 0.43/0.59 (((((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))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[532])).
% 0.43/0.59 tff(534,plain,
% 0.43/0.59 (((((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))),
% 0.43/0.59 inference(transitivity,[status(thm)],[533, 531])).
% 0.43/0.59 tff(535,plain,
% 0.43/0.59 ((((op(e3, e0) = e2) | (op(e3, e1) = e2)) | (op(e3, e2) = e2)) | (op(e3, e3) = e2)),
% 0.43/0.59 inference(and_elim,[status(thm)],[116])).
% 0.43/0.59 tff(536,plain,
% 0.43/0.59 ((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2) | (op(e3, e3) = e2)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[535, 534])).
% 0.43/0.59 tff(537,plain,
% 0.43/0.59 ((op(e3, e0) = e2) | (op(e3, e1) = e2) | (op(e3, e2) = e2) | (op(e3, e3) = e2)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[536, 530])).
% 0.43/0.59 tff(538,plain,
% 0.43/0.59 (op(e3, e0) = e2),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[537, 529, 374, 75])).
% 0.43/0.59 tff(539,plain,
% 0.43/0.59 ((op(e3, e0) = e0) <=> (e2 = e0)),
% 0.43/0.59 inference(monotonicity,[status(thm)],[538])).
% 0.43/0.59 tff(540,plain,
% 0.43/0.59 ((op(e3, e0) = e0) <=> (e0 = e2)),
% 0.43/0.59 inference(transitivity,[status(thm)],[539, 217])).
% 0.43/0.59 tff(541,plain,
% 0.43/0.59 ((e0 = e2) <=> (op(e3, e0) = e0)),
% 0.43/0.59 inference(symmetry,[status(thm)],[540])).
% 0.43/0.59 tff(542,plain,
% 0.43/0.59 ((~(e0 = e2)) <=> (~(op(e3, e0) = e0))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[541])).
% 0.43/0.59 tff(543,plain,
% 0.43/0.59 (~(op(e3, e0) = e0)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[238, 542])).
% 0.43/0.59 tff(544,assumption,(~(op(e0, e1) = e3)), introduced(assumption)).
% 0.43/0.59 tff(545,plain,
% 0.43/0.59 (op(e1, e3) = e2),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[147, 516, 104, 75])).
% 0.43/0.59 tff(546,plain,
% 0.43/0.59 (((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))) | (op(e1, op(e2, e1)) = e1)),
% 0.43/0.59 inference(tautology,[status(thm)],[])).
% 0.43/0.59 tff(547,plain,
% 0.43/0.59 (op(e1, op(e2, e1)) = e1),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[546, 470])).
% 0.43/0.59 tff(548,assumption,(op(e1, e3) = e2), introduced(assumption)).
% 0.43/0.59 tff(549,assumption,(op(e2, e1) = e3), introduced(assumption)).
% 0.43/0.59 tff(550,plain,
% 0.43/0.59 (op(e1, op(e2, e1)) = op(e1, e3)),
% 0.43/0.59 inference(monotonicity,[status(thm)],[549])).
% 0.43/0.59 tff(551,assumption,(op(e1, op(e2, e1)) = e1), introduced(assumption)).
% 0.43/0.59 tff(552,plain,
% 0.43/0.59 (e1 = op(e1, op(e2, e1))),
% 0.43/0.59 inference(symmetry,[status(thm)],[551])).
% 0.43/0.59 tff(553,plain,
% 0.43/0.59 (e1 = e2),
% 0.43/0.59 inference(transitivity,[status(thm)],[552, 550, 548])).
% 0.43/0.59 tff(554,plain,
% 0.43/0.59 ($false),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[324, 553])).
% 0.43/0.59 tff(555,plain,((~(op(e2, e1) = e3)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e1, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.43/0.59 tff(556,plain,
% 0.43/0.59 (~(op(e2, e1) = e3)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[555, 547, 545])).
% 0.43/0.59 tff(557,assumption,(~(op(e2, e1) = e3)), introduced(assumption)).
% 0.43/0.59 tff(558,assumption,(op(e3, e1) = e0), introduced(assumption)).
% 0.43/0.59 tff(559,plain,
% 0.43/0.59 ((op(e3, e1) = e3) <=> (e0 = e3)),
% 0.43/0.59 inference(monotonicity,[status(thm)],[558])).
% 0.43/0.59 tff(560,plain,
% 0.43/0.59 ((e0 = e3) <=> (op(e3, e1) = e3)),
% 0.43/0.59 inference(symmetry,[status(thm)],[559])).
% 0.43/0.59 tff(561,plain,
% 0.43/0.59 ((~(e0 = e3)) <=> (~(op(e3, e1) = e3))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[560])).
% 0.43/0.59 tff(562,plain,
% 0.43/0.59 (~(op(e3, e1) = e3)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[286, 561])).
% 0.43/0.59 tff(563,plain,
% 0.43/0.59 (((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))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(564,plain,
% 0.43/0.59 ((((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))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(565,plain,
% 0.43/0.59 ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) <=> ((op(e0, e1) = e3) | (op(e1, e1) = e3) | (op(e2, e1) = e3))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(566,plain,
% 0.43/0.59 (((((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))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[565])).
% 0.43/0.59 tff(567,plain,
% 0.43/0.59 (((((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))),
% 0.43/0.59 inference(transitivity,[status(thm)],[566, 564])).
% 0.43/0.59 tff(568,plain,
% 0.43/0.59 ((((op(e0, e1) = e3) | (op(e1, e1) = e3)) | (op(e2, e1) = e3)) | (op(e3, e1) = e3)),
% 0.43/0.59 inference(and_elim,[status(thm)],[129])).
% 0.43/0.59 tff(569,plain,
% 0.43/0.59 ((op(e0, e1) = e3) | (op(e1, e1) = e3) | (op(e2, e1) = e3) | (op(e3, e1) = e3)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.43/0.59 tff(570,plain,
% 0.43/0.59 ((op(e0, e1) = e3) | (op(e1, e1) = e3) | (op(e2, e1) = e3) | (op(e3, e1) = e3)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[569, 563])).
% 0.43/0.59 tff(571,plain,
% 0.43/0.59 (op(e1, e1) = e3),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[570, 562, 544, 557])).
% 0.43/0.59 tff(572,plain,
% 0.43/0.59 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e0)),
% 0.43/0.59 inference(monotonicity,[status(thm)],[558])).
% 0.43/0.59 tff(573,plain,
% 0.43/0.59 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e0))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[572])).
% 0.43/0.59 tff(574,plain,
% 0.43/0.59 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = op(e3, e1)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(575,plain,
% 0.43/0.59 (~(op(e2, e1) = op(e3, e1))),
% 0.43/0.59 inference(and_elim,[status(thm)],[55])).
% 0.43/0.59 tff(576,plain,
% 0.43/0.59 (~(op(e2, e1) = op(e3, e1))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.43/0.59 tff(577,plain,
% 0.43/0.59 (~(op(e2, e1) = e0)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[576, 573])).
% 0.43/0.59 tff(578,plain,
% 0.43/0.59 (((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))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(579,plain,
% 0.43/0.59 ((((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))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(580,plain,
% 0.43/0.59 ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) <=> ((op(e2, e1) = e0) | (op(e2, e1) = e1) | (op(e2, e1) = e2))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(581,plain,
% 0.43/0.59 (((((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))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[580])).
% 0.43/0.59 tff(582,plain,
% 0.43/0.59 (((((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))),
% 0.43/0.59 inference(transitivity,[status(thm)],[581, 579])).
% 0.43/0.59 tff(583,plain,
% 0.43/0.59 ((((op(e2, e1) = e0) | (op(e2, e1) = e1)) | (op(e2, e1) = e2)) | (op(e2, e1) = e3)),
% 0.43/0.59 inference(and_elim,[status(thm)],[187])).
% 0.43/0.59 tff(584,plain,
% 0.43/0.59 ((op(e2, e1) = e0) | (op(e2, e1) = e1) | (op(e2, e1) = e2) | (op(e2, e1) = e3)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[583, 582])).
% 0.43/0.59 tff(585,plain,
% 0.43/0.59 ((op(e2, e1) = e0) | (op(e2, e1) = e1) | (op(e2, e1) = e2) | (op(e2, e1) = e3)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[584, 578])).
% 0.43/0.59 tff(586,plain,
% 0.43/0.59 (op(e2, e1) = e1),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[585, 577, 10, 557])).
% 0.43/0.59 tff(587,plain,
% 0.43/0.59 (op(e1, op(e2, e1)) = op(e1, e1)),
% 0.43/0.59 inference(monotonicity,[status(thm)],[586])).
% 0.43/0.59 tff(588,plain,
% 0.43/0.59 (e1 = e3),
% 0.43/0.59 inference(transitivity,[status(thm)],[552, 587, 571])).
% 0.43/0.59 tff(589,plain,
% 0.43/0.59 ((~(e1 = e3)) <=> (~(e1 = e3))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(590,plain,
% 0.43/0.59 (~(e1 = e3)),
% 0.43/0.59 inference(and_elim,[status(thm)],[233])).
% 0.43/0.59 tff(591,plain,
% 0.43/0.59 (~(e1 = e3)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[590, 589])).
% 0.43/0.59 tff(592,plain,
% 0.43/0.59 ($false),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[591, 588])).
% 0.43/0.59 tff(593,plain,((~(op(e3, e1) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (op(e2, e1) = e2) | (op(e2, e1) = e3) | (op(e0, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.59 tff(594,plain,
% 0.43/0.59 (~(op(e3, e1) = e0)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[593, 547, 10, 556, 544])).
% 0.43/0.59 tff(595,plain,
% 0.43/0.59 (op(e3, e2) = e0),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[295, 594, 543, 63])).
% 0.43/0.59 tff(596,plain,
% 0.43/0.59 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e0)),
% 0.43/0.59 inference(monotonicity,[status(thm)],[595])).
% 0.43/0.59 tff(597,plain,
% 0.43/0.59 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e0))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[596])).
% 0.43/0.59 tff(598,plain,
% 0.43/0.59 (~(op(e1, e2) = e0)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[165, 597])).
% 0.43/0.59 tff(599,plain,
% 0.43/0.59 ((op(e1, e3) = e0) <=> (e2 = e0)),
% 0.43/0.59 inference(monotonicity,[status(thm)],[545])).
% 0.43/0.59 tff(600,plain,
% 0.43/0.59 ((op(e1, e3) = e0) <=> (e0 = e2)),
% 0.43/0.59 inference(transitivity,[status(thm)],[599, 217])).
% 0.43/0.59 tff(601,plain,
% 0.43/0.59 ((e0 = e2) <=> (op(e1, e3) = e0)),
% 0.43/0.59 inference(symmetry,[status(thm)],[600])).
% 0.43/0.59 tff(602,plain,
% 0.43/0.59 ((~(e0 = e2)) <=> (~(op(e1, e3) = e0))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[601])).
% 0.43/0.59 tff(603,plain,
% 0.43/0.59 (~(op(e1, e3) = e0)),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[238, 602])).
% 0.43/0.59 tff(604,assumption,(~(op(e0, e1) = e0)), introduced(assumption)).
% 0.43/0.59 tff(605,assumption,(~(op(e2, e1) = e0)), introduced(assumption)).
% 0.43/0.59 tff(606,plain,
% 0.43/0.59 (op(e2, e1) = e1),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[585, 605, 10, 557])).
% 0.43/0.59 tff(607,plain,
% 0.43/0.59 (op(e1, op(e2, e1)) = op(e1, e1)),
% 0.43/0.59 inference(monotonicity,[status(thm)],[606])).
% 0.43/0.59 tff(608,plain,
% 0.43/0.59 (op(e1, e1) = op(e1, op(e2, e1))),
% 0.43/0.59 inference(symmetry,[status(thm)],[607])).
% 0.43/0.59 tff(609,assumption,(~(op(e3, e1) = e0)), introduced(assumption)).
% 0.43/0.59 tff(610,plain,
% 0.43/0.59 (((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))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(611,plain,
% 0.43/0.59 ((((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))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(612,plain,
% 0.43/0.60 ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) <=> ((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e2, e1) = e0))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(613,plain,
% 0.43/0.60 (((((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))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[612])).
% 0.43/0.60 tff(614,plain,
% 0.43/0.60 (((((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))),
% 0.43/0.60 inference(transitivity,[status(thm)],[613, 611])).
% 0.43/0.60 tff(615,plain,
% 0.43/0.60 ((((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))) & ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1))),
% 0.43/0.60 inference(and_elim,[status(thm)],[447])).
% 0.43/0.60 tff(616,plain,
% 0.43/0.60 (((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))) & ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0))),
% 0.43/0.60 inference(and_elim,[status(thm)],[615])).
% 0.43/0.60 tff(617,plain,
% 0.43/0.60 ((((op(e0, e1) = e0) | (op(e1, e1) = e0)) | (op(e2, e1) = e0)) | (op(e3, e1) = e0)),
% 0.43/0.60 inference(and_elim,[status(thm)],[616])).
% 0.43/0.60 tff(618,plain,
% 0.43/0.60 ((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e2, e1) = e0) | (op(e3, e1) = e0)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[617, 614])).
% 0.43/0.60 tff(619,plain,
% 0.43/0.60 ((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e2, e1) = e0) | (op(e3, e1) = e0)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[618, 610])).
% 0.43/0.60 tff(620,plain,
% 0.43/0.60 (op(e1, e1) = e0),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[619, 605, 604, 609])).
% 0.43/0.60 tff(621,plain,
% 0.43/0.60 (e0 = op(e1, e1)),
% 0.43/0.60 inference(symmetry,[status(thm)],[620])).
% 0.43/0.60 tff(622,plain,
% 0.43/0.60 (e0 = e1),
% 0.43/0.60 inference(transitivity,[status(thm)],[621, 608, 551])).
% 0.43/0.60 tff(623,plain,
% 0.43/0.60 ((~(e0 = e1)) <=> (~(e0 = e1))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(624,plain,
% 0.43/0.60 (~(e0 = e1)),
% 0.43/0.60 inference(and_elim,[status(thm)],[236])).
% 0.43/0.60 tff(625,plain,
% 0.43/0.60 (~(e0 = e1)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[624, 623])).
% 0.43/0.60 tff(626,plain,
% 0.43/0.60 ($false),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[625, 622])).
% 0.43/0.60 tff(627,plain,((op(e2, e1) = e0) | (~(op(e1, op(e2, e1)) = e1)) | (op(e2, e1) = e2) | (op(e2, e1) = e3) | (op(e0, e1) = e0) | (op(e3, e1) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.60 tff(628,plain,
% 0.43/0.60 (op(e2, e1) = e0),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[627, 547, 10, 556, 604, 594])).
% 0.43/0.60 tff(629,plain,
% 0.43/0.60 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e0)),
% 0.43/0.60 inference(monotonicity,[status(thm)],[628])).
% 0.43/0.60 tff(630,plain,
% 0.43/0.60 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e0))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[629])).
% 0.43/0.60 tff(631,plain,
% 0.43/0.60 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = op(e2, e1)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(632,plain,
% 0.43/0.60 (~(op(e1, e1) = op(e2, e1))),
% 0.43/0.60 inference(and_elim,[status(thm)],[57])).
% 0.43/0.60 tff(633,plain,
% 0.43/0.60 (~(op(e1, e1) = op(e2, e1))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[632, 631])).
% 0.43/0.60 tff(634,plain,
% 0.43/0.60 (~(op(e1, e1) = e0)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[633, 630])).
% 0.43/0.60 tff(635,plain,
% 0.43/0.60 ((e1 = e0) <=> (e0 = e1)),
% 0.43/0.60 inference(commutativity,[status(thm)],[])).
% 0.43/0.60 tff(636,assumption,(op(e2, e1) = e0), introduced(assumption)).
% 0.43/0.60 tff(637,plain,
% 0.43/0.60 (e0 = op(e2, e1)),
% 0.43/0.60 inference(symmetry,[status(thm)],[636])).
% 0.43/0.60 tff(638,plain,
% 0.43/0.60 (op(e1, e0) = op(e1, op(e2, e1))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[637])).
% 0.43/0.60 tff(639,plain,
% 0.43/0.60 (op(e1, e0) = e1),
% 0.43/0.60 inference(transitivity,[status(thm)],[638, 551])).
% 0.43/0.60 tff(640,assumption,(~(op(e1, e0) = e1)), introduced(assumption)).
% 0.43/0.60 tff(641,plain,
% 0.43/0.60 ($false),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[640, 639])).
% 0.43/0.60 tff(642,plain,((~(op(e2, e1) = e0)) | (op(e1, e0) = e1) | (~(op(e1, op(e2, e1)) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.43/0.60 tff(643,plain,
% 0.43/0.60 (op(e1, e0) = e1),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[642, 628, 547])).
% 0.43/0.60 tff(644,plain,
% 0.43/0.60 ((op(e1, e0) = e0) <=> (e1 = e0)),
% 0.43/0.60 inference(monotonicity,[status(thm)],[643])).
% 0.43/0.60 tff(645,plain,
% 0.43/0.60 ((op(e1, e0) = e0) <=> (e0 = e1)),
% 0.43/0.60 inference(transitivity,[status(thm)],[644, 635])).
% 0.43/0.60 tff(646,plain,
% 0.43/0.60 ((e0 = e1) <=> (op(e1, e0) = e0)),
% 0.43/0.60 inference(symmetry,[status(thm)],[645])).
% 0.43/0.60 tff(647,plain,
% 0.43/0.60 ((~(e0 = e1)) <=> (~(op(e1, e0) = e0))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[646])).
% 0.43/0.60 tff(648,plain,
% 0.43/0.60 (~(op(e1, e0) = e0)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[625, 647])).
% 0.43/0.60 tff(649,plain,
% 0.43/0.60 (((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))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(650,plain,
% 0.43/0.60 ((((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))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(651,plain,
% 0.43/0.60 ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) <=> ((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e0))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(652,plain,
% 0.43/0.60 (((((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))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[651])).
% 0.43/0.60 tff(653,plain,
% 0.43/0.60 (((((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))),
% 0.43/0.60 inference(transitivity,[status(thm)],[652, 650])).
% 0.43/0.60 tff(654,plain,
% 0.43/0.60 ((((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))) & ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0))),
% 0.43/0.60 inference(and_elim,[status(thm)],[616])).
% 0.43/0.61 tff(655,plain,
% 0.43/0.61 ((((op(e1, e0) = e0) | (op(e1, e1) = e0)) | (op(e1, e2) = e0)) | (op(e1, e3) = e0)),
% 0.43/0.61 inference(and_elim,[status(thm)],[654])).
% 0.43/0.61 tff(656,plain,
% 0.43/0.61 ((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e0) | (op(e1, e3) = e0)),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[655, 653])).
% 0.43/0.61 tff(657,plain,
% 0.43/0.61 ((op(e1, e0) = e0) | (op(e1, e1) = e0) | (op(e1, e2) = e0) | (op(e1, e3) = e0)),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[656, 649])).
% 0.43/0.61 tff(658,plain,
% 0.43/0.61 ($false),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[657, 648, 634, 603, 598])).
% 0.43/0.61 tff(659,plain,(((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))) | (op(e2, e1) = e2) | (op(e0, e1) = e0) | (op(e3, e3) = e0) | (op(e0, e1) = e3) | (op(e3, e1) = e2) | (op(e3, e3) = e2) | (op(e0, e3) = e2) | (op(e2, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.61 tff(660,plain,
% 0.43/0.61 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[659, 75, 468, 63, 463, 333, 62, 92, 74])).
% 0.43/0.61 tff(661,plain,
% 0.43/0.61 ((((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1) & (op(e2, op(e0, e2)) = e2) & (op(e3, op(e0, e3)) = e3)) | ((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1) & (op(e2, op(e1, e2)) = e2) & (op(e3, op(e1, e3)) = e3)) | ((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1) & (op(e2, op(e2, e2)) = e2) & (op(e3, op(e2, e3)) = e3)) | ((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1) & (op(e2, op(e3, e2)) = e2) & (op(e3, op(e3, e3)) = e3))) <=> ((~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))) | (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))) | (~((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3)))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(662,plain,
% 0.43/0.61 ((((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1) & (op(e2, op(e0, e2)) = e2) & (op(e3, op(e0, e3)) = e3)) | ((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1) & (op(e2, op(e1, e2)) = e2) & (op(e3, op(e1, e3)) = e3)) | ((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1) & (op(e2, op(e2, e2)) = e2) & (op(e3, op(e2, e3)) = e3)) | ((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1) & (op(e2, op(e3, e2)) = e2) & (op(e3, op(e3, e3)) = e3))) <=> (((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1) & (op(e2, op(e0, e2)) = e2) & (op(e3, op(e0, e3)) = e3)) | ((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1) & (op(e2, op(e1, e2)) = e2) & (op(e3, op(e1, e3)) = e3)) | ((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1) & (op(e2, op(e2, e2)) = e2) & (op(e3, op(e2, e3)) = e3)) | ((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1) & (op(e2, op(e3, e2)) = e2) & (op(e3, op(e3, e3)) = e3)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(663,plain,
% 0.43/0.61 (((((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1) & (op(e2, op(e0, e2)) = e2) & (op(e3, op(e0, e3)) = e3)) | ((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1) & (op(e2, op(e1, e2)) = e2) & (op(e3, op(e1, e3)) = e3)) | ((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1) & (op(e2, op(e2, e2)) = e2) & (op(e3, op(e2, e3)) = e3))) | ((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1) & (op(e2, op(e3, e2)) = e2) & (op(e3, op(e3, e3)) = e3))) <=> (((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1) & (op(e2, op(e0, e2)) = e2) & (op(e3, op(e0, e3)) = e3)) | ((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1) & (op(e2, op(e1, e2)) = e2) & (op(e3, op(e1, e3)) = e3)) | ((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1) & (op(e2, op(e2, e2)) = e2) & (op(e3, op(e2, e3)) = e3)) | ((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1) & (op(e2, op(e3, e2)) = e2) & (op(e3, op(e3, e3)) = e3)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(664,plain,
% 0.43/0.61 ((((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1) & (op(e2, op(e3, e2)) = e2)) & (op(e3, op(e3, e3)) = e3)) <=> ((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1) & (op(e2, op(e3, e2)) = e2) & (op(e3, op(e3, e3)) = e3))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(665,plain,
% 0.43/0.61 ((((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1)) & (op(e2, op(e3, e2)) = e2)) <=> ((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1) & (op(e2, op(e3, e2)) = e2))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(666,plain,
% 0.43/0.61 (((((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1)) & (op(e2, op(e3, e2)) = e2)) & (op(e3, op(e3, e3)) = e3)) <=> (((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1) & (op(e2, op(e3, e2)) = e2)) & (op(e3, op(e3, e3)) = e3))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[665])).
% 0.43/0.61 tff(667,plain,
% 0.43/0.61 (((((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1)) & (op(e2, op(e3, e2)) = e2)) & (op(e3, op(e3, e3)) = e3)) <=> ((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1) & (op(e2, op(e3, e2)) = e2) & (op(e3, op(e3, e3)) = e3))),
% 0.43/0.61 inference(transitivity,[status(thm)],[666, 664])).
% 0.43/0.61 tff(668,plain,
% 0.43/0.61 (((((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1) & (op(e2, op(e0, e2)) = e2) & (op(e3, op(e0, e3)) = e3)) | ((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1) & (op(e2, op(e1, e2)) = e2) & (op(e3, op(e1, e3)) = e3))) | ((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1) & (op(e2, op(e2, e2)) = e2) & (op(e3, op(e2, e3)) = e3))) <=> (((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1) & (op(e2, op(e0, e2)) = e2) & (op(e3, op(e0, e3)) = e3)) | ((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1) & (op(e2, op(e1, e2)) = e2) & (op(e3, op(e1, e3)) = e3)) | ((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1) & (op(e2, op(e2, e2)) = e2) & (op(e3, op(e2, e3)) = e3)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(669,plain,
% 0.43/0.61 ((((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1) & (op(e2, op(e2, e2)) = e2)) & (op(e3, op(e2, e3)) = e3)) <=> ((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1) & (op(e2, op(e2, e2)) = e2) & (op(e3, op(e2, e3)) = e3))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(670,plain,
% 0.43/0.61 ((((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1)) & (op(e2, op(e2, e2)) = e2)) <=> ((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1) & (op(e2, op(e2, e2)) = e2))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(671,plain,
% 0.43/0.61 (((((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1)) & (op(e2, op(e2, e2)) = e2)) & (op(e3, op(e2, e3)) = e3)) <=> (((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1) & (op(e2, op(e2, e2)) = e2)) & (op(e3, op(e2, e3)) = e3))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[670])).
% 0.43/0.61 tff(672,plain,
% 0.43/0.61 (((((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1)) & (op(e2, op(e2, e2)) = e2)) & (op(e3, op(e2, e3)) = e3)) <=> ((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1) & (op(e2, op(e2, e2)) = e2) & (op(e3, op(e2, e3)) = e3))),
% 0.43/0.61 inference(transitivity,[status(thm)],[671, 669])).
% 0.43/0.61 tff(673,plain,
% 0.43/0.61 ((((((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1)) & (op(e2, op(e0, e2)) = e2)) & (op(e3, op(e0, e3)) = e3)) | ((((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1)) & (op(e2, op(e1, e2)) = e2)) & (op(e3, op(e1, e3)) = e3))) <=> (((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1) & (op(e2, op(e0, e2)) = e2) & (op(e3, op(e0, e3)) = e3)) | ((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1) & (op(e2, op(e1, e2)) = e2) & (op(e3, op(e1, e3)) = e3)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(674,plain,
% 0.43/0.61 (((((((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1)) & (op(e2, op(e0, e2)) = e2)) & (op(e3, op(e0, e3)) = e3)) | ((((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1)) & (op(e2, op(e1, e2)) = e2)) & (op(e3, op(e1, e3)) = e3))) | ((((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1)) & (op(e2, op(e2, e2)) = e2)) & (op(e3, op(e2, e3)) = e3))) <=> ((((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1) & (op(e2, op(e0, e2)) = e2) & (op(e3, op(e0, e3)) = e3)) | ((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1) & (op(e2, op(e1, e2)) = e2) & (op(e3, op(e1, e3)) = e3))) | ((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1) & (op(e2, op(e2, e2)) = e2) & (op(e3, op(e2, e3)) = e3)))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[673, 672])).
% 0.43/0.61 tff(675,plain,
% 0.43/0.61 (((((((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1)) & (op(e2, op(e0, e2)) = e2)) & (op(e3, op(e0, e3)) = e3)) | ((((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1)) & (op(e2, op(e1, e2)) = e2)) & (op(e3, op(e1, e3)) = e3))) | ((((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1)) & (op(e2, op(e2, e2)) = e2)) & (op(e3, op(e2, e3)) = e3))) <=> (((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1) & (op(e2, op(e0, e2)) = e2) & (op(e3, op(e0, e3)) = e3)) | ((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1) & (op(e2, op(e1, e2)) = e2) & (op(e3, op(e1, e3)) = e3)) | ((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1) & (op(e2, op(e2, e2)) = e2) & (op(e3, op(e2, e3)) = e3)))),
% 0.43/0.61 inference(transitivity,[status(thm)],[674, 668])).
% 0.43/0.61 tff(676,plain,
% 0.43/0.61 ((((((((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1)) & (op(e2, op(e0, e2)) = e2)) & (op(e3, op(e0, e3)) = e3)) | ((((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1)) & (op(e2, op(e1, e2)) = e2)) & (op(e3, op(e1, e3)) = e3))) | ((((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1)) & (op(e2, op(e2, e2)) = e2)) & (op(e3, op(e2, e3)) = e3))) | ((((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1)) & (op(e2, op(e3, e2)) = e2)) & (op(e3, op(e3, e3)) = e3))) <=> ((((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1) & (op(e2, op(e0, e2)) = e2) & (op(e3, op(e0, e3)) = e3)) | ((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1) & (op(e2, op(e1, e2)) = e2) & (op(e3, op(e1, e3)) = e3)) | ((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1) & (op(e2, op(e2, e2)) = e2) & (op(e3, op(e2, e3)) = e3))) | ((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1) & (op(e2, op(e3, e2)) = e2) & (op(e3, op(e3, e3)) = e3)))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[675, 667])).
% 0.43/0.61 tff(677,plain,
% 0.43/0.61 ((((((((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1)) & (op(e2, op(e0, e2)) = e2)) & (op(e3, op(e0, e3)) = e3)) | ((((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1)) & (op(e2, op(e1, e2)) = e2)) & (op(e3, op(e1, e3)) = e3))) | ((((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1)) & (op(e2, op(e2, e2)) = e2)) & (op(e3, op(e2, e3)) = e3))) | ((((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1)) & (op(e2, op(e3, e2)) = e2)) & (op(e3, op(e3, e3)) = e3))) <=> (((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1) & (op(e2, op(e0, e2)) = e2) & (op(e3, op(e0, e3)) = e3)) | ((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1) & (op(e2, op(e1, e2)) = e2) & (op(e3, op(e1, e3)) = e3)) | ((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1) & (op(e2, op(e2, e2)) = e2) & (op(e3, op(e2, e3)) = e3)) | ((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1) & (op(e2, op(e3, e2)) = e2) & (op(e3, op(e3, e3)) = e3)))),
% 0.43/0.61 inference(transitivity,[status(thm)],[676, 663])).
% 0.43/0.61 tff(678,axiom,(((((((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1)) & (op(e2, op(e0, e2)) = e2)) & (op(e3, op(e0, e3)) = e3)) | ((((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1)) & (op(e2, op(e1, e2)) = e2)) & (op(e3, op(e1, e3)) = e3))) | ((((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1)) & (op(e2, op(e2, e2)) = e2)) & (op(e3, op(e2, e3)) = e3))) | ((((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1)) & (op(e2, op(e3, e2)) = e2)) & (op(e3, op(e3, e3)) = e3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax5')).
% 0.43/0.61 tff(679,plain,
% 0.43/0.61 (((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1) & (op(e2, op(e0, e2)) = e2) & (op(e3, op(e0, e3)) = e3)) | ((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1) & (op(e2, op(e1, e2)) = e2) & (op(e3, op(e1, e3)) = e3)) | ((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1) & (op(e2, op(e2, e2)) = e2) & (op(e3, op(e2, e3)) = e3)) | ((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1) & (op(e2, op(e3, e2)) = e2) & (op(e3, op(e3, e3)) = e3))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[678, 677])).
% 0.43/0.62 tff(680,plain,
% 0.43/0.62 (((op(e0, op(e0, e0)) = e0) & (op(e1, op(e0, e1)) = e1) & (op(e2, op(e0, e2)) = e2) & (op(e3, op(e0, e3)) = e3)) | ((op(e0, op(e1, e0)) = e0) & (op(e1, op(e1, e1)) = e1) & (op(e2, op(e1, e2)) = e2) & (op(e3, op(e1, e3)) = e3)) | ((op(e0, op(e2, e0)) = e0) & (op(e1, op(e2, e1)) = e1) & (op(e2, op(e2, e2)) = e2) & (op(e3, op(e2, e3)) = e3)) | ((op(e0, op(e3, e0)) = e0) & (op(e1, op(e3, e1)) = e1) & (op(e2, op(e3, e2)) = e2) & (op(e3, op(e3, e3)) = e3))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[679, 662])).
% 0.43/0.62 tff(681,plain,
% 0.43/0.62 ((~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))) | (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))) | (~((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[680, 661])).
% 0.43/0.62 tff(682,plain,
% 0.43/0.62 (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[681, 660, 456, 316])).
% 0.43/0.62 tff(683,plain,
% 0.43/0.62 (op(e0, op(e0, e0)) = e0),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[6, 682])).
% 0.43/0.62 tff(684,assumption,(op(e0, e0) = e1), introduced(assumption)).
% 0.43/0.62 tff(685,plain,
% 0.43/0.62 (e1 = op(e0, e0)),
% 0.43/0.62 inference(symmetry,[status(thm)],[684])).
% 0.43/0.62 tff(686,plain,
% 0.43/0.62 (op(e0, e1) = op(e0, op(e0, e0))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[685])).
% 0.43/0.62 tff(687,plain,
% 0.43/0.62 (op(e0, op(e0, e0)) = op(e0, e1)),
% 0.43/0.62 inference(symmetry,[status(thm)],[686])).
% 0.43/0.62 tff(688,assumption,(op(e0, op(e0, e0)) = e0), introduced(assumption)).
% 0.43/0.62 tff(689,plain,
% 0.43/0.62 (e0 = op(e0, op(e0, e0))),
% 0.43/0.62 inference(symmetry,[status(thm)],[688])).
% 0.43/0.62 tff(690,plain,
% 0.43/0.62 (e0 = e2),
% 0.43/0.62 inference(transitivity,[status(thm)],[689, 687, 14])).
% 0.43/0.62 tff(691,plain,
% 0.43/0.62 ($false),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[238, 690])).
% 0.43/0.62 tff(692,plain,((~(op(e0, e0) = e1)) | (~(op(e0, e1) = e2)) | (~(op(e0, op(e0, e0)) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.43/0.62 tff(693,plain,
% 0.43/0.62 (~(op(e0, e0) = e1)),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[692, 683, 14])).
% 0.43/0.62 tff(694,plain,
% 0.43/0.62 (op(e1, op(e0, e1)) = op(e1, e2)),
% 0.43/0.62 inference(monotonicity,[status(thm)],[14])).
% 0.43/0.62 tff(695,plain,
% 0.43/0.62 (op(e1, op(e0, e1)) = e1),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[4, 682])).
% 0.43/0.62 tff(696,plain,
% 0.43/0.62 (e1 = op(e1, op(e0, e1))),
% 0.43/0.62 inference(symmetry,[status(thm)],[695])).
% 0.43/0.62 tff(697,plain,
% 0.43/0.62 (e1 = op(e1, e2)),
% 0.43/0.62 inference(transitivity,[status(thm)],[696, 694])).
% 0.43/0.62 tff(698,plain,
% 0.43/0.62 ((op(e0, e2) = e1) <=> (op(e0, e2) = op(e1, e2))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[697])).
% 0.43/0.62 tff(699,plain,
% 0.43/0.62 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e1)),
% 0.43/0.62 inference(symmetry,[status(thm)],[698])).
% 0.43/0.62 tff(700,plain,
% 0.43/0.62 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e1))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[699])).
% 0.43/0.62 tff(701,plain,
% 0.43/0.62 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = op(e1, e2)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(702,plain,
% 0.43/0.62 (~(op(e0, e2) = op(e1, e2))),
% 0.43/0.62 inference(and_elim,[status(thm)],[54])).
% 0.43/0.62 tff(703,plain,
% 0.43/0.62 (~(op(e0, e2) = op(e1, e2))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[702, 701])).
% 0.43/0.62 tff(704,plain,
% 0.43/0.62 (~(op(e0, e2) = e1)),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[703, 700])).
% 0.43/0.62 tff(705,plain,
% 0.43/0.62 (((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))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(706,plain,
% 0.43/0.62 ((((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))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(707,plain,
% 0.43/0.62 ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) <=> ((op(e0, e0) = e1) | (op(e0, e1) = e1) | (op(e0, e2) = e1))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(708,plain,
% 0.43/0.62 (((((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))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[707])).
% 0.43/0.62 tff(709,plain,
% 0.43/0.62 (((((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))),
% 0.43/0.62 inference(transitivity,[status(thm)],[708, 706])).
% 0.43/0.62 tff(710,plain,
% 0.43/0.62 (((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))) & ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3))),
% 0.43/0.62 inference(and_elim,[status(thm)],[654])).
% 0.43/0.62 tff(711,plain,
% 0.43/0.62 ((((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))) & ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3))),
% 0.43/0.62 inference(and_elim,[status(thm)],[710])).
% 0.43/0.62 tff(712,plain,
% 0.43/0.62 (((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))) & ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2))),
% 0.43/0.62 inference(and_elim,[status(thm)],[711])).
% 0.43/0.62 tff(713,plain,
% 0.43/0.62 ((((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))) & ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2))),
% 0.43/0.62 inference(and_elim,[status(thm)],[712])).
% 0.43/0.62 tff(714,plain,
% 0.43/0.62 (((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))) & ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1))),
% 0.43/0.62 inference(and_elim,[status(thm)],[713])).
% 0.43/0.62 tff(715,plain,
% 0.43/0.62 ((((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))) & ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1))),
% 0.43/0.62 inference(and_elim,[status(thm)],[714])).
% 0.43/0.62 tff(716,plain,
% 0.43/0.62 ((((op(e0, e0) = e1) | (op(e0, e1) = e1)) | (op(e0, e2) = e1)) | (op(e0, e3) = e1)),
% 0.43/0.62 inference(and_elim,[status(thm)],[715])).
% 0.43/0.62 tff(717,plain,
% 0.43/0.62 ((op(e0, e0) = e1) | (op(e0, e1) = e1) | (op(e0, e2) = e1) | (op(e0, e3) = e1)),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[716, 709])).
% 0.43/0.62 tff(718,plain,
% 0.43/0.62 ((op(e0, e0) = e1) | (op(e0, e1) = e1) | (op(e0, e2) = e1) | (op(e0, e3) = e1)),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[717, 705])).
% 0.43/0.62 tff(719,plain,
% 0.43/0.62 (op(e0, e3) = e1),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[718, 704, 325, 693])).
% 0.43/0.62 tff(720,plain,
% 0.43/0.62 ((op(e0, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[719])).
% 0.43/0.62 tff(721,plain,
% 0.43/0.62 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 0.43/0.62 inference(transitivity,[status(thm)],[720, 76])).
% 0.43/0.62 tff(722,plain,
% 0.43/0.62 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[721])).
% 0.43/0.62 tff(723,plain,
% 0.43/0.62 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = op(e3, e3)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(724,plain,
% 0.43/0.62 (~(op(e0, e3) = op(e3, e3))),
% 0.43/0.62 inference(and_elim,[status(thm)],[46])).
% 0.43/0.62 tff(725,plain,
% 0.43/0.62 (~(op(e0, e3) = op(e3, e3))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[724, 723])).
% 0.43/0.62 tff(726,plain,
% 0.43/0.62 (~(op(e3, e3) = e1)),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[725, 722])).
% 0.43/0.62 tff(727,plain,
% 0.43/0.62 (op(e3, op(e0, e3)) = e3),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[2, 682])).
% 0.43/0.62 tff(728,plain,
% 0.43/0.62 (e1 = op(e0, e3)),
% 0.43/0.62 inference(symmetry,[status(thm)],[719])).
% 0.43/0.62 tff(729,plain,
% 0.43/0.62 (op(e3, e1) = op(e3, op(e0, e3))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[728])).
% 0.43/0.62 tff(730,plain,
% 0.43/0.62 (op(e3, e1) = e3),
% 0.43/0.62 inference(transitivity,[status(thm)],[729, 727])).
% 0.43/0.62 tff(731,plain,
% 0.43/0.62 ((op(e3, e1) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[730])).
% 0.43/0.62 tff(732,plain,
% 0.43/0.62 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.43/0.62 inference(transitivity,[status(thm)],[731, 78])).
% 0.43/0.62 tff(733,plain,
% 0.43/0.62 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[732])).
% 0.43/0.62 tff(734,plain,
% 0.43/0.62 (~(op(e3, e3) = e3)),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[399, 733])).
% 0.43/0.62 tff(735,plain,
% 0.43/0.62 ($false),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[266, 734, 726, 63, 75])).
% 0.43/0.62 tff(736,plain,((op(e3, e3) = e2) | (op(e3, e3) = e0) | (~(op(e0, e1) = e2)) | (op(e2, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.62 tff(737,plain,
% 0.43/0.62 (op(e3, e3) = e2),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[736, 74, 14, 63])).
% 0.43/0.62 tff(738,plain,
% 0.43/0.62 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e2)),
% 0.43/0.62 inference(monotonicity,[status(thm)],[737])).
% 0.43/0.62 tff(739,plain,
% 0.43/0.62 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e2))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[738])).
% 0.43/0.62 tff(740,plain,
% 0.43/0.62 (~(op(e2, e3) = e2)),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[387, 739])).
% 0.43/0.62 tff(741,plain,
% 0.43/0.62 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e2)),
% 0.43/0.62 inference(monotonicity,[status(thm)],[14])).
% 0.43/0.62 tff(742,plain,
% 0.43/0.62 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e2))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[741])).
% 0.43/0.62 tff(743,plain,
% 0.43/0.62 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = op(e0, e1)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(744,plain,
% 0.43/0.62 (~(op(e0, e0) = op(e0, e1))),
% 0.43/0.62 inference(and_elim,[status(thm)],[42])).
% 0.43/0.62 tff(745,plain,
% 0.43/0.62 (~(op(e0, e0) = op(e0, e1))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[744, 743])).
% 0.43/0.62 tff(746,plain,
% 0.43/0.62 (~(op(e0, e0) = e2)),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[745, 742])).
% 0.43/0.62 tff(747,plain,
% 0.43/0.62 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e2)),
% 0.43/0.62 inference(monotonicity,[status(thm)],[737])).
% 0.43/0.62 tff(748,plain,
% 0.43/0.62 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e2))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[747])).
% 0.43/0.62 tff(749,plain,
% 0.43/0.62 (~(op(e3, e0) = e2)),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[257, 748])).
% 0.43/0.62 tff(750,plain,
% 0.43/0.62 (((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))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(751,plain,
% 0.43/0.62 ((((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))),
% 0.43/0.63 inference(rewrite,[status(thm)],[])).
% 0.43/0.63 tff(752,plain,
% 0.43/0.63 ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) <=> ((op(e0, e0) = e2) | (op(e1, e0) = e2) | (op(e2, e0) = e2))),
% 0.43/0.63 inference(rewrite,[status(thm)],[])).
% 0.43/0.63 tff(753,plain,
% 0.43/0.63 (((((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))),
% 0.43/0.63 inference(monotonicity,[status(thm)],[752])).
% 0.43/0.63 tff(754,plain,
% 0.43/0.63 (((((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))),
% 0.43/0.63 inference(transitivity,[status(thm)],[753, 751])).
% 0.43/0.63 tff(755,plain,
% 0.43/0.63 ((((op(e0, e0) = e2) | (op(e1, e0) = e2)) | (op(e2, e0) = e2)) | (op(e3, e0) = e2)),
% 0.43/0.63 inference(and_elim,[status(thm)],[712])).
% 0.43/0.63 tff(756,plain,
% 0.43/0.63 ((op(e0, e0) = e2) | (op(e1, e0) = e2) | (op(e2, e0) = e2) | (op(e3, e0) = e2)),
% 0.43/0.63 inference(modus_ponens,[status(thm)],[755, 754])).
% 0.43/0.63 tff(757,plain,
% 0.43/0.63 ((op(e0, e0) = e2) | (op(e1, e0) = e2) | (op(e2, e0) = e2) | (op(e3, e0) = e2)),
% 0.43/0.63 inference(modus_ponens,[status(thm)],[756, 750])).
% 0.43/0.63 tff(758,plain,
% 0.43/0.63 (op(e1, e0) = e2),
% 0.43/0.63 inference(unit_resolution,[status(thm)],[757, 749, 74, 746])).
% 0.43/0.63 tff(759,plain,
% 0.43/0.63 (op(e2, e2) = e2),
% 0.43/0.63 inference(unit_resolution,[status(thm)],[524, 740, 62, 74])).
% 0.43/0.63 tff(760,plain,
% 0.43/0.63 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e2)),
% 0.43/0.63 inference(monotonicity,[status(thm)],[759])).
% 0.43/0.63 tff(761,plain,
% 0.43/0.63 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e2))),
% 0.43/0.63 inference(monotonicity,[status(thm)],[760])).
% 0.43/0.63 tff(762,plain,
% 0.43/0.63 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = op(e2, e2)))),
% 0.43/0.63 inference(rewrite,[status(thm)],[])).
% 0.43/0.63 tff(763,plain,
% 0.43/0.63 (~(op(e1, e2) = op(e2, e2))),
% 0.43/0.63 inference(and_elim,[status(thm)],[51])).
% 0.43/0.63 tff(764,plain,
% 0.43/0.63 (~(op(e1, e2) = op(e2, e2))),
% 0.43/0.63 inference(modus_ponens,[status(thm)],[763, 762])).
% 0.43/0.63 tff(765,plain,
% 0.43/0.63 (~(op(e1, e2) = e2)),
% 0.43/0.63 inference(modus_ponens,[status(thm)],[764, 761])).
% 0.43/0.63 tff(766,assumption,(~(op(e1, e2) = e2)), introduced(assumption)).
% 0.43/0.63 tff(767,assumption,(~(op(e2, e3) = e2)), introduced(assumption)).
% 0.43/0.63 tff(768,assumption,(op(e1, e2) = e3), introduced(assumption)).
% 0.43/0.63 tff(769,plain,
% 0.43/0.63 (e3 = op(e1, e2)),
% 0.43/0.63 inference(symmetry,[status(thm)],[768])).
% 0.43/0.63 tff(770,plain,
% 0.43/0.63 (op(e2, e3) = op(e2, op(e1, e2))),
% 0.43/0.63 inference(monotonicity,[status(thm)],[769])).
% 0.43/0.63 tff(771,plain,
% 0.43/0.63 (op(e2, e3) = e2),
% 0.43/0.63 inference(transitivity,[status(thm)],[770, 106])).
% 0.43/0.63 tff(772,plain,
% 0.43/0.63 ($false),
% 0.43/0.63 inference(unit_resolution,[status(thm)],[767, 771])).
% 0.43/0.63 tff(773,plain,((~(op(e1, e2) = e3)) | (op(e2, e3) = e2) | (~(op(e2, op(e1, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.43/0.63 tff(774,plain,
% 0.43/0.63 (~(op(e1, e2) = e3)),
% 0.43/0.63 inference(unit_resolution,[status(thm)],[773, 103, 767])).
% 0.43/0.63 tff(775,plain,
% 0.43/0.63 ((op(e1, e2) = op(e0, e2)) <=> (op(e0, e2) = op(e1, e2))),
% 0.43/0.63 inference(commutativity,[status(thm)],[])).
% 0.43/0.63 tff(776,assumption,(op(e1, e0) = e2), introduced(assumption)).
% 0.43/0.63 tff(777,plain,
% 0.43/0.63 (op(e0, op(e1, e0)) = op(e0, e2)),
% 0.43/0.63 inference(monotonicity,[status(thm)],[776])).
% 0.43/0.63 tff(778,plain,
% 0.43/0.63 (e0 = op(e0, op(e1, e0))),
% 0.43/0.63 inference(symmetry,[status(thm)],[84])).
% 0.43/0.63 tff(779,plain,
% 0.43/0.63 (e0 = op(e0, e2)),
% 0.43/0.63 inference(transitivity,[status(thm)],[778, 777])).
% 0.43/0.63 tff(780,plain,
% 0.43/0.63 ((op(e1, e2) = e0) <=> (op(e1, e2) = op(e0, e2))),
% 0.43/0.63 inference(monotonicity,[status(thm)],[779])).
% 0.43/0.63 tff(781,plain,
% 0.43/0.63 ((op(e1, e2) = e0) <=> (op(e0, e2) = op(e1, e2))),
% 0.43/0.63 inference(transitivity,[status(thm)],[780, 775])).
% 0.43/0.63 tff(782,plain,
% 0.43/0.63 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 0.43/0.63 inference(symmetry,[status(thm)],[781])).
% 0.43/0.63 tff(783,plain,
% 0.43/0.63 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e0))),
% 0.43/0.63 inference(monotonicity,[status(thm)],[782])).
% 0.43/0.63 tff(784,plain,
% 0.43/0.63 (~(op(e1, e2) = e0)),
% 0.43/0.63 inference(modus_ponens,[status(thm)],[703, 783])).
% 0.43/0.63 tff(785,plain,
% 0.43/0.63 (op(e1, e2) = e1),
% 0.43/0.63 inference(unit_resolution,[status(thm)],[193, 784, 774, 766])).
% 0.47/0.63 tff(786,plain,
% 0.47/0.63 (e1 = op(e1, e2)),
% 0.47/0.63 inference(symmetry,[status(thm)],[785])).
% 0.47/0.63 tff(787,plain,
% 0.47/0.63 (op(e2, e1) = op(e2, op(e1, e2))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[786])).
% 0.47/0.63 tff(788,plain,
% 0.47/0.63 (op(e2, e1) = e2),
% 0.47/0.63 inference(transitivity,[status(thm)],[787, 103])).
% 0.47/0.63 tff(789,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[10, 788])).
% 0.47/0.63 tff(790,plain,(((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))) | (op(e2, e1) = e2) | (op(e1, e2) = e2) | (~(op(e1, e0) = e2)) | (op(e2, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.63 tff(791,plain,
% 0.47/0.63 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[790, 765, 62, 758, 740])).
% 0.47/0.63 tff(792,plain,
% 0.47/0.63 ((op(e3, e3) = e3) <=> (e2 = e3)),
% 0.47/0.63 inference(monotonicity,[status(thm)],[737])).
% 0.47/0.63 tff(793,plain,
% 0.47/0.63 ((e2 = e3) <=> (op(e3, e3) = e3)),
% 0.47/0.63 inference(symmetry,[status(thm)],[792])).
% 0.47/0.63 tff(794,plain,
% 0.47/0.63 ((~(e2 = e3)) <=> (~(op(e3, e3) = e3))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[793])).
% 0.47/0.63 tff(795,plain,
% 0.47/0.63 (~(op(e3, e3) = e3)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[462, 794])).
% 0.47/0.63 tff(796,assumption,(~(op(e0, e2) = e2)), introduced(assumption)).
% 0.47/0.63 tff(797,assumption,(~(op(e3, e3) = e3)), introduced(assumption)).
% 0.47/0.63 tff(798,assumption,(op(e0, e2) = e1), introduced(assumption)).
% 0.47/0.63 tff(799,assumption,(op(e2, op(e0, e2)) = e2), introduced(assumption)).
% 0.47/0.63 tff(800,plain,
% 0.47/0.63 (e1 = op(e0, e2)),
% 0.47/0.63 inference(symmetry,[status(thm)],[798])).
% 0.47/0.63 tff(801,plain,
% 0.47/0.63 (op(e2, e1) = op(e2, op(e0, e2))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[800])).
% 0.47/0.63 tff(802,plain,
% 0.47/0.63 (op(e2, e1) = e2),
% 0.47/0.63 inference(transitivity,[status(thm)],[801, 799])).
% 0.47/0.63 tff(803,plain,
% 0.47/0.63 ((op(e0, e1) = op(e2, e1)) <=> (op(e0, e1) = e2)),
% 0.47/0.63 inference(monotonicity,[status(thm)],[802])).
% 0.47/0.63 tff(804,plain,
% 0.47/0.63 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = e2))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[803])).
% 0.47/0.63 tff(805,plain,
% 0.47/0.63 (~(op(e0, e1) = e2)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[61, 804])).
% 0.47/0.63 tff(806,assumption,(op(e0, e2) = e2), introduced(assumption)).
% 0.47/0.63 tff(807,plain,
% 0.47/0.63 (e2 = op(e0, e2)),
% 0.47/0.63 inference(symmetry,[status(thm)],[806])).
% 0.47/0.63 tff(808,plain,
% 0.47/0.63 (op(e2, e2) = op(e2, op(e0, e2))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[807])).
% 0.47/0.63 tff(809,plain,
% 0.47/0.63 (op(e2, e2) = e2),
% 0.47/0.63 inference(transitivity,[status(thm)],[808, 799])).
% 0.47/0.63 tff(810,plain,
% 0.47/0.63 ((e2 = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.47/0.63 inference(commutativity,[status(thm)],[])).
% 0.47/0.63 tff(811,plain,
% 0.47/0.63 ((op(e0, e2) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[806])).
% 0.47/0.63 tff(812,plain,
% 0.47/0.63 ((op(e0, e2) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.47/0.63 inference(transitivity,[status(thm)],[811, 810])).
% 0.47/0.63 tff(813,plain,
% 0.47/0.63 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[812])).
% 0.47/0.63 tff(814,plain,
% 0.47/0.63 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = op(e2, e2)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(815,plain,
% 0.47/0.63 (~(op(e0, e2) = op(e2, e2))),
% 0.47/0.63 inference(and_elim,[status(thm)],[53])).
% 0.47/0.63 tff(816,plain,
% 0.47/0.63 (~(op(e0, e2) = op(e2, e2))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[815, 814])).
% 0.47/0.63 tff(817,plain,
% 0.47/0.63 (~(op(e2, e2) = e2)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[816, 813])).
% 0.47/0.63 tff(818,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[817, 809])).
% 0.47/0.63 tff(819,plain,((~(op(e0, e2) = e2)) | (~(op(e2, op(e0, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.63 tff(820,plain,
% 0.47/0.63 (~(op(e0, e2) = e2)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[819, 799])).
% 0.47/0.63 tff(821,plain,
% 0.47/0.63 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e1)),
% 0.47/0.63 inference(monotonicity,[status(thm)],[798])).
% 0.47/0.63 tff(822,plain,
% 0.47/0.63 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e1))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[821])).
% 0.47/0.63 tff(823,plain,
% 0.47/0.63 (~(op(e0, e1) = e1)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[70, 822])).
% 0.47/0.63 tff(824,plain,
% 0.47/0.63 ((op(e2, e1) = e1) <=> (e2 = e1)),
% 0.47/0.63 inference(monotonicity,[status(thm)],[802])).
% 0.47/0.63 tff(825,plain,
% 0.47/0.63 ((op(e2, e1) = e1) <=> (e1 = e2)),
% 0.47/0.63 inference(transitivity,[status(thm)],[824, 317])).
% 0.47/0.63 tff(826,plain,
% 0.47/0.63 ((e1 = e2) <=> (op(e2, e1) = e1)),
% 0.47/0.63 inference(symmetry,[status(thm)],[825])).
% 0.47/0.63 tff(827,plain,
% 0.47/0.63 ((~(e1 = e2)) <=> (~(op(e2, e1) = e1))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[826])).
% 0.47/0.63 tff(828,plain,
% 0.47/0.63 (~(op(e2, e1) = e1)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[324, 827])).
% 0.47/0.63 tff(829,assumption,(op(e1, op(e0, e1)) = e1), introduced(assumption)).
% 0.47/0.63 tff(830,assumption,(~(op(e0, e1) = e2)), introduced(assumption)).
% 0.47/0.63 tff(831,plain,
% 0.47/0.63 ((e1 = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 0.47/0.63 inference(commutativity,[status(thm)],[])).
% 0.47/0.63 tff(832,assumption,(op(e1, e1) = e1), introduced(assumption)).
% 0.47/0.63 tff(833,plain,
% 0.47/0.63 ((op(e1, e1) = op(e1, e3)) <=> (e1 = op(e1, e3))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[832])).
% 0.47/0.63 tff(834,plain,
% 0.47/0.63 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 0.47/0.63 inference(transitivity,[status(thm)],[833, 831])).
% 0.47/0.63 tff(835,plain,
% 0.47/0.63 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e1))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[834])).
% 0.47/0.63 tff(836,plain,
% 0.47/0.63 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = op(e1, e3)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(837,plain,
% 0.47/0.63 (~(op(e1, e1) = op(e1, e3))),
% 0.47/0.63 inference(and_elim,[status(thm)],[32])).
% 0.47/0.63 tff(838,plain,
% 0.47/0.63 (~(op(e1, e1) = op(e1, e3))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[837, 836])).
% 0.47/0.63 tff(839,plain,
% 0.47/0.63 (~(op(e1, e3) = e1)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[838, 835])).
% 0.47/0.63 tff(840,assumption,(op(e0, e1) = e3), introduced(assumption)).
% 0.47/0.63 tff(841,plain,
% 0.47/0.63 (e3 = op(e0, e1)),
% 0.47/0.63 inference(symmetry,[status(thm)],[840])).
% 0.47/0.63 tff(842,plain,
% 0.47/0.63 (op(e1, e3) = op(e1, op(e0, e1))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[841])).
% 0.47/0.63 tff(843,plain,
% 0.47/0.63 (op(e1, e3) = e1),
% 0.47/0.63 inference(transitivity,[status(thm)],[842, 829])).
% 0.47/0.63 tff(844,assumption,(~(op(e1, e3) = e1)), introduced(assumption)).
% 0.47/0.63 tff(845,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[844, 843])).
% 0.47/0.63 tff(846,plain,((~(op(e0, e1) = e3)) | (op(e1, e3) = e1) | (~(op(e1, op(e0, e1)) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.63 tff(847,plain,
% 0.47/0.63 (~(op(e0, e1) = e3)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[846, 839, 829])).
% 0.47/0.63 tff(848,plain,
% 0.47/0.63 (((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))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(849,plain,
% 0.47/0.63 ((((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))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(850,plain,
% 0.47/0.63 ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) <=> ((op(e0, e1) = e0) | (op(e0, e1) = e1) | (op(e0, e1) = e2))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(851,plain,
% 0.47/0.63 (((((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))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[850])).
% 0.47/0.63 tff(852,plain,
% 0.47/0.63 (((((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))),
% 0.47/0.63 inference(transitivity,[status(thm)],[851, 849])).
% 0.47/0.63 tff(853,plain,
% 0.47/0.63 (((((((((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))),
% 0.47/0.63 inference(and_elim,[status(thm)],[190])).
% 0.47/0.63 tff(854,plain,
% 0.47/0.63 ((((((((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))),
% 0.47/0.63 inference(and_elim,[status(thm)],[853])).
% 0.47/0.63 tff(855,plain,
% 0.47/0.63 (((((((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))),
% 0.47/0.63 inference(and_elim,[status(thm)],[854])).
% 0.47/0.63 tff(856,plain,
% 0.47/0.63 ((((((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))),
% 0.47/0.63 inference(and_elim,[status(thm)],[855])).
% 0.47/0.63 tff(857,plain,
% 0.47/0.63 (((((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))),
% 0.47/0.63 inference(and_elim,[status(thm)],[856])).
% 0.47/0.63 tff(858,plain,
% 0.47/0.63 ((((op(e0, e1) = e0) | (op(e0, e1) = e1)) | (op(e0, e1) = e2)) | (op(e0, e1) = e3)),
% 0.47/0.63 inference(and_elim,[status(thm)],[857])).
% 0.47/0.63 tff(859,plain,
% 0.47/0.63 ((op(e0, e1) = e0) | (op(e0, e1) = e1) | (op(e0, e1) = e2) | (op(e0, e1) = e3)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[858, 852])).
% 0.47/0.63 tff(860,plain,
% 0.47/0.63 ((op(e0, e1) = e0) | (op(e0, e1) = e1) | (op(e0, e1) = e2) | (op(e0, e1) = e3)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[859, 848])).
% 0.47/0.63 tff(861,plain,
% 0.47/0.63 (op(e0, e1) = e0),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[860, 847, 830, 433])).
% 0.47/0.63 tff(862,plain,
% 0.47/0.63 (e0 = op(e0, e1)),
% 0.47/0.63 inference(symmetry,[status(thm)],[861])).
% 0.47/0.63 tff(863,plain,
% 0.47/0.63 (op(e1, e0) = op(e1, op(e0, e1))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[862])).
% 0.47/0.63 tff(864,plain,
% 0.47/0.63 (op(e1, e0) = e1),
% 0.47/0.63 inference(transitivity,[status(thm)],[863, 829])).
% 0.47/0.63 tff(865,plain,
% 0.47/0.63 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e1)),
% 0.47/0.63 inference(monotonicity,[status(thm)],[832])).
% 0.47/0.63 tff(866,plain,
% 0.47/0.63 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e1))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[865])).
% 0.47/0.63 tff(867,plain,
% 0.47/0.63 (~(op(e1, e0) = e1)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[440, 866])).
% 0.47/0.63 tff(868,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[867, 864])).
% 0.47/0.63 tff(869,plain,((~(op(e1, e1) = e1)) | (~(op(e1, op(e0, e1)) = e1)) | (op(e0, e1) = e2) | (op(e0, e1) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.63 tff(870,plain,
% 0.47/0.63 (~(op(e1, e1) = e1)),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[869, 805, 829, 823])).
% 0.47/0.63 tff(871,plain,
% 0.47/0.63 (op(e3, e1) = e1),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[450, 870, 828, 823])).
% 0.47/0.63 tff(872,plain,
% 0.47/0.63 ((op(e3, e1) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[871])).
% 0.47/0.63 tff(873,plain,
% 0.47/0.63 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 0.47/0.63 inference(transitivity,[status(thm)],[872, 76])).
% 0.47/0.63 tff(874,plain,
% 0.47/0.63 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[873])).
% 0.47/0.63 tff(875,plain,
% 0.47/0.63 (~(op(e3, e3) = e1)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[399, 874])).
% 0.47/0.63 tff(876,plain,
% 0.47/0.63 (op(e3, e3) = e2),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[266, 875, 63, 797])).
% 0.47/0.63 tff(877,plain,
% 0.47/0.63 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e2)),
% 0.47/0.63 inference(monotonicity,[status(thm)],[876])).
% 0.47/0.63 tff(878,plain,
% 0.47/0.63 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e2))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[877])).
% 0.47/0.63 tff(879,plain,
% 0.47/0.63 (~(op(e0, e3) = e2)),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[725, 878])).
% 0.47/0.63 tff(880,plain,
% 0.47/0.63 (((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))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(881,plain,
% 0.47/0.64 ((((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))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(882,plain,
% 0.47/0.64 ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) <=> ((op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e2))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(883,plain,
% 0.47/0.64 (((((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))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[882])).
% 0.47/0.64 tff(884,plain,
% 0.47/0.64 (((((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))),
% 0.47/0.64 inference(transitivity,[status(thm)],[883, 881])).
% 0.47/0.64 tff(885,plain,
% 0.47/0.64 ((((op(e0, e0) = e2) | (op(e0, e1) = e2)) | (op(e0, e2) = e2)) | (op(e0, e3) = e2)),
% 0.47/0.64 inference(and_elim,[status(thm)],[713])).
% 0.47/0.64 tff(886,plain,
% 0.47/0.64 ((op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e2) | (op(e0, e3) = e2)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[885, 884])).
% 0.47/0.64 tff(887,plain,
% 0.47/0.64 ((op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e2) | (op(e0, e3) = e2)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[886, 880])).
% 0.47/0.64 tff(888,plain,
% 0.47/0.64 (op(e0, e0) = e2),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[887, 879, 820, 805])).
% 0.47/0.64 tff(889,plain,
% 0.47/0.64 (e2 = op(e0, e0)),
% 0.47/0.64 inference(symmetry,[status(thm)],[888])).
% 0.47/0.64 tff(890,plain,
% 0.47/0.64 (op(e0, e2) = op(e0, op(e0, e0))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[889])).
% 0.47/0.64 tff(891,plain,
% 0.47/0.64 (op(e0, op(e0, e0)) = op(e0, e2)),
% 0.47/0.64 inference(symmetry,[status(thm)],[890])).
% 0.47/0.64 tff(892,plain,
% 0.47/0.64 (e0 = e1),
% 0.47/0.64 inference(transitivity,[status(thm)],[689, 891, 798])).
% 0.47/0.64 tff(893,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[625, 892])).
% 0.47/0.64 tff(894,plain,((~(op(e0, e2) = e1)) | (~(op(e0, op(e0, e0)) = e0)) | (op(e3, e3) = e0) | (op(e3, e3) = e3) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(895,plain,
% 0.47/0.64 (~(op(e0, e2) = e1)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[894, 7, 63, 797, 5, 9])).
% 0.47/0.64 tff(896,assumption,(op(e0, e2) = e0), introduced(assumption)).
% 0.47/0.64 tff(897,plain,
% 0.47/0.64 (e0 = op(e0, e2)),
% 0.47/0.64 inference(symmetry,[status(thm)],[896])).
% 0.47/0.64 tff(898,plain,
% 0.47/0.64 (op(e2, e0) = op(e2, op(e0, e2))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[897])).
% 0.47/0.64 tff(899,plain,
% 0.47/0.64 (op(e2, e0) = e2),
% 0.47/0.64 inference(transitivity,[status(thm)],[898, 799])).
% 0.47/0.64 tff(900,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[74, 899])).
% 0.47/0.64 tff(901,plain,((~(op(e0, e2) = e0)) | (op(e2, e0) = e2) | (~(op(e2, op(e0, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(902,plain,
% 0.47/0.64 (~(op(e0, e2) = e0)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[901, 9, 74])).
% 0.47/0.64 tff(903,assumption,(op(e0, e2) = e3), introduced(assumption)).
% 0.47/0.64 tff(904,plain,
% 0.47/0.64 (e3 = op(e0, e2)),
% 0.47/0.64 inference(symmetry,[status(thm)],[903])).
% 0.47/0.64 tff(905,plain,
% 0.47/0.64 (op(e2, e3) = op(e2, op(e0, e2))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[904])).
% 0.47/0.64 tff(906,plain,
% 0.47/0.64 (op(e2, e3) = e2),
% 0.47/0.64 inference(transitivity,[status(thm)],[905, 799])).
% 0.47/0.64 tff(907,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[767, 906])).
% 0.47/0.64 tff(908,plain,((~(op(e0, e2) = e3)) | (op(e2, e3) = e2) | (~(op(e2, op(e0, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(909,plain,
% 0.47/0.64 (~(op(e0, e2) = e3)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[908, 9, 767])).
% 0.47/0.64 tff(910,plain,
% 0.47/0.64 (((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))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(911,plain,
% 0.47/0.64 ((((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))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(912,plain,
% 0.47/0.64 ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) <=> ((op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e2) = e2))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(913,plain,
% 0.47/0.64 (((((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))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[912])).
% 0.47/0.64 tff(914,plain,
% 0.47/0.64 (((((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))),
% 0.47/0.64 inference(transitivity,[status(thm)],[913, 911])).
% 0.47/0.64 tff(915,plain,
% 0.47/0.64 ((((op(e0, e2) = e0) | (op(e0, e2) = e1)) | (op(e0, e2) = e2)) | (op(e0, e2) = e3)),
% 0.47/0.64 inference(and_elim,[status(thm)],[856])).
% 0.47/0.64 tff(916,plain,
% 0.47/0.64 ((op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e2) = e2) | (op(e0, e2) = e3)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[915, 914])).
% 0.47/0.64 tff(917,plain,
% 0.47/0.64 ((op(e0, e2) = e0) | (op(e0, e2) = e1) | (op(e0, e2) = e2) | (op(e0, e2) = e3)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[916, 910])).
% 0.47/0.64 tff(918,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[917, 909, 902, 895, 796])).
% 0.47/0.64 tff(919,plain,(((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))) | (op(e0, e2) = e2) | (op(e2, e3) = e2) | (op(e2, e0) = e2) | (op(e3, e3) = e0) | (op(e3, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(920,plain,
% 0.47/0.64 ((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[919, 740, 71, 74, 63, 795])).
% 0.47/0.64 tff(921,plain,
% 0.47/0.64 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[681, 920, 456, 791])).
% 0.47/0.64 tff(922,plain,
% 0.47/0.64 (op(e1, op(e2, e1)) = e1),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[546, 921])).
% 0.47/0.64 tff(923,plain,
% 0.47/0.64 ((op(e1, e0) = e1) <=> (e2 = e1)),
% 0.47/0.64 inference(monotonicity,[status(thm)],[758])).
% 0.47/0.64 tff(924,plain,
% 0.47/0.64 ((op(e1, e0) = e1) <=> (e1 = e2)),
% 0.47/0.64 inference(transitivity,[status(thm)],[923, 317])).
% 0.47/0.64 tff(925,plain,
% 0.47/0.64 ((e1 = e2) <=> (op(e1, e0) = e1)),
% 0.47/0.64 inference(symmetry,[status(thm)],[924])).
% 0.47/0.64 tff(926,plain,
% 0.47/0.64 ((~(e1 = e2)) <=> (~(op(e1, e0) = e1))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[925])).
% 0.47/0.64 tff(927,plain,
% 0.47/0.64 (~(op(e1, e0) = e1)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[324, 926])).
% 0.47/0.64 tff(928,plain,
% 0.47/0.64 (~(op(e2, e1) = e0)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[642, 922, 927])).
% 0.47/0.64 tff(929,plain,
% 0.47/0.64 (~(op(e3, e1) = e0)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[593, 557, 10, 551, 544])).
% 0.47/0.64 tff(930,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[627, 929, 557, 10, 551, 604, 605])).
% 0.47/0.64 tff(931,plain,((op(e2, e1) = e3) | (op(e2, e1) = e2) | (~(op(e1, op(e2, e1)) = e1)) | (op(e0, e1) = e0) | (op(e2, e1) = e0) | (op(e0, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(932,plain,
% 0.47/0.64 (op(e2, e1) = e3),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[931, 922, 62, 468, 928, 463])).
% 0.47/0.64 tff(933,plain,
% 0.47/0.64 (e3 = op(e2, e1)),
% 0.47/0.64 inference(symmetry,[status(thm)],[549])).
% 0.47/0.64 tff(934,plain,
% 0.47/0.64 (op(e1, e3) = op(e1, op(e2, e1))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[933])).
% 0.47/0.64 tff(935,plain,
% 0.47/0.64 (op(e1, e3) = e1),
% 0.47/0.64 inference(transitivity,[status(thm)],[934, 551])).
% 0.47/0.64 tff(936,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[844, 935])).
% 0.47/0.64 tff(937,plain,((~(op(e2, e1) = e3)) | (op(e1, e3) = e1) | (~(op(e1, op(e2, e1)) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(938,plain,
% 0.47/0.64 (op(e1, e3) = e1),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[937, 932, 922])).
% 0.47/0.64 tff(939,plain,
% 0.47/0.64 ((op(e1, e3) = op(e2, e3)) <=> (e1 = op(e2, e3))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[938])).
% 0.47/0.64 tff(940,plain,
% 0.47/0.64 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e1)),
% 0.47/0.64 inference(transitivity,[status(thm)],[939, 73])).
% 0.47/0.64 tff(941,plain,
% 0.47/0.64 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e1))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[940])).
% 0.47/0.64 tff(942,plain,
% 0.47/0.64 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = op(e2, e3)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(943,plain,
% 0.47/0.64 (~(op(e1, e3) = op(e2, e3))),
% 0.47/0.64 inference(and_elim,[status(thm)],[45])).
% 0.47/0.64 tff(944,plain,
% 0.47/0.64 (~(op(e1, e3) = op(e2, e3))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[943, 942])).
% 0.47/0.64 tff(945,plain,
% 0.47/0.64 (~(op(e2, e3) = e1)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[944, 941])).
% 0.47/0.64 tff(946,plain,
% 0.47/0.64 ((op(e2, e2) = e1) <=> (e2 = e1)),
% 0.47/0.64 inference(monotonicity,[status(thm)],[759])).
% 0.47/0.64 tff(947,plain,
% 0.47/0.64 ((op(e2, e2) = e1) <=> (e1 = e2)),
% 0.47/0.64 inference(transitivity,[status(thm)],[946, 317])).
% 0.47/0.64 tff(948,plain,
% 0.47/0.64 ((e1 = e2) <=> (op(e2, e2) = e1)),
% 0.47/0.64 inference(symmetry,[status(thm)],[947])).
% 0.47/0.64 tff(949,plain,
% 0.47/0.64 ((~(e1 = e2)) <=> (~(op(e2, e2) = e1))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[948])).
% 0.47/0.64 tff(950,plain,
% 0.47/0.64 (~(op(e2, e2) = e1)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[324, 949])).
% 0.49/0.64 tff(951,plain,
% 0.49/0.64 ((e3 = e1) <=> (e1 = e3)),
% 0.49/0.64 inference(commutativity,[status(thm)],[])).
% 0.49/0.64 tff(952,plain,
% 0.49/0.64 ((op(e2, e1) = e1) <=> (e3 = e1)),
% 0.49/0.64 inference(monotonicity,[status(thm)],[932])).
% 0.49/0.64 tff(953,plain,
% 0.49/0.64 ((op(e2, e1) = e1) <=> (e1 = e3)),
% 0.49/0.64 inference(transitivity,[status(thm)],[952, 951])).
% 0.49/0.64 tff(954,plain,
% 0.49/0.64 ((e1 = e3) <=> (op(e2, e1) = e1)),
% 0.49/0.64 inference(symmetry,[status(thm)],[953])).
% 0.49/0.64 tff(955,plain,
% 0.49/0.64 ((~(e1 = e3)) <=> (~(op(e2, e1) = e1))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[954])).
% 0.49/0.64 tff(956,plain,
% 0.49/0.64 (~(op(e2, e1) = e1)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[591, 955])).
% 0.49/0.64 tff(957,plain,
% 0.49/0.64 (((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))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(958,plain,
% 0.49/0.64 ((((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))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(959,plain,
% 0.49/0.64 ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) <=> ((op(e2, e0) = e1) | (op(e2, e1) = e1) | (op(e2, e2) = e1))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(960,plain,
% 0.49/0.64 (((((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))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[959])).
% 0.49/0.64 tff(961,plain,
% 0.49/0.64 (((((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))),
% 0.49/0.64 inference(transitivity,[status(thm)],[960, 958])).
% 0.49/0.64 tff(962,plain,
% 0.49/0.64 ((((op(e2, e0) = e1) | (op(e2, e1) = e1)) | (op(e2, e2) = e1)) | (op(e2, e3) = e1)),
% 0.49/0.64 inference(and_elim,[status(thm)],[126])).
% 0.49/0.64 tff(963,plain,
% 0.49/0.64 ((op(e2, e0) = e1) | (op(e2, e1) = e1) | (op(e2, e2) = e1) | (op(e2, e3) = e1)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[962, 961])).
% 0.49/0.64 tff(964,plain,
% 0.49/0.64 ((op(e2, e0) = e1) | (op(e2, e1) = e1) | (op(e2, e2) = e1) | (op(e2, e3) = e1)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[963, 957])).
% 0.49/0.64 tff(965,plain,
% 0.49/0.64 (op(e2, e0) = e1),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[964, 956, 950, 945])).
% 0.49/0.64 tff(966,plain,
% 0.49/0.64 (op(e0, op(e2, e0)) = op(e0, e1)),
% 0.49/0.64 inference(monotonicity,[status(thm)],[965])).
% 0.49/0.64 tff(967,plain,
% 0.49/0.64 (((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))) | (op(e0, op(e2, e0)) = e0)),
% 0.49/0.64 inference(tautology,[status(thm)],[])).
% 0.49/0.64 tff(968,plain,
% 0.49/0.64 (op(e0, op(e2, e0)) = e0),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[967, 921])).
% 0.49/0.64 tff(969,plain,
% 0.49/0.64 (e0 = op(e0, op(e2, e0))),
% 0.49/0.64 inference(symmetry,[status(thm)],[968])).
% 0.49/0.64 tff(970,plain,
% 0.49/0.64 (e0 = e2),
% 0.49/0.64 inference(transitivity,[status(thm)],[969, 966, 14])).
% 0.49/0.64 tff(971,plain,
% 0.49/0.64 ($false),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[238, 970])).
% 0.49/0.64 tff(972,plain,((op(e2, e0) = e2) | (~(op(e0, e1) = e2)) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.64 tff(973,plain,
% 0.49/0.64 (op(e2, e0) = e2),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[972, 63, 14])).
% 0.49/0.64 tff(974,plain,
% 0.49/0.64 ((op(e2, e0) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[973])).
% 0.49/0.64 tff(975,plain,
% 0.49/0.64 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.49/0.64 inference(transitivity,[status(thm)],[974, 72])).
% 0.49/0.64 tff(976,plain,
% 0.49/0.64 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[975])).
% 0.49/0.64 tff(977,plain,
% 0.49/0.64 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = op(e2, e3)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(978,plain,
% 0.49/0.64 (~(op(e2, e0) = op(e2, e3))),
% 0.49/0.64 inference(and_elim,[status(thm)],[28])).
% 0.49/0.64 tff(979,plain,
% 0.49/0.64 (~(op(e2, e0) = op(e2, e3))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[978, 977])).
% 0.49/0.64 tff(980,plain,
% 0.49/0.64 (~(op(e2, e3) = e2)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[979, 976])).
% 0.49/0.64 tff(981,plain,
% 0.49/0.64 (~(op(e0, e2) = e3)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[908, 9, 980])).
% 0.49/0.64 tff(982,plain,
% 0.49/0.64 (e1 = op(e1, op(e0, e1))),
% 0.49/0.64 inference(symmetry,[status(thm)],[5])).
% 0.49/0.64 tff(983,plain,
% 0.49/0.64 (e1 = op(e1, e2)),
% 0.49/0.64 inference(transitivity,[status(thm)],[982, 694])).
% 0.49/0.64 tff(984,plain,
% 0.49/0.64 ((op(e0, e2) = e1) <=> (op(e0, e2) = op(e1, e2))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[983])).
% 0.49/0.64 tff(985,plain,
% 0.49/0.64 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e1)),
% 0.49/0.64 inference(symmetry,[status(thm)],[984])).
% 0.49/0.64 tff(986,plain,
% 0.49/0.64 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e1))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[985])).
% 0.49/0.64 tff(987,plain,
% 0.49/0.64 (~(op(e0, e2) = e1)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[703, 986])).
% 0.49/0.64 tff(988,plain,
% 0.49/0.64 ((e0 = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 0.49/0.64 inference(commutativity,[status(thm)],[])).
% 0.49/0.64 tff(989,assumption,(~(op(e0, e0) = e0)), introduced(assumption)).
% 0.49/0.64 tff(990,plain,
% 0.49/0.64 (~(op(e0, e2) = e1)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[894, 797, 63, 688, 829, 799])).
% 0.49/0.64 tff(991,assumption,(~(op(e0, e2) = e1)), introduced(assumption)).
% 0.49/0.64 tff(992,assumption,(op(e2, e1) = e2), introduced(assumption)).
% 0.49/0.64 tff(993,plain,
% 0.49/0.64 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e0) = e2)),
% 0.49/0.64 inference(monotonicity,[status(thm)],[992])).
% 0.49/0.64 tff(994,plain,
% 0.49/0.64 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = e2))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[993])).
% 0.49/0.64 tff(995,plain,
% 0.49/0.64 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = op(e2, e1)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(996,plain,
% 0.49/0.64 (~(op(e2, e0) = op(e2, e1))),
% 0.49/0.64 inference(and_elim,[status(thm)],[30])).
% 0.49/0.64 tff(997,plain,
% 0.49/0.64 (~(op(e2, e0) = op(e2, e1))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[996, 995])).
% 0.49/0.64 tff(998,plain,
% 0.49/0.64 (~(op(e2, e0) = e2)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[997, 994])).
% 0.49/0.64 tff(999,plain,
% 0.49/0.64 (~(op(e0, e2) = e0)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[901, 998, 799])).
% 0.49/0.64 tff(1000,plain,
% 0.49/0.64 ((op(e2, e1) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[992])).
% 0.49/0.64 tff(1001,plain,
% 0.49/0.64 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.49/0.64 inference(transitivity,[status(thm)],[1000, 72])).
% 0.49/0.64 tff(1002,plain,
% 0.49/0.64 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[1001])).
% 0.49/0.64 tff(1003,plain,
% 0.49/0.64 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e1) = op(e2, e3)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(1004,plain,
% 0.49/0.64 (~(op(e2, e1) = op(e2, e3))),
% 0.49/0.64 inference(and_elim,[status(thm)],[26])).
% 0.49/0.64 tff(1005,plain,
% 0.49/0.64 (~(op(e2, e1) = op(e2, e3))),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[1004, 1003])).
% 0.49/0.64 tff(1006,plain,
% 0.49/0.64 (~(op(e2, e3) = e2)),
% 0.49/0.64 inference(modus_ponens,[status(thm)],[1005, 1002])).
% 0.49/0.64 tff(1007,plain,
% 0.49/0.64 (~(op(e0, e2) = e3)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[908, 1006, 799])).
% 0.49/0.64 tff(1008,plain,
% 0.49/0.64 ($false),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[917, 1007, 999, 820, 991])).
% 0.49/0.64 tff(1009,plain,((~(op(e2, e1) = e2)) | (op(e0, e2) = e1) | (~(op(e2, op(e0, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.64 tff(1010,plain,
% 0.49/0.64 (~(op(e2, e1) = e2)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[1009, 990, 799])).
% 0.49/0.65 tff(1011,plain,
% 0.49/0.65 (((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))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(1012,plain,
% 0.49/0.65 ((((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))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(1013,plain,
% 0.49/0.65 ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) <=> ((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(1014,plain,
% 0.49/0.65 (((((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))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1013])).
% 0.49/0.65 tff(1015,plain,
% 0.49/0.65 (((((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))),
% 0.49/0.65 inference(transitivity,[status(thm)],[1014, 1012])).
% 0.49/0.65 tff(1016,plain,
% 0.49/0.65 ((((op(e0, e1) = e2) | (op(e1, e1) = e2)) | (op(e2, e1) = e2)) | (op(e3, e1) = e2)),
% 0.49/0.65 inference(and_elim,[status(thm)],[131])).
% 0.49/0.65 tff(1017,plain,
% 0.49/0.65 ((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e3, e1) = e2)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[1016, 1015])).
% 0.49/0.65 tff(1018,plain,
% 0.49/0.65 ((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e3, e1) = e2)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[1017, 1011])).
% 0.49/0.65 tff(1019,plain,
% 0.49/0.65 (op(e3, e1) = e2),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[1018, 830, 12, 10])).
% 0.49/0.65 tff(1020,assumption,(op(e2, e1) = e1), introduced(assumption)).
% 0.49/0.65 tff(1021,plain,
% 0.49/0.65 ((op(e0, e1) = op(e2, e1)) <=> (op(e0, e1) = e1)),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1020])).
% 0.49/0.65 tff(1022,plain,
% 0.49/0.65 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e0, e1) = e1))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1021])).
% 0.49/0.65 tff(1023,plain,
% 0.49/0.65 (~(op(e0, e1) = e1)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[61, 1022])).
% 0.49/0.65 tff(1024,plain,
% 0.49/0.65 ((e2 = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.49/0.65 inference(commutativity,[status(thm)],[])).
% 0.49/0.65 tff(1025,plain,
% 0.49/0.65 ((op(e2, e1) = e2) <=> (e1 = e2)),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1020])).
% 0.49/0.65 tff(1026,plain,
% 0.49/0.65 ((e1 = e2) <=> (op(e2, e1) = e2)),
% 0.49/0.65 inference(symmetry,[status(thm)],[1025])).
% 0.49/0.65 tff(1027,plain,
% 0.49/0.65 ((~(e1 = e2)) <=> (~(op(e2, e1) = e2))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1026])).
% 0.49/0.65 tff(1028,plain,
% 0.49/0.65 (~(op(e2, e1) = e2)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[324, 1027])).
% 0.49/0.65 tff(1029,plain,
% 0.49/0.65 (op(e3, e1) = e2),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[1018, 1028, 12, 830])).
% 0.49/0.65 tff(1030,plain,
% 0.49/0.65 ((op(e3, e1) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1029])).
% 0.49/0.65 tff(1031,plain,
% 0.49/0.65 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.49/0.65 inference(transitivity,[status(thm)],[1030, 1024])).
% 0.49/0.65 tff(1032,plain,
% 0.49/0.65 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1031])).
% 0.49/0.65 tff(1033,plain,
% 0.49/0.65 (~(op(e3, e3) = e2)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[399, 1032])).
% 0.49/0.65 tff(1034,plain,
% 0.49/0.65 (op(e3, e3) = e1),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[266, 1033, 63, 797])).
% 0.49/0.65 tff(1035,plain,
% 0.49/0.65 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e1)),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1034])).
% 0.49/0.65 tff(1036,plain,
% 0.49/0.65 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e1))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1035])).
% 0.49/0.65 tff(1037,plain,
% 0.49/0.65 (~(op(e1, e3) = e1)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[368, 1036])).
% 0.49/0.65 tff(1038,plain,
% 0.49/0.65 (~(op(e0, e1) = e3)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[846, 1037, 829])).
% 0.49/0.65 tff(1039,plain,
% 0.49/0.65 (op(e0, e1) = e0),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[860, 1038, 830, 1023])).
% 0.49/0.65 tff(1040,plain,
% 0.49/0.65 (e0 = op(e0, e1)),
% 0.49/0.65 inference(symmetry,[status(thm)],[1039])).
% 0.49/0.65 tff(1041,plain,
% 0.49/0.65 (op(e1, e0) = op(e1, op(e0, e1))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1040])).
% 0.49/0.65 tff(1042,plain,
% 0.49/0.65 (op(e1, e0) = e1),
% 0.49/0.65 inference(transitivity,[status(thm)],[1041, 829])).
% 0.49/0.65 tff(1043,plain,
% 0.49/0.65 ((e1 = op(e1, e0)) <=> (op(e1, e0) = e1)),
% 0.49/0.65 inference(commutativity,[status(thm)],[])).
% 0.49/0.65 tff(1044,plain,
% 0.49/0.65 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e1)),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1034])).
% 0.49/0.65 tff(1045,plain,
% 0.49/0.65 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e1))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1044])).
% 0.49/0.65 tff(1046,plain,
% 0.49/0.65 (~(op(e0, e3) = e1)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[725, 1045])).
% 0.49/0.65 tff(1047,plain,
% 0.49/0.65 (op(e0, e0) = e1),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[718, 1046, 991, 1023])).
% 0.49/0.65 tff(1048,plain,
% 0.49/0.65 ((op(e0, e0) = op(e1, e0)) <=> (e1 = op(e1, e0))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1047])).
% 0.49/0.65 tff(1049,plain,
% 0.49/0.65 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e1)),
% 0.49/0.65 inference(transitivity,[status(thm)],[1048, 1043])).
% 0.49/0.65 tff(1050,plain,
% 0.49/0.65 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e1))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1049])).
% 0.49/0.65 tff(1051,plain,
% 0.49/0.65 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = op(e1, e0)))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(1052,plain,
% 0.49/0.65 ((((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))) & (~(op(e1, e0) = op(e2, e0)))),
% 0.49/0.65 inference(and_elim,[status(thm)],[418])).
% 0.49/0.65 tff(1053,plain,
% 0.49/0.65 (((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))) & (~(op(e0, e0) = op(e3, e0)))),
% 0.49/0.65 inference(and_elim,[status(thm)],[1052])).
% 0.49/0.65 tff(1054,plain,
% 0.49/0.65 ((~(op(e0, e0) = op(e1, e0))) & (~(op(e0, e0) = op(e2, e0)))),
% 0.49/0.65 inference(and_elim,[status(thm)],[1053])).
% 0.49/0.65 tff(1055,plain,
% 0.49/0.65 (~(op(e0, e0) = op(e1, e0))),
% 0.49/0.65 inference(and_elim,[status(thm)],[1054])).
% 0.49/0.65 tff(1056,plain,
% 0.49/0.65 (~(op(e0, e0) = op(e1, e0))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[1055, 1051])).
% 0.49/0.65 tff(1057,plain,
% 0.49/0.65 (~(op(e1, e0) = e1)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[1056, 1050])).
% 0.49/0.65 tff(1058,plain,
% 0.49/0.65 ($false),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[1057, 1042])).
% 0.49/0.65 tff(1059,plain,((~(op(e2, e1) = e1)) | (~(op(e1, op(e0, e1)) = e1)) | (op(e0, e1) = e2) | (op(e0, e2) = e1) | (op(e3, e3) = e0) | (op(e3, e3) = e3) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.65 tff(1060,plain,
% 0.49/0.65 (~(op(e2, e1) = e1)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[1059, 830, 829, 991, 63, 797, 12])).
% 0.49/0.65 tff(1061,plain,
% 0.49/0.65 ((op(e0, e1) = op(e1, e1)) <=> (op(e0, e1) = e1)),
% 0.49/0.65 inference(monotonicity,[status(thm)],[832])).
% 0.49/0.65 tff(1062,plain,
% 0.49/0.65 ((op(e0, e1) = e1) <=> (op(e0, e1) = op(e1, e1))),
% 0.49/0.65 inference(symmetry,[status(thm)],[1061])).
% 0.49/0.65 tff(1063,plain,
% 0.49/0.65 (op(e0, e1) = e1),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[869, 832, 829, 830])).
% 0.49/0.65 tff(1064,plain,
% 0.49/0.65 (op(e0, e1) = op(e1, e1)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[1063, 1062])).
% 0.49/0.65 tff(1065,plain,
% 0.49/0.65 ($false),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[100, 1064])).
% 0.49/0.65 tff(1066,plain,((~(op(e1, e1) = e1)) | (~(op(e1, op(e0, e1)) = e1)) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.65 tff(1067,plain,
% 0.49/0.65 (~(op(e1, e1) = e1)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[1066, 830, 829])).
% 0.49/0.65 tff(1068,assumption,(~(op(e3, e1) = e1)), introduced(assumption)).
% 0.49/0.65 tff(1069,assumption,(~(op(e2, e1) = e1)), introduced(assumption)).
% 0.49/0.65 tff(1070,assumption,(~(op(e1, e1) = e1)), introduced(assumption)).
% 0.49/0.65 tff(1071,plain,
% 0.49/0.65 (op(e0, e1) = e1),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[450, 1070, 1069, 1068])).
% 0.49/0.65 tff(1072,plain,
% 0.49/0.65 (e1 = op(e0, e1)),
% 0.49/0.65 inference(symmetry,[status(thm)],[1071])).
% 0.49/0.65 tff(1073,plain,
% 0.49/0.65 (op(e1, e1) = op(e1, op(e0, e1))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1072])).
% 0.49/0.65 tff(1074,plain,
% 0.49/0.65 (op(e1, e1) = e1),
% 0.49/0.65 inference(transitivity,[status(thm)],[1073, 829])).
% 0.49/0.65 tff(1075,plain,
% 0.49/0.65 ($false),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[1070, 1074])).
% 0.49/0.65 tff(1076,plain,((op(e1, e1) = e1) | (~(op(e1, op(e0, e1)) = e1)) | (op(e2, e1) = e1) | (op(e3, e1) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.65 tff(1077,plain,
% 0.49/0.65 (op(e3, e1) = e1),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[1076, 1067, 829, 1060])).
% 0.49/0.65 tff(1078,plain,
% 0.49/0.65 (e1 = op(e3, e1)),
% 0.49/0.65 inference(symmetry,[status(thm)],[1077])).
% 0.49/0.65 tff(1079,plain,
% 0.49/0.65 (e1 = e2),
% 0.49/0.65 inference(transitivity,[status(thm)],[1078, 1019])).
% 0.49/0.65 tff(1080,plain,
% 0.49/0.65 ($false),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[324, 1079])).
% 0.49/0.65 tff(1081,plain,((op(e0, e1) = e2) | (~(op(e1, op(e0, e1)) = e1)) | (op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e0, e2) = e1) | (op(e3, e3) = e0) | (op(e3, e3) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.65 tff(1082,plain,
% 0.49/0.65 (op(e0, e1) = e2),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[1081, 1010, 12, 829, 990, 63, 797])).
% 0.49/0.65 tff(1083,plain,
% 0.49/0.65 ((op(e0, e1) = e1) <=> (e2 = e1)),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1082])).
% 0.49/0.65 tff(1084,plain,
% 0.49/0.65 ((op(e0, e1) = e1) <=> (e1 = e2)),
% 0.49/0.65 inference(transitivity,[status(thm)],[1083, 317])).
% 0.49/0.65 tff(1085,plain,
% 0.49/0.65 ((e1 = e2) <=> (op(e0, e1) = e1)),
% 0.49/0.65 inference(symmetry,[status(thm)],[1084])).
% 0.49/0.65 tff(1086,plain,
% 0.49/0.65 ((~(e1 = e2)) <=> (~(op(e0, e1) = e1))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1085])).
% 0.49/0.65 tff(1087,plain,
% 0.49/0.65 (~(op(e0, e1) = e1)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[324, 1086])).
% 0.49/0.65 tff(1088,plain,
% 0.49/0.65 (~(op(e0, e0) = e1)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[692, 1082, 688])).
% 0.49/0.65 tff(1089,plain,
% 0.49/0.65 (op(e0, e3) = e1),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[718, 1088, 990, 1087])).
% 0.49/0.65 tff(1090,plain,
% 0.49/0.65 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e2)),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1082])).
% 0.49/0.65 tff(1091,plain,
% 0.49/0.65 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e2))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1090])).
% 0.49/0.65 tff(1092,plain,
% 0.49/0.65 (~(op(e0, e0) = e2)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[745, 1091])).
% 0.49/0.65 tff(1093,plain,
% 0.49/0.65 (((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))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(1094,plain,
% 0.49/0.65 ((((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))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(1095,plain,
% 0.49/0.65 ((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) <=> ((op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e0) = e2))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(1096,plain,
% 0.49/0.65 (((((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))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1095])).
% 0.49/0.65 tff(1097,plain,
% 0.49/0.65 (((((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))),
% 0.49/0.65 inference(transitivity,[status(thm)],[1096, 1094])).
% 0.49/0.65 tff(1098,plain,
% 0.49/0.65 ((((op(e0, e0) = e0) | (op(e0, e0) = e1)) | (op(e0, e0) = e2)) | (op(e0, e0) = e3)),
% 0.49/0.65 inference(and_elim,[status(thm)],[857])).
% 0.49/0.65 tff(1099,plain,
% 0.49/0.65 ((op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e0) = e2) | (op(e0, e0) = e3)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 0.49/0.65 tff(1100,plain,
% 0.49/0.65 ((op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e0) = e2) | (op(e0, e0) = e3)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[1099, 1093])).
% 0.49/0.65 tff(1101,plain,
% 0.49/0.65 (op(e0, e0) = e3),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[1100, 1088, 989, 1092])).
% 0.49/0.65 tff(1102,plain,
% 0.49/0.65 (op(e0, op(e0, e0)) = op(e0, e3)),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1101])).
% 0.49/0.65 tff(1103,plain,
% 0.49/0.65 (e0 = e1),
% 0.49/0.65 inference(transitivity,[status(thm)],[689, 1102, 1089])).
% 0.49/0.65 tff(1104,plain,
% 0.49/0.65 ($false),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[625, 1103])).
% 0.49/0.65 tff(1105,plain,((op(e3, e3) = e3) | (~(op(e0, op(e0, e0)) = e0)) | (op(e0, e0) = e0) | (op(e1, e1) = e2) | (~(op(e1, op(e0, e1)) = e1)) | (op(e3, e3) = e0) | (~(op(e2, op(e0, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.65 tff(1106,plain,
% 0.49/0.65 (op(e3, e3) = e3),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[1105, 7, 989, 12, 5, 63, 9])).
% 0.49/0.65 tff(1107,plain,
% 0.49/0.65 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1106])).
% 0.49/0.65 tff(1108,plain,
% 0.49/0.65 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1107])).
% 0.49/0.65 tff(1109,plain,
% 0.49/0.65 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = op(e3, e3)))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(1110,plain,
% 0.49/0.65 (~(op(e3, e2) = op(e3, e3))),
% 0.49/0.65 inference(and_elim,[status(thm)],[19])).
% 0.49/0.65 tff(1111,plain,
% 0.49/0.65 (~(op(e3, e2) = op(e3, e3))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[1110, 1109])).
% 0.49/0.65 tff(1112,plain,
% 0.49/0.65 (~(op(e3, e2) = e3)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[1111, 1108])).
% 0.49/0.65 tff(1113,assumption,(op(e3, op(e0, e3)) = e3), introduced(assumption)).
% 0.49/0.65 tff(1114,assumption,(op(e0, e3) = e2), introduced(assumption)).
% 0.49/0.65 tff(1115,plain,
% 0.49/0.65 (e2 = op(e0, e3)),
% 0.49/0.65 inference(symmetry,[status(thm)],[1114])).
% 0.49/0.65 tff(1116,plain,
% 0.49/0.65 (op(e3, e2) = op(e3, op(e0, e3))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1115])).
% 0.49/0.65 tff(1117,plain,
% 0.49/0.65 (op(e3, e2) = e3),
% 0.49/0.65 inference(transitivity,[status(thm)],[1116, 1113])).
% 0.49/0.65 tff(1118,assumption,(~(op(e3, e2) = e3)), introduced(assumption)).
% 0.49/0.65 tff(1119,plain,
% 0.49/0.65 ($false),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[1118, 1117])).
% 0.49/0.65 tff(1120,plain,((~(op(e0, e3) = e2)) | (op(e3, e2) = e3) | (~(op(e3, op(e0, e3)) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.65 tff(1121,plain,
% 0.49/0.65 (~(op(e0, e3) = e2)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[1120, 1112, 3])).
% 0.49/0.65 tff(1122,plain,
% 0.49/0.65 (e0 = op(e0, e1)),
% 0.49/0.65 inference(transitivity,[status(thm)],[689, 687])).
% 0.49/0.65 tff(1123,plain,
% 0.49/0.65 (op(e1, e0) = op(e1, op(e0, e1))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1122])).
% 0.49/0.65 tff(1124,plain,
% 0.49/0.65 (op(e1, e0) = e1),
% 0.49/0.65 inference(transitivity,[status(thm)],[1123, 829])).
% 0.49/0.65 tff(1125,plain,
% 0.49/0.65 ((op(e0, e0) = op(e1, e0)) <=> (e1 = op(e1, e0))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[684])).
% 0.49/0.65 tff(1126,plain,
% 0.49/0.65 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e1)),
% 0.49/0.65 inference(transitivity,[status(thm)],[1125, 1043])).
% 0.49/0.65 tff(1127,plain,
% 0.49/0.65 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e1))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1126])).
% 0.49/0.65 tff(1128,plain,
% 0.49/0.65 (~(op(e1, e0) = e1)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[1056, 1127])).
% 0.49/0.65 tff(1129,plain,
% 0.49/0.65 ($false),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[1128, 1124])).
% 0.49/0.65 tff(1130,plain,((~(op(e0, e0) = e1)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e0, op(e0, e0)) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.65 tff(1131,plain,
% 0.49/0.65 (~(op(e0, e0) = e1)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[1130, 829, 688])).
% 0.49/0.65 tff(1132,assumption,(op(e0, e1) = e1), introduced(assumption)).
% 0.49/0.65 tff(1133,plain,
% 0.49/0.65 (e1 = op(e0, e1)),
% 0.49/0.65 inference(symmetry,[status(thm)],[1132])).
% 0.49/0.65 tff(1134,plain,
% 0.49/0.65 (op(e1, e1) = op(e1, op(e0, e1))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1133])).
% 0.49/0.65 tff(1135,plain,
% 0.49/0.65 (op(e1, e1) = e1),
% 0.49/0.65 inference(transitivity,[status(thm)],[1134, 829])).
% 0.49/0.65 tff(1136,plain,
% 0.49/0.65 ($false),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[1070, 1135])).
% 0.49/0.65 tff(1137,plain,((~(op(e0, e1) = e1)) | (op(e1, e1) = e1) | (~(op(e1, op(e0, e1)) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.65 tff(1138,plain,
% 0.49/0.65 (~(op(e0, e1) = e1)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[1137, 1067, 829])).
% 0.49/0.65 tff(1139,assumption,(~(op(e0, e0) = e1)), introduced(assumption)).
% 0.49/0.65 tff(1140,plain,
% 0.49/0.65 (op(e0, e3) = e1),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[718, 991, 1139, 433])).
% 0.49/0.65 tff(1141,plain,
% 0.49/0.65 (~(op(e2, e1) = e2)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[1009, 991, 799])).
% 0.49/0.65 tff(1142,plain,
% 0.49/0.65 (op(e3, e1) = e2),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[1018, 1141, 12, 830])).
% 0.49/0.65 tff(1143,assumption,(op(e0, e3) = e1), introduced(assumption)).
% 0.49/0.65 tff(1144,plain,
% 0.49/0.65 (e1 = op(e0, e3)),
% 0.49/0.65 inference(symmetry,[status(thm)],[1143])).
% 0.49/0.65 tff(1145,plain,
% 0.49/0.65 (op(e3, e1) = op(e3, op(e0, e3))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[1144])).
% 0.49/0.65 tff(1146,assumption,(op(e3, e1) = e2), introduced(assumption)).
% 0.49/0.65 tff(1147,plain,
% 0.49/0.65 (e2 = op(e3, e1)),
% 0.49/0.65 inference(symmetry,[status(thm)],[1146])).
% 0.49/0.65 tff(1148,plain,
% 0.49/0.65 (e2 = e3),
% 0.49/0.66 inference(transitivity,[status(thm)],[1147, 1145, 1113])).
% 0.49/0.66 tff(1149,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[462, 1148])).
% 0.49/0.66 tff(1150,plain,((~(op(e0, e3) = e1)) | (~(op(e3, e1) = e2)) | (~(op(e3, op(e0, e3)) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(1151,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1150, 1142, 1140, 1113])).
% 0.49/0.66 tff(1152,plain,((op(e0, e2) = e1) | (~(op(e3, op(e0, e3)) = e3)) | (op(e1, e1) = e2) | (op(e0, e1) = e2) | (op(e0, e0) = e1) | (op(e0, e1) = e1) | (~(op(e2, op(e0, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(1153,plain,
% 0.49/0.66 (op(e0, e2) = e1),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1152, 1138, 12, 1113, 1131, 830, 799])).
% 0.49/0.66 tff(1154,plain,
% 0.49/0.66 (op(e0, e0) = e2),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[887, 830, 820, 104])).
% 0.49/0.66 tff(1155,plain,
% 0.49/0.66 (op(e0, op(e0, e0)) = op(e0, e2)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1154])).
% 0.49/0.66 tff(1156,plain,
% 0.49/0.66 (e0 = e1),
% 0.49/0.66 inference(transitivity,[status(thm)],[689, 1155, 1153])).
% 0.49/0.66 tff(1157,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[625, 1156])).
% 0.49/0.66 tff(1158,plain,((op(e0, e1) = e2) | (~(op(e0, op(e0, e0)) = e0)) | (op(e1, e1) = e2) | (~(op(e3, op(e0, e3)) = e3)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e1, op(e0, e1)) = e1)) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(1159,plain,
% 0.49/0.66 (op(e0, e1) = e2),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1158, 7, 12, 3, 9, 5, 1121])).
% 0.49/0.66 tff(1160,plain,
% 0.49/0.66 ((op(e0, e1) = e1) <=> (e2 = e1)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1159])).
% 0.49/0.66 tff(1161,plain,
% 0.49/0.66 ((op(e0, e1) = e1) <=> (e1 = e2)),
% 0.49/0.66 inference(transitivity,[status(thm)],[1160, 317])).
% 0.49/0.66 tff(1162,plain,
% 0.49/0.66 ((e1 = e2) <=> (op(e0, e1) = e1)),
% 0.49/0.66 inference(symmetry,[status(thm)],[1161])).
% 0.49/0.66 tff(1163,plain,
% 0.49/0.66 ((~(e1 = e2)) <=> (~(op(e0, e1) = e1))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1162])).
% 0.49/0.66 tff(1164,plain,
% 0.49/0.66 (~(op(e0, e1) = e1)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[324, 1163])).
% 0.49/0.66 tff(1165,plain,
% 0.49/0.66 (~(op(e0, e0) = e1)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1130, 5, 7])).
% 0.49/0.66 tff(1166,plain,
% 0.49/0.66 (op(e1, e2) = op(e1, op(e0, e1))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[302])).
% 0.49/0.66 tff(1167,plain,
% 0.49/0.66 (op(e1, e2) = e1),
% 0.49/0.66 inference(transitivity,[status(thm)],[1166, 829])).
% 0.49/0.66 tff(1168,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[168, 1167])).
% 0.49/0.66 tff(1169,plain,((~(op(e0, e1) = e2)) | (op(e1, e2) = e1) | (~(op(e1, op(e0, e1)) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(1170,plain,
% 0.49/0.66 (op(e1, e2) = e1),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1169, 1159, 5])).
% 0.49/0.66 tff(1171,plain,
% 0.49/0.66 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e1)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1170])).
% 0.49/0.66 tff(1172,plain,
% 0.49/0.66 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e1))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1171])).
% 0.49/0.66 tff(1173,plain,
% 0.49/0.66 (~(op(e0, e2) = e1)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[703, 1172])).
% 0.49/0.66 tff(1174,plain,
% 0.49/0.66 (op(e0, e3) = e1),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[718, 1173, 1165, 1164])).
% 0.49/0.66 tff(1175,plain,
% 0.49/0.66 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e2)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1159])).
% 0.49/0.66 tff(1176,plain,
% 0.49/0.66 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e2))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1175])).
% 0.49/0.66 tff(1177,plain,
% 0.49/0.66 (~(op(e0, e0) = e2)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[745, 1176])).
% 0.49/0.66 tff(1178,plain,
% 0.49/0.66 (op(e0, e0) = e3),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1100, 1177, 989, 1165])).
% 0.49/0.66 tff(1179,plain,
% 0.49/0.66 (op(e0, op(e0, e0)) = op(e0, e3)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1178])).
% 0.49/0.66 tff(1180,plain,
% 0.49/0.66 (e0 = op(e0, op(e0, e0))),
% 0.49/0.66 inference(symmetry,[status(thm)],[7])).
% 0.49/0.66 tff(1181,plain,
% 0.49/0.66 (e0 = e1),
% 0.49/0.66 inference(transitivity,[status(thm)],[1180, 1179, 1174])).
% 0.49/0.66 tff(1182,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[625, 1181])).
% 0.49/0.66 tff(1183,plain,(((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))) | (op(e0, e0) = e0) | (op(e1, e1) = e2) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(1184,plain,
% 0.49/0.66 (op(e0, e0) = e0),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1183, 1, 101, 63])).
% 0.49/0.66 tff(1185,plain,
% 0.49/0.66 ((op(e0, e0) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1184])).
% 0.49/0.66 tff(1186,plain,
% 0.49/0.66 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 0.49/0.66 inference(transitivity,[status(thm)],[1185, 988])).
% 0.49/0.66 tff(1187,plain,
% 0.49/0.66 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1186])).
% 0.49/0.66 tff(1188,plain,
% 0.49/0.66 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = op(e0, e2)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(1189,plain,
% 0.49/0.66 (~(op(e0, e0) = op(e0, e2))),
% 0.49/0.66 inference(and_elim,[status(thm)],[41])).
% 0.49/0.66 tff(1190,plain,
% 0.49/0.66 (~(op(e0, e0) = op(e0, e2))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 0.49/0.66 tff(1191,plain,
% 0.49/0.66 (~(op(e0, e2) = e0)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1190, 1187])).
% 0.49/0.66 tff(1192,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[917, 1191, 987, 981, 71])).
% 0.49/0.66 tff(1193,plain,(((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))) | (~(op(e0, e1) = e2)) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(1194,plain,
% 0.49/0.66 ((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1193, 63, 14])).
% 0.49/0.66 tff(1195,plain,
% 0.49/0.66 ((op(e2, e0) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[973])).
% 0.49/0.66 tff(1196,plain,
% 0.49/0.66 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.49/0.66 inference(transitivity,[status(thm)],[1195, 810])).
% 0.49/0.66 tff(1197,plain,
% 0.49/0.66 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1196])).
% 0.49/0.66 tff(1198,plain,
% 0.49/0.66 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = op(e2, e2)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(1199,plain,
% 0.49/0.66 (~(op(e2, e0) = op(e2, e2))),
% 0.49/0.66 inference(and_elim,[status(thm)],[29])).
% 0.49/0.66 tff(1200,plain,
% 0.49/0.66 (~(op(e2, e0) = op(e2, e2))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1199, 1198])).
% 0.49/0.66 tff(1201,plain,
% 0.49/0.66 (~(op(e2, e2) = e2)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1200, 1197])).
% 0.49/0.66 tff(1202,plain,
% 0.49/0.66 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e2)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[973])).
% 0.49/0.66 tff(1203,plain,
% 0.49/0.66 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e2))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1202])).
% 0.49/0.66 tff(1204,plain,
% 0.49/0.66 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = op(e2, e0)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(1205,plain,
% 0.49/0.66 (~(op(e1, e0) = op(e2, e0))),
% 0.49/0.66 inference(and_elim,[status(thm)],[1052])).
% 0.49/0.66 tff(1206,plain,
% 0.49/0.66 (~(op(e1, e0) = op(e2, e0))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1205, 1204])).
% 0.49/0.66 tff(1207,plain,
% 0.49/0.66 (~(op(e1, e0) = e2)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1206, 1203])).
% 0.49/0.66 tff(1208,assumption,(op(e2, e0) = e2), introduced(assumption)).
% 0.49/0.66 tff(1209,plain,
% 0.49/0.66 ((op(e2, e0) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1208])).
% 0.49/0.66 tff(1210,plain,
% 0.49/0.66 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.49/0.66 inference(transitivity,[status(thm)],[1209, 72])).
% 0.49/0.66 tff(1211,plain,
% 0.49/0.66 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1210])).
% 0.49/0.66 tff(1212,plain,
% 0.49/0.66 (~(op(e2, e3) = e2)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[979, 1211])).
% 0.49/0.66 tff(1213,plain,
% 0.49/0.66 (op(e1, e3) = e2),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[147, 75, 104, 1212])).
% 0.49/0.66 tff(1214,plain,
% 0.49/0.66 ((op(e1, e3) = e0) <=> (e2 = e0)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1213])).
% 0.49/0.66 tff(1215,plain,
% 0.49/0.66 ((op(e1, e3) = e0) <=> (e0 = e2)),
% 0.49/0.66 inference(transitivity,[status(thm)],[1214, 217])).
% 0.49/0.66 tff(1216,plain,
% 0.49/0.66 ((e0 = e2) <=> (op(e1, e3) = e0)),
% 0.49/0.66 inference(symmetry,[status(thm)],[1215])).
% 0.49/0.66 tff(1217,plain,
% 0.49/0.66 ((~(e0 = e2)) <=> (~(op(e1, e3) = e0))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1216])).
% 0.49/0.66 tff(1218,plain,
% 0.49/0.66 (~(op(e1, e3) = e0)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[238, 1217])).
% 0.49/0.66 tff(1219,plain,
% 0.49/0.66 ((op(e0, e3) = op(e0, e2)) <=> (op(e0, e2) = op(e0, e3))),
% 0.49/0.66 inference(commutativity,[status(thm)],[])).
% 0.49/0.66 tff(1220,plain,
% 0.49/0.66 (op(e0, op(e2, e0)) = op(e0, e2)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1208])).
% 0.49/0.66 tff(1221,assumption,((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))), introduced(assumption)).
% 0.49/0.66 tff(1222,assumption,((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))), introduced(assumption)).
% 0.49/0.66 tff(1223,plain,
% 0.49/0.66 ((e2 = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 0.49/0.66 inference(commutativity,[status(thm)],[])).
% 0.49/0.66 tff(1224,plain,
% 0.49/0.66 ((op(e2, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1208])).
% 0.49/0.66 tff(1225,plain,
% 0.49/0.66 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 0.49/0.66 inference(transitivity,[status(thm)],[1224, 1223])).
% 0.49/0.66 tff(1226,plain,
% 0.49/0.66 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1225])).
% 0.49/0.66 tff(1227,plain,
% 0.49/0.66 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = op(e3, e0)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(1228,plain,
% 0.49/0.66 (~(op(e2, e0) = op(e3, e0))),
% 0.49/0.66 inference(and_elim,[status(thm)],[417])).
% 0.49/0.66 tff(1229,plain,
% 0.49/0.66 (~(op(e2, e0) = op(e3, e0))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 0.49/0.66 tff(1230,plain,
% 0.49/0.66 (~(op(e3, e0) = e2)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1229, 1226])).
% 0.49/0.66 tff(1231,plain,
% 0.49/0.66 (op(e3, e2) = e2),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[537, 75, 374, 1230])).
% 0.49/0.66 tff(1232,plain,
% 0.49/0.66 (op(e3, op(e1, e3)) = op(e3, e2)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1213])).
% 0.49/0.66 tff(1233,plain,
% 0.49/0.66 (op(e3, op(e1, e3)) = e2),
% 0.49/0.66 inference(transitivity,[status(thm)],[1232, 1231])).
% 0.49/0.66 tff(1234,plain,
% 0.49/0.66 ((op(e3, op(e1, e3)) = e3) <=> (e2 = e3)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1233])).
% 0.49/0.66 tff(1235,plain,
% 0.49/0.66 ((e2 = e3) <=> (op(e3, op(e1, e3)) = e3)),
% 0.49/0.66 inference(symmetry,[status(thm)],[1234])).
% 0.49/0.66 tff(1236,plain,
% 0.49/0.66 ((~(e2 = e3)) <=> (~(op(e3, op(e1, e3)) = e3))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1235])).
% 0.49/0.66 tff(1237,plain,
% 0.49/0.66 (~(op(e3, op(e1, e3)) = e3)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[462, 1236])).
% 0.49/0.66 tff(1238,plain,
% 0.49/0.66 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[80, 1237])).
% 0.49/0.66 tff(1239,plain,
% 0.49/0.66 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[681, 1238, 1222, 1221])).
% 0.49/0.66 tff(1240,plain,
% 0.49/0.66 (op(e0, op(e2, e0)) = e0),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[967, 1239])).
% 0.49/0.66 tff(1241,plain,
% 0.49/0.66 (e0 = op(e0, op(e2, e0))),
% 0.49/0.66 inference(symmetry,[status(thm)],[1240])).
% 0.49/0.66 tff(1242,plain,
% 0.49/0.66 (e0 = op(e0, e2)),
% 0.49/0.66 inference(transitivity,[status(thm)],[1241, 1220])).
% 0.49/0.66 tff(1243,plain,
% 0.49/0.66 ((op(e0, e3) = e0) <=> (op(e0, e3) = op(e0, e2))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1242])).
% 0.49/0.66 tff(1244,plain,
% 0.49/0.66 ((op(e0, e3) = e0) <=> (op(e0, e2) = op(e0, e3))),
% 0.49/0.66 inference(transitivity,[status(thm)],[1243, 1219])).
% 0.49/0.66 tff(1245,plain,
% 0.49/0.66 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e3) = e0)),
% 0.49/0.66 inference(symmetry,[status(thm)],[1244])).
% 0.49/0.66 tff(1246,plain,
% 0.49/0.66 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e3) = e0))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1245])).
% 0.49/0.66 tff(1247,plain,
% 0.49/0.66 (~(op(e0, e3) = e0)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[215, 1246])).
% 0.49/0.66 tff(1248,plain,
% 0.49/0.66 ((e0 = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 0.49/0.66 inference(commutativity,[status(thm)],[])).
% 0.49/0.66 tff(1249,plain,
% 0.49/0.66 (op(e1, op(e2, e1)) = e1),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[546, 1239])).
% 0.49/0.66 tff(1250,plain,
% 0.49/0.66 (~(op(e2, e1) = e3)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[555, 1249, 1213])).
% 0.49/0.66 tff(1251,plain,
% 0.49/0.66 (op(e2, e1) = e0),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[931, 1250, 10, 604, 1249, 544])).
% 0.49/0.66 tff(1252,plain,
% 0.49/0.66 ((op(e2, e1) = op(e2, e3)) <=> (e0 = op(e2, e3))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1251])).
% 0.49/0.66 tff(1253,plain,
% 0.49/0.66 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 0.49/0.66 inference(transitivity,[status(thm)],[1252, 1248])).
% 0.49/0.66 tff(1254,plain,
% 0.49/0.66 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1253])).
% 0.49/0.66 tff(1255,plain,
% 0.49/0.66 (~(op(e2, e3) = e0)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[1005, 1254])).
% 0.49/0.66 tff(1256,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[247, 1255, 1247, 1218, 63])).
% 0.49/0.66 tff(1257,plain,((op(e3, e3) = e2) | (op(e3, e3) = e0) | (~(op(e2, e0) = e2)) | (op(e2, e1) = e2) | (op(e0, e1) = e0) | (op(e0, e1) = e3) | (~((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3)))) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e3, e1) = e2) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(1258,plain,
% 0.49/0.66 (op(e3, e3) = e2),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1257, 63, 973, 62, 468, 463, 456, 1194, 333, 92])).
% 0.49/0.66 tff(1259,plain,
% 0.49/0.66 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e2)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1258])).
% 0.49/0.66 tff(1260,plain,
% 0.49/0.66 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e2))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1259])).
% 0.49/0.66 tff(1261,plain,
% 0.49/0.66 (~(op(e1, e3) = e2)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[368, 1260])).
% 0.49/0.66 tff(1262,plain,
% 0.49/0.66 (op(e1, e2) = e2),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[135, 1261, 101, 1207])).
% 0.49/0.66 tff(1263,assumption,(op(e1, e2) = e2), introduced(assumption)).
% 0.49/0.66 tff(1264,plain,
% 0.49/0.66 (e2 = op(e1, e2)),
% 0.49/0.66 inference(symmetry,[status(thm)],[1263])).
% 0.49/0.66 tff(1265,plain,
% 0.49/0.66 (op(e2, e2) = op(e2, op(e1, e2))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1264])).
% 0.49/0.66 tff(1266,plain,
% 0.49/0.66 (op(e2, e2) = e2),
% 0.49/0.66 inference(transitivity,[status(thm)],[1265, 106])).
% 0.49/0.66 tff(1267,assumption,(~(op(e2, e2) = e2)), introduced(assumption)).
% 0.49/0.66 tff(1268,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1267, 1266])).
% 0.49/0.66 tff(1269,plain,((~(op(e1, e2) = e2)) | (op(e2, e2) = e2) | (~(op(e2, op(e1, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(1270,plain,
% 0.49/0.66 (~(op(e2, op(e1, e2)) = e2)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1269, 1262, 1201])).
% 0.49/0.66 tff(1271,plain,
% 0.49/0.66 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[102, 1270])).
% 0.49/0.66 tff(1272,plain,
% 0.49/0.66 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[681, 1271, 456, 1194])).
% 0.49/0.66 tff(1273,plain,
% 0.49/0.66 (op(e2, op(e2, e2)) = e2),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[473, 1272])).
% 0.49/0.66 tff(1274,plain,
% 0.49/0.66 (~(op(e2, e2) = e1)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[488, 1273, 62])).
% 0.49/0.66 tff(1275,plain,
% 0.49/0.66 ((e0 = op(e2, e2)) <=> (op(e2, e2) = e0)),
% 0.49/0.66 inference(commutativity,[status(thm)],[])).
% 0.49/0.66 tff(1276,plain,
% 0.49/0.66 (op(e0, op(e2, e0)) = e0),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[967, 1272])).
% 0.49/0.66 tff(1277,plain,
% 0.49/0.66 (op(e0, op(e2, e0)) = op(e0, e2)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[973])).
% 0.49/0.66 tff(1278,plain,
% 0.49/0.66 (op(e0, e2) = op(e0, op(e2, e0))),
% 0.49/0.66 inference(symmetry,[status(thm)],[1277])).
% 0.49/0.66 tff(1279,plain,
% 0.49/0.66 (op(e0, e2) = e0),
% 0.49/0.66 inference(transitivity,[status(thm)],[1278, 1276])).
% 0.49/0.66 tff(1280,plain,
% 0.49/0.66 ((op(e0, e2) = op(e2, e2)) <=> (e0 = op(e2, e2))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1279])).
% 0.49/0.66 tff(1281,plain,
% 0.49/0.66 ((op(e0, e2) = op(e2, e2)) <=> (op(e2, e2) = e0)),
% 0.49/0.66 inference(transitivity,[status(thm)],[1280, 1275])).
% 0.49/0.66 tff(1282,plain,
% 0.49/0.66 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e0))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1281])).
% 0.49/0.66 tff(1283,plain,
% 0.49/0.66 (~(op(e2, e2) = e0)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[816, 1282])).
% 0.49/0.66 tff(1284,plain,
% 0.49/0.66 (op(e2, e2) = e3),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[513, 1283, 1201, 1274])).
% 0.49/0.66 tff(1285,plain,
% 0.49/0.66 (e3 = op(e2, e2)),
% 0.49/0.66 inference(symmetry,[status(thm)],[1284])).
% 0.49/0.66 tff(1286,plain,
% 0.49/0.66 (op(e2, e3) = op(e2, op(e2, e2))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1285])).
% 0.49/0.66 tff(1287,plain,
% 0.49/0.66 (op(e2, e3) = e2),
% 0.49/0.66 inference(transitivity,[status(thm)],[1286, 1273])).
% 0.49/0.66 tff(1288,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[980, 1287])).
% 0.49/0.66 tff(1289,plain,((op(e3, e3) = e0) | (~(op(e0, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(1290,plain,
% 0.49/0.66 (op(e3, e3) = e0),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1289, 14])).
% 0.49/0.66 tff(1291,plain,
% 0.49/0.66 ((op(e3, e3) = e2) <=> (e0 = e2)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1290])).
% 0.49/0.66 tff(1292,plain,
% 0.49/0.66 ((e0 = e2) <=> (op(e3, e3) = e2)),
% 0.49/0.66 inference(symmetry,[status(thm)],[1291])).
% 0.49/0.66 tff(1293,plain,
% 0.49/0.66 ((~(e0 = e2)) <=> (~(op(e3, e3) = e2))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1292])).
% 0.49/0.66 tff(1294,plain,
% 0.49/0.66 (~(op(e3, e3) = e2)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[238, 1293])).
% 0.49/0.66 tff(1295,plain,
% 0.49/0.66 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e0)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1290])).
% 0.49/0.66 tff(1296,plain,
% 0.49/0.66 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e0))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1295])).
% 0.49/0.66 tff(1297,plain,
% 0.49/0.66 (~(op(e1, e3) = e0)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[368, 1296])).
% 0.49/0.66 tff(1298,plain,
% 0.49/0.66 (op(e1, e0) = e2),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[205, 79, 10, 12, 74, 75, 104])).
% 0.49/0.66 tff(1299,plain,
% 0.49/0.66 ((e0 = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 0.49/0.66 inference(commutativity,[status(thm)],[])).
% 0.49/0.66 tff(1300,plain,
% 0.49/0.66 (e2 = op(e1, e0)),
% 0.49/0.66 inference(symmetry,[status(thm)],[1298])).
% 0.49/0.66 tff(1301,plain,
% 0.49/0.66 (op(e0, e2) = op(e0, op(e1, e0))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1300])).
% 0.49/0.66 tff(1302,plain,
% 0.49/0.66 (op(e0, e2) = e0),
% 0.49/0.66 inference(transitivity,[status(thm)],[1301, 84])).
% 0.49/0.66 tff(1303,plain,
% 0.49/0.66 ((op(e0, e2) = op(e1, e2)) <=> (e0 = op(e1, e2))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1302])).
% 0.49/0.66 tff(1304,plain,
% 0.49/0.66 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 0.49/0.66 inference(transitivity,[status(thm)],[1303, 1299])).
% 0.49/0.66 tff(1305,plain,
% 0.49/0.66 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e0))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1304])).
% 0.49/0.66 tff(1306,plain,
% 0.49/0.66 (~(op(e1, e2) = e0)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[703, 1305])).
% 0.49/0.66 tff(1307,assumption,(~(op(e1, e3) = e0)), introduced(assumption)).
% 0.49/0.66 tff(1308,plain,
% 0.49/0.66 ((op(e1, e0) = e0) <=> (e2 = e0)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1298])).
% 0.49/0.66 tff(1309,plain,
% 0.49/0.66 ((op(e1, e0) = e0) <=> (e0 = e2)),
% 0.49/0.66 inference(transitivity,[status(thm)],[1308, 217])).
% 0.49/0.66 tff(1310,plain,
% 0.49/0.66 ((e0 = e2) <=> (op(e1, e0) = e0)),
% 0.49/0.66 inference(symmetry,[status(thm)],[1309])).
% 0.49/0.66 tff(1311,plain,
% 0.49/0.66 ((~(e0 = e2)) <=> (~(op(e1, e0) = e0))),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1310])).
% 0.49/0.66 tff(1312,plain,
% 0.49/0.66 (~(op(e1, e0) = e0)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[238, 1311])).
% 0.49/0.66 tff(1313,plain,
% 0.49/0.66 (op(e1, e1) = e0),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[657, 1312, 1307, 1306])).
% 0.49/0.66 tff(1314,plain,
% 0.49/0.66 (op(e1, op(e1, e1)) = op(e1, e0)),
% 0.49/0.66 inference(monotonicity,[status(thm)],[1313])).
% 0.49/0.66 tff(1315,plain,
% 0.49/0.66 (((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))) | (op(e1, op(e1, e1)) = e1)),
% 0.49/0.66 inference(tautology,[status(thm)],[])).
% 0.49/0.66 tff(1316,plain,
% 0.49/0.66 (op(e1, op(e1, e1)) = e1),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[1315, 79])).
% 0.49/0.66 tff(1317,plain,
% 0.49/0.66 (e1 = op(e1, op(e1, e1))),
% 0.49/0.66 inference(symmetry,[status(thm)],[1316])).
% 0.49/0.66 tff(1318,plain,
% 0.49/0.66 (e1 = e2),
% 0.49/0.66 inference(transitivity,[status(thm)],[1317, 1314, 1298])).
% 0.49/0.66 tff(1319,plain,
% 0.49/0.66 ($false),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[324, 1318])).
% 0.49/0.66 tff(1320,plain,(((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))) | (op(e1, e3) = e0) | (op(e2, e1) = e2) | (op(e1, e1) = e2) | (op(e2, e0) = e2) | (op(e3, e3) = e2) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.66 tff(1321,plain,
% 0.49/0.67 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1320, 74, 62, 101, 1297, 1294, 92])).
% 0.49/0.67 tff(1322,assumption,(op(e3, e3) = e0), introduced(assumption)).
% 0.49/0.67 tff(1323,plain,
% 0.49/0.67 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e0)),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1322])).
% 0.49/0.67 tff(1324,plain,
% 0.49/0.67 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e0))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1323])).
% 0.49/0.67 tff(1325,plain,
% 0.49/0.67 (~(op(e3, e1) = e0)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[399, 1324])).
% 0.49/0.67 tff(1326,plain,
% 0.49/0.67 (op(e3, e1) = e3),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[408, 352, 374, 1325])).
% 0.49/0.67 tff(1327,plain,
% 0.49/0.67 (e3 = op(e3, e1)),
% 0.49/0.67 inference(symmetry,[status(thm)],[1326])).
% 0.49/0.67 tff(1328,plain,
% 0.49/0.67 (op(e3, op(e3, e3)) = op(e3, e0)),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1322])).
% 0.49/0.67 tff(1329,plain,
% 0.49/0.67 (op(e3, e0) = op(e3, op(e3, e3))),
% 0.49/0.67 inference(symmetry,[status(thm)],[1328])).
% 0.49/0.67 tff(1330,plain,
% 0.49/0.67 (op(e3, e0) = op(e3, e1)),
% 0.49/0.67 inference(transitivity,[status(thm)],[1329, 354, 1327])).
% 0.49/0.67 tff(1331,plain,
% 0.49/0.67 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = op(e3, e1)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1332,plain,
% 0.49/0.67 (~(op(e3, e0) = op(e3, e1))),
% 0.49/0.67 inference(and_elim,[status(thm)],[24])).
% 0.49/0.67 tff(1333,plain,
% 0.49/0.67 (~(op(e3, e0) = op(e3, e1))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 0.49/0.67 tff(1334,plain,
% 0.49/0.67 ($false),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1333, 1330])).
% 0.49/0.67 tff(1335,plain,(((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (~(op(e3, e3) = e0)) | (op(e3, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.67 tff(1336,plain,
% 0.49/0.67 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1335, 1290, 333])).
% 0.49/0.67 tff(1337,plain,
% 0.49/0.67 ((e3 = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 0.49/0.67 inference(commutativity,[status(thm)],[])).
% 0.49/0.67 tff(1338,plain,
% 0.49/0.67 (op(e1, e2) = op(e1, op(e0, e1))),
% 0.49/0.67 inference(symmetry,[status(thm)],[694])).
% 0.49/0.67 tff(1339,plain,
% 0.49/0.67 (op(e1, e2) = e1),
% 0.49/0.67 inference(transitivity,[status(thm)],[1338, 5])).
% 0.49/0.67 tff(1340,plain,
% 0.49/0.67 ((op(e1, e2) = e0) <=> (e1 = e0)),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1339])).
% 0.49/0.67 tff(1341,plain,
% 0.49/0.67 ((op(e1, e2) = e0) <=> (e0 = e1)),
% 0.49/0.67 inference(transitivity,[status(thm)],[1340, 635])).
% 0.49/0.67 tff(1342,plain,
% 0.49/0.67 ((e0 = e1) <=> (op(e1, e2) = e0)),
% 0.49/0.67 inference(symmetry,[status(thm)],[1341])).
% 0.49/0.67 tff(1343,plain,
% 0.49/0.67 ((~(e0 = e1)) <=> (~(op(e1, e2) = e0))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1342])).
% 0.49/0.67 tff(1344,plain,
% 0.49/0.67 (~(op(e1, e2) = e0)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[625, 1343])).
% 0.49/0.67 tff(1345,plain,
% 0.49/0.67 ((e0 = op(e1, e0)) <=> (op(e1, e0) = e0)),
% 0.49/0.67 inference(commutativity,[status(thm)],[])).
% 0.49/0.67 tff(1346,plain,
% 0.49/0.67 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e0)),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1290])).
% 0.49/0.67 tff(1347,plain,
% 0.49/0.67 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e0))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1346])).
% 0.49/0.67 tff(1348,plain,
% 0.49/0.67 (~(op(e0, e3) = e0)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[725, 1347])).
% 0.49/0.67 tff(1349,plain,
% 0.49/0.67 (((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0)) <=> ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1350,plain,
% 0.49/0.67 ((((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) <=> ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1351,plain,
% 0.49/0.67 ((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) <=> ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1352,plain,
% 0.49/0.67 (((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) <=> (((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0)) | (op(e0, e3) = e0))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1351])).
% 0.49/0.67 tff(1353,plain,
% 0.49/0.67 (((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) <=> ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0))),
% 0.49/0.67 inference(transitivity,[status(thm)],[1352, 1350])).
% 0.49/0.67 tff(1354,plain,
% 0.49/0.67 (((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)) & ((((op(e0, e0) = e0) | (op(e1, e0) = e0)) | (op(e2, e0) = e0)) | (op(e3, e0) = e0))),
% 0.49/0.67 inference(and_elim,[status(thm)],[715])).
% 0.49/0.67 tff(1355,plain,
% 0.49/0.67 ((((op(e0, e0) = e0) | (op(e0, e1) = e0)) | (op(e0, e2) = e0)) | (op(e0, e3) = e0)),
% 0.49/0.67 inference(and_elim,[status(thm)],[1354])).
% 0.49/0.67 tff(1356,plain,
% 0.49/0.67 ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1355, 1353])).
% 0.49/0.67 tff(1357,plain,
% 0.49/0.67 ((op(e0, e0) = e0) | (op(e0, e1) = e0) | (op(e0, e2) = e0) | (op(e0, e3) = e0)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1356, 1349])).
% 0.49/0.67 tff(1358,plain,
% 0.49/0.67 (op(e0, e0) = e0),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1357, 902, 1348, 468])).
% 0.49/0.67 tff(1359,plain,
% 0.49/0.67 ((op(e0, e0) = op(e1, e0)) <=> (e0 = op(e1, e0))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1358])).
% 0.49/0.67 tff(1360,plain,
% 0.49/0.67 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e0)),
% 0.49/0.67 inference(transitivity,[status(thm)],[1359, 1345])).
% 0.49/0.67 tff(1361,plain,
% 0.49/0.67 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e0))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1360])).
% 0.49/0.67 tff(1362,plain,
% 0.49/0.67 (~(op(e1, e0) = e0)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1056, 1361])).
% 0.49/0.67 tff(1363,plain,
% 0.49/0.67 (op(e1, e1) = e0),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[657, 1362, 1297, 1344])).
% 0.49/0.67 tff(1364,plain,
% 0.49/0.67 (op(e3, op(e3, e3)) = op(e3, e0)),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1290])).
% 0.49/0.67 tff(1365,plain,
% 0.49/0.67 ((op(e3, op(e3, e3)) = e3) <=> (op(e3, e0) = e3)),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1364])).
% 0.49/0.67 tff(1366,plain,
% 0.49/0.67 ((op(e3, e0) = e3) <=> (op(e3, op(e3, e3)) = e3)),
% 0.49/0.67 inference(symmetry,[status(thm)],[1365])).
% 0.49/0.67 tff(1367,plain,
% 0.49/0.67 (op(e2, e2) = e2),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[524, 767, 62, 74])).
% 0.49/0.67 tff(1368,plain,
% 0.49/0.67 ((op(e2, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1367])).
% 0.49/0.67 tff(1369,plain,
% 0.49/0.67 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.49/0.67 inference(transitivity,[status(thm)],[1368, 469])).
% 0.49/0.67 tff(1370,plain,
% 0.49/0.67 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1369])).
% 0.49/0.67 tff(1371,plain,
% 0.49/0.67 (~(op(e3, e2) = e2)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[504, 1370])).
% 0.49/0.67 tff(1372,plain,
% 0.49/0.67 (op(e3, e0) = e2),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[537, 1371, 333, 1294])).
% 0.49/0.67 tff(1373,plain,
% 0.49/0.67 ((op(e3, e0) = e3) <=> (e2 = e3)),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1372])).
% 0.49/0.67 tff(1374,plain,
% 0.49/0.67 ((e2 = e3) <=> (op(e3, e0) = e3)),
% 0.49/0.67 inference(symmetry,[status(thm)],[1373])).
% 0.49/0.67 tff(1375,plain,
% 0.49/0.67 ((e2 = e3) <=> (op(e3, op(e3, e3)) = e3)),
% 0.49/0.67 inference(transitivity,[status(thm)],[1374, 1366])).
% 0.49/0.67 tff(1376,plain,
% 0.49/0.67 ((~(e2 = e3)) <=> (~(op(e3, op(e3, e3)) = e3))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1375])).
% 0.49/0.67 tff(1377,plain,
% 0.49/0.67 (~(op(e3, op(e3, e3)) = e3)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[462, 1376])).
% 0.49/0.67 tff(1378,plain,
% 0.49/0.67 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[353, 1377])).
% 0.49/0.67 tff(1379,plain,
% 0.49/0.67 (op(e1, e3) = e2),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[147, 767, 92, 1294])).
% 0.49/0.67 tff(1380,plain,
% 0.49/0.67 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e2)),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1379])).
% 0.49/0.67 tff(1381,plain,
% 0.49/0.67 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e2))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1380])).
% 0.49/0.67 tff(1382,plain,
% 0.49/0.67 (~(op(e1, e0) = e2)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[224, 1381])).
% 0.49/0.67 tff(1383,plain,
% 0.49/0.67 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[205, 1382, 62, 101, 74, 1294, 92])).
% 0.49/0.67 tff(1384,plain,
% 0.49/0.67 ((e1 = op(e2, e0)) <=> (op(e2, e0) = e1)),
% 0.49/0.67 inference(commutativity,[status(thm)],[])).
% 0.49/0.67 tff(1385,plain,
% 0.49/0.67 (op(e3, op(e3, e3)) = e2),
% 0.49/0.67 inference(transitivity,[status(thm)],[1364, 1372])).
% 0.49/0.67 tff(1386,plain,
% 0.49/0.67 (op(op(e3, op(e3, e3)), op(e3, e3)) = op(e2, e0)),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1385, 1290])).
% 0.49/0.67 tff(1387,plain,
% 0.49/0.67 ((e1 = op(op(e3, op(e3, e3)), op(e3, e3))) <=> (e1 = op(e2, e0))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1386])).
% 0.49/0.67 tff(1388,plain,
% 0.49/0.67 ((e1 = op(op(e3, op(e3, e3)), op(e3, e3))) <=> (op(e2, e0) = e1)),
% 0.49/0.67 inference(transitivity,[status(thm)],[1387, 1384])).
% 0.49/0.67 tff(1389,plain,
% 0.49/0.67 ((~(e1 = op(op(e3, op(e3, e3)), op(e3, e3)))) <=> (~(op(e2, e0) = e1))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1388])).
% 0.49/0.67 tff(1390,plain,
% 0.49/0.67 ((op(e3, e3) = e0) <=> (e0 = op(e3, e3))),
% 0.49/0.67 inference(symmetry,[status(thm)],[11])).
% 0.49/0.67 tff(1391,plain,
% 0.49/0.67 (e0 = op(e3, e3)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1290, 1390])).
% 0.49/0.67 tff(1392,plain,
% 0.49/0.67 ((e2 = op(e3, op(e3, e3))) <=> (e2 = op(e3, e0))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1364])).
% 0.49/0.67 tff(1393,plain,
% 0.49/0.67 ((e2 = op(e3, op(e3, e3))) <=> (op(e3, e0) = e2)),
% 0.49/0.67 inference(transitivity,[status(thm)],[1392, 1223])).
% 0.49/0.67 tff(1394,plain,
% 0.49/0.67 ((op(e3, e0) = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 0.49/0.67 inference(symmetry,[status(thm)],[1393])).
% 0.49/0.67 tff(1395,plain,
% 0.49/0.67 (e2 = op(e3, op(e3, e3))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1372, 1394])).
% 0.49/0.67 tff(1396,plain,
% 0.49/0.67 ((~(~((~(e0 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3)))) | (~(e1 = op(op(e3, op(e3, e3)), op(e3, e3))))))) <=> ((~(e0 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3)))) | (~(e1 = op(op(e3, op(e3, e3)), op(e3, e3)))))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1397,plain,
% 0.49/0.67 (((e0 = op(e3, e3)) & (e2 = op(e3, op(e3, e3))) & (e1 = op(op(e3, op(e3, e3)), op(e3, e3)))) <=> (~((~(e0 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3)))) | (~(e1 = op(op(e3, op(e3, e3)), op(e3, e3))))))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1398,plain,
% 0.49/0.67 ((~((e0 = op(e3, e3)) & (e2 = op(e3, op(e3, e3))) & (e1 = op(op(e3, op(e3, e3)), op(e3, e3))))) <=> (~(~((~(e0 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3)))) | (~(e1 = op(op(e3, op(e3, e3)), op(e3, e3)))))))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1397])).
% 0.49/0.67 tff(1399,plain,
% 0.49/0.67 ((~((e0 = op(e3, e3)) & (e2 = op(e3, op(e3, e3))) & (e1 = op(op(e3, op(e3, e3)), op(e3, e3))))) <=> ((~(e0 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3)))) | (~(e1 = op(op(e3, op(e3, e3)), op(e3, e3)))))),
% 0.49/0.67 inference(transitivity,[status(thm)],[1398, 1396])).
% 0.49/0.67 tff(1400,plain,
% 0.49/0.67 ((~((e0 = op(e3, e3)) & (e2 = op(e3, op(e3, e3))) & (e1 = op(op(e3, op(e3, e3)), op(e3, e3))))) <=> (~((e0 = op(e3, e3)) & (e2 = op(e3, op(e3, e3))) & (e1 = op(op(e3, op(e3, e3)), op(e3, e3)))))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1401,plain,
% 0.49/0.67 ((~(((e0 = op(e3, e3)) & (e2 = op(e3, op(e3, e3)))) & (e1 = op(op(e3, op(e3, e3)), op(e3, e3))))) <=> (~((e0 = op(e3, e3)) & (e2 = op(e3, op(e3, e3))) & (e1 = op(op(e3, op(e3, e3)), op(e3, e3)))))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1402,axiom,(~(((e0 = op(e3, e3)) & (e2 = op(e3, op(e3, e3)))) & (e1 = op(op(e3, op(e3, e3)), op(e3, e3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax9')).
% 0.49/0.67 tff(1403,plain,
% 0.49/0.67 (~((e0 = op(e3, e3)) & (e2 = op(e3, op(e3, e3))) & (e1 = op(op(e3, op(e3, e3)), op(e3, e3))))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1402, 1401])).
% 0.49/0.67 tff(1404,plain,
% 0.49/0.67 (~((e0 = op(e3, e3)) & (e2 = op(e3, op(e3, e3))) & (e1 = op(op(e3, op(e3, e3)), op(e3, e3))))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1403, 1400])).
% 0.49/0.67 tff(1405,plain,
% 0.49/0.67 ((~(e0 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3)))) | (~(e1 = op(op(e3, op(e3, e3)), op(e3, e3))))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1404, 1399])).
% 0.49/0.67 tff(1406,plain,
% 0.49/0.67 (~(e1 = op(op(e3, op(e3, e3)), op(e3, e3)))),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1405, 1395, 1391])).
% 0.49/0.67 tff(1407,plain,
% 0.49/0.67 (~(op(e2, e0) = e1)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1406, 1389])).
% 0.49/0.67 tff(1408,plain,
% 0.49/0.67 ((op(e3, e0) = e1) <=> (e2 = e1)),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1372])).
% 0.49/0.67 tff(1409,plain,
% 0.49/0.67 ((op(e3, e0) = e1) <=> (e1 = e2)),
% 0.49/0.67 inference(transitivity,[status(thm)],[1408, 317])).
% 0.49/0.67 tff(1410,plain,
% 0.49/0.67 ((e1 = e2) <=> (op(e3, e0) = e1)),
% 0.49/0.67 inference(symmetry,[status(thm)],[1409])).
% 0.49/0.67 tff(1411,plain,
% 0.49/0.67 ((~(e1 = e2)) <=> (~(op(e3, e0) = e1))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1410])).
% 0.49/0.67 tff(1412,plain,
% 0.49/0.67 (~(op(e3, e0) = e1)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[324, 1411])).
% 0.49/0.67 tff(1413,assumption,(~(op(e2, e0) = e1)), introduced(assumption)).
% 0.49/0.67 tff(1414,assumption,(~(op(e3, e0) = e1)), introduced(assumption)).
% 0.49/0.67 tff(1415,plain,
% 0.49/0.67 (~(op(e0, e0) = e1)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[692, 7, 14])).
% 0.49/0.67 tff(1416,plain,
% 0.49/0.67 (((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))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1417,plain,
% 0.49/0.67 ((((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))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1418,plain,
% 0.49/0.67 ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) <=> ((op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e1))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1419,plain,
% 0.49/0.67 (((((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))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1418])).
% 0.49/0.67 tff(1420,plain,
% 0.49/0.67 (((((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))),
% 0.49/0.67 inference(transitivity,[status(thm)],[1419, 1417])).
% 0.49/0.67 tff(1421,plain,
% 0.49/0.67 ((((op(e0, e0) = e1) | (op(e1, e0) = e1)) | (op(e2, e0) = e1)) | (op(e3, e0) = e1)),
% 0.49/0.67 inference(and_elim,[status(thm)],[714])).
% 0.49/0.67 tff(1422,plain,
% 0.49/0.67 ((op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e1) | (op(e3, e0) = e1)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 0.49/0.67 tff(1423,plain,
% 0.49/0.67 ((op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e1) | (op(e3, e0) = e1)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1422, 1416])).
% 0.49/0.67 tff(1424,plain,
% 0.49/0.67 (op(e1, e0) = e1),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1423, 1415, 1414, 1413])).
% 0.49/0.67 tff(1425,plain,
% 0.49/0.67 (op(e1, e0) = op(e1, e2)),
% 0.49/0.67 inference(transitivity,[status(thm)],[1424, 982, 694])).
% 0.49/0.67 tff(1426,plain,
% 0.49/0.67 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = op(e1, e2)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(1427,plain,
% 0.49/0.67 (~(op(e1, e0) = op(e1, e2))),
% 0.49/0.67 inference(and_elim,[status(thm)],[35])).
% 0.49/0.67 tff(1428,plain,
% 0.49/0.67 (~(op(e1, e0) = op(e1, e2))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[1427, 1426])).
% 0.49/0.67 tff(1429,plain,
% 0.49/0.67 ($false),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1428, 1425])).
% 0.49/0.67 tff(1430,plain,(((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))) | (~(op(e0, e1) = e2)) | (op(e3, e0) = e1) | (op(e2, e0) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.67 tff(1431,plain,
% 0.49/0.67 ((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[1430, 1412, 14, 1407])).
% 0.49/0.67 tff(1432,plain,
% 0.49/0.67 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[681, 1431, 1383, 1378])).
% 0.49/0.67 tff(1433,plain,
% 0.49/0.67 (op(e3, op(e2, e3)) = e3),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[471, 1432])).
% 0.49/0.67 tff(1434,plain,
% 0.49/0.67 ((op(e2, e2) = e1) <=> (e2 = e1)),
% 0.49/0.67 inference(monotonicity,[status(thm)],[1367])).
% 0.49/0.67 tff(1435,plain,
% 0.49/0.67 ((op(e2, e2) = e1) <=> (e1 = e2)),
% 0.49/0.67 inference(transitivity,[status(thm)],[1434, 317])).
% 0.49/0.67 tff(1436,plain,
% 0.49/0.67 ((e1 = e2) <=> (op(e2, e2) = e1)),
% 0.49/0.67 inference(symmetry,[status(thm)],[1435])).
% 0.49/0.68 tff(1437,plain,
% 0.49/0.68 ((~(e1 = e2)) <=> (~(op(e2, e2) = e1))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1436])).
% 0.49/0.68 tff(1438,plain,
% 0.49/0.68 (~(op(e2, e2) = e1)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[324, 1437])).
% 0.49/0.68 tff(1439,plain,
% 0.49/0.68 (op(e1, op(e2, e1)) = e1),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[546, 1432])).
% 0.49/0.68 tff(1440,plain,
% 0.49/0.68 (~(op(e2, e1) = e3)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[555, 1439, 1379])).
% 0.49/0.68 tff(1441,plain,
% 0.49/0.68 (op(e2, e1) = e0),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[931, 1440, 62, 468, 1439, 463])).
% 0.49/0.68 tff(1442,plain,
% 0.49/0.68 ((op(e2, e1) = e1) <=> (e0 = e1)),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1441])).
% 0.49/0.68 tff(1443,plain,
% 0.49/0.68 ((e0 = e1) <=> (op(e2, e1) = e1)),
% 0.49/0.68 inference(symmetry,[status(thm)],[1442])).
% 0.49/0.68 tff(1444,plain,
% 0.49/0.68 ((~(e0 = e1)) <=> (~(op(e2, e1) = e1))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1443])).
% 0.49/0.68 tff(1445,plain,
% 0.49/0.68 (~(op(e2, e1) = e1)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[625, 1444])).
% 0.49/0.68 tff(1446,plain,
% 0.49/0.68 (op(e2, e3) = e1),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[964, 1445, 1407, 1438])).
% 0.49/0.68 tff(1447,plain,
% 0.49/0.68 (e1 = op(e2, e3)),
% 0.49/0.68 inference(symmetry,[status(thm)],[1446])).
% 0.49/0.68 tff(1448,plain,
% 0.49/0.68 (op(e3, e1) = op(e3, op(e2, e3))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1447])).
% 0.49/0.68 tff(1449,plain,
% 0.49/0.68 (op(e1, e0) = e1),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[642, 1441, 1439])).
% 0.49/0.68 tff(1450,plain,
% 0.49/0.68 ((op(e1, e0) = op(e1, e1)) <=> (e1 = op(e1, e1))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1449])).
% 0.49/0.68 tff(1451,plain,
% 0.49/0.68 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e1) = e1)),
% 0.49/0.68 inference(transitivity,[status(thm)],[1450, 434])).
% 0.49/0.68 tff(1452,plain,
% 0.49/0.68 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e1) = e1))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1451])).
% 0.49/0.68 tff(1453,plain,
% 0.49/0.68 (~(op(e1, e1) = e1)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[440, 1452])).
% 0.49/0.68 tff(1454,plain,
% 0.49/0.68 (op(e3, e1) = e1),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[450, 1445, 325, 1453])).
% 0.49/0.68 tff(1455,plain,
% 0.49/0.68 (e1 = op(e3, e1)),
% 0.49/0.68 inference(symmetry,[status(thm)],[1454])).
% 0.49/0.68 tff(1456,plain,
% 0.49/0.68 (e1 = e3),
% 0.49/0.68 inference(transitivity,[status(thm)],[1455, 1448, 1433])).
% 0.49/0.68 tff(1457,plain,
% 0.49/0.68 ($false),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[591, 1456])).
% 0.49/0.68 tff(1458,plain,((op(e2, e3) = e2) | (~(op(e0, e1) = e2)) | (op(e2, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.68 tff(1459,plain,
% 0.49/0.68 (op(e2, e3) = e2),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1458, 74, 14])).
% 0.49/0.68 tff(1460,plain,
% 0.49/0.68 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e2)),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1459])).
% 0.49/0.68 tff(1461,plain,
% 0.49/0.68 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e2))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1460])).
% 0.49/0.68 tff(1462,plain,
% 0.49/0.68 (~(op(e1, e3) = e2)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[944, 1461])).
% 0.49/0.68 tff(1463,plain,
% 0.49/0.68 ((op(e1, e2) = e2) <=> (e1 = e2)),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1339])).
% 0.49/0.68 tff(1464,plain,
% 0.49/0.68 ((e1 = e2) <=> (op(e1, e2) = e2)),
% 0.49/0.68 inference(symmetry,[status(thm)],[1463])).
% 0.49/0.68 tff(1465,plain,
% 0.49/0.68 ((~(e1 = e2)) <=> (~(op(e1, e2) = e2))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1464])).
% 0.49/0.68 tff(1466,plain,
% 0.49/0.68 (~(op(e1, e2) = e2)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[324, 1465])).
% 0.49/0.68 tff(1467,plain,
% 0.49/0.68 (op(e1, e0) = e2),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[135, 1466, 101, 1462])).
% 0.49/0.68 tff(1468,plain,
% 0.49/0.68 (op(e1, op(e1, e1)) = op(e1, e0)),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1363])).
% 0.49/0.68 tff(1469,plain,
% 0.49/0.68 (op(e1, op(e1, e1)) = e2),
% 0.49/0.68 inference(transitivity,[status(thm)],[1468, 1467])).
% 0.49/0.68 tff(1470,plain,
% 0.49/0.68 (op(op(e1, op(e1, e1)), op(e1, e1)) = op(e2, e0)),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1469, 1363])).
% 0.49/0.68 tff(1471,plain,
% 0.49/0.68 ((e3 = op(op(e1, op(e1, e1)), op(e1, e1))) <=> (e3 = op(e2, e0))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1470])).
% 0.49/0.68 tff(1472,plain,
% 0.49/0.68 ((e3 = op(op(e1, op(e1, e1)), op(e1, e1))) <=> (op(e2, e0) = e3)),
% 0.49/0.68 inference(transitivity,[status(thm)],[1471, 1337])).
% 0.49/0.68 tff(1473,plain,
% 0.49/0.68 ((op(e2, e0) = e3) <=> (e3 = op(op(e1, op(e1, e1)), op(e1, e1)))),
% 0.49/0.68 inference(symmetry,[status(thm)],[1472])).
% 0.49/0.68 tff(1474,plain,
% 0.49/0.68 (op(e0, e3) = e1),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[718, 987, 325, 1415])).
% 0.49/0.68 tff(1475,plain,
% 0.49/0.68 (e1 = op(e0, e3)),
% 0.49/0.68 inference(symmetry,[status(thm)],[1474])).
% 0.49/0.68 tff(1476,plain,
% 0.49/0.68 (op(e3, e1) = op(e3, op(e0, e3))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1475])).
% 0.49/0.68 tff(1477,plain,
% 0.49/0.68 (op(e3, e1) = e3),
% 0.49/0.68 inference(transitivity,[status(thm)],[1476, 3])).
% 0.49/0.68 tff(1478,plain,
% 0.49/0.68 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e3)),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1477])).
% 0.49/0.68 tff(1479,plain,
% 0.49/0.68 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e3))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1478])).
% 0.49/0.68 tff(1480,plain,
% 0.49/0.68 (~(op(e2, e1) = e3)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[576, 1479])).
% 0.49/0.68 tff(1481,plain,
% 0.49/0.68 ((op(e2, e3) = e3) <=> (e2 = e3)),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1459])).
% 0.49/0.68 tff(1482,plain,
% 0.49/0.68 ((e2 = e3) <=> (op(e2, e3) = e3)),
% 0.49/0.68 inference(symmetry,[status(thm)],[1481])).
% 0.49/0.68 tff(1483,plain,
% 0.49/0.68 ((~(e2 = e3)) <=> (~(op(e2, e3) = e3))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1482])).
% 0.49/0.68 tff(1484,plain,
% 0.49/0.68 (~(op(e2, e3) = e3)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[462, 1483])).
% 0.49/0.68 tff(1485,plain,
% 0.49/0.68 ((e3 = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 0.49/0.68 inference(commutativity,[status(thm)],[])).
% 0.49/0.68 tff(1486,plain,
% 0.49/0.68 (op(e0, e2) = e3),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[917, 987, 902, 71])).
% 0.49/0.68 tff(1487,plain,
% 0.49/0.68 ((op(e0, e2) = op(e2, e2)) <=> (e3 = op(e2, e2))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1486])).
% 0.49/0.68 tff(1488,plain,
% 0.49/0.68 ((op(e0, e2) = op(e2, e2)) <=> (op(e2, e2) = e3)),
% 0.49/0.68 inference(transitivity,[status(thm)],[1487, 1485])).
% 0.49/0.68 tff(1489,plain,
% 0.49/0.68 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e3))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1488])).
% 0.49/0.68 tff(1490,plain,
% 0.49/0.68 (~(op(e2, e2) = e3)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[816, 1489])).
% 0.49/0.68 tff(1491,plain,
% 0.49/0.68 (((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3) | (op(e2, e3) = e3)) <=> ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3) | (op(e2, e3) = e3))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1492,plain,
% 0.49/0.68 ((((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3)) | (op(e2, e3) = e3)) <=> ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3) | (op(e2, e3) = e3))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1493,plain,
% 0.49/0.68 ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) <=> ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1494,plain,
% 0.49/0.68 (((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3)) <=> (((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3)) | (op(e2, e3) = e3))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1493])).
% 0.49/0.68 tff(1495,plain,
% 0.49/0.68 (((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3)) <=> ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3) | (op(e2, e3) = e3))),
% 0.49/0.68 inference(transitivity,[status(thm)],[1494, 1492])).
% 0.49/0.68 tff(1496,plain,
% 0.49/0.68 ((((op(e2, e0) = e3) | (op(e2, e1) = e3)) | (op(e2, e2) = e3)) | (op(e2, e3) = e3)),
% 0.49/0.68 inference(and_elim,[status(thm)],[122])).
% 0.49/0.68 tff(1497,plain,
% 0.49/0.68 ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3) | (op(e2, e3) = e3)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1496, 1495])).
% 0.49/0.68 tff(1498,plain,
% 0.49/0.68 ((op(e2, e0) = e3) | (op(e2, e1) = e3) | (op(e2, e2) = e3) | (op(e2, e3) = e3)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1497, 1491])).
% 0.49/0.68 tff(1499,plain,
% 0.49/0.68 (op(e2, e0) = e3),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1498, 1490, 1484, 1480])).
% 0.49/0.68 tff(1500,plain,
% 0.49/0.68 (e3 = op(op(e1, op(e1, e1)), op(e1, e1))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1499, 1473])).
% 0.49/0.68 tff(1501,plain,
% 0.49/0.68 ((e0 = op(e1, e1)) <=> (op(e1, e1) = e0)),
% 0.49/0.68 inference(commutativity,[status(thm)],[])).
% 0.49/0.68 tff(1502,plain,
% 0.49/0.68 ((op(e1, e1) = e0) <=> (e0 = op(e1, e1))),
% 0.49/0.68 inference(symmetry,[status(thm)],[1501])).
% 0.49/0.68 tff(1503,plain,
% 0.49/0.68 (e0 = op(e1, e1)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1363, 1502])).
% 0.49/0.68 tff(1504,plain,
% 0.49/0.68 (op(e1, e0) = op(e1, op(e1, e1))),
% 0.49/0.68 inference(symmetry,[status(thm)],[1468])).
% 0.49/0.68 tff(1505,plain,
% 0.49/0.68 (e2 = op(e1, e0)),
% 0.49/0.68 inference(symmetry,[status(thm)],[1467])).
% 0.49/0.68 tff(1506,plain,
% 0.49/0.68 (e2 = op(e1, op(e1, e1))),
% 0.49/0.68 inference(transitivity,[status(thm)],[1505, 1504])).
% 0.49/0.68 tff(1507,plain,
% 0.49/0.68 ((~(~((~(e0 = op(e1, e1))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e3 = op(op(e1, op(e1, e1)), op(e1, e1))))))) <=> ((~(e0 = op(e1, e1))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e3 = op(op(e1, op(e1, e1)), op(e1, e1)))))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1508,plain,
% 0.49/0.68 (((e0 = op(e1, e1)) & (e2 = op(e1, op(e1, e1))) & (e3 = op(op(e1, op(e1, e1)), op(e1, e1)))) <=> (~((~(e0 = op(e1, e1))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e3 = op(op(e1, op(e1, e1)), op(e1, e1))))))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1509,plain,
% 0.49/0.68 ((~((e0 = op(e1, e1)) & (e2 = op(e1, op(e1, e1))) & (e3 = op(op(e1, op(e1, e1)), op(e1, e1))))) <=> (~(~((~(e0 = op(e1, e1))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e3 = op(op(e1, op(e1, e1)), op(e1, e1)))))))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1508])).
% 0.49/0.68 tff(1510,plain,
% 0.49/0.68 ((~((e0 = op(e1, e1)) & (e2 = op(e1, op(e1, e1))) & (e3 = op(op(e1, op(e1, e1)), op(e1, e1))))) <=> ((~(e0 = op(e1, e1))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e3 = op(op(e1, op(e1, e1)), op(e1, e1)))))),
% 0.49/0.68 inference(transitivity,[status(thm)],[1509, 1507])).
% 0.49/0.68 tff(1511,plain,
% 0.49/0.68 ((~((e0 = op(e1, e1)) & (e2 = op(e1, op(e1, e1))) & (e3 = op(op(e1, op(e1, e1)), op(e1, e1))))) <=> (~((e0 = op(e1, e1)) & (e2 = op(e1, op(e1, e1))) & (e3 = op(op(e1, op(e1, e1)), op(e1, e1)))))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1512,plain,
% 0.49/0.68 ((~(((e0 = op(e1, e1)) & (e2 = op(e1, op(e1, e1)))) & (e3 = op(op(e1, op(e1, e1)), op(e1, e1))))) <=> (~((e0 = op(e1, e1)) & (e2 = op(e1, op(e1, e1))) & (e3 = op(op(e1, op(e1, e1)), op(e1, e1)))))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1513,axiom,(~(((e0 = op(e1, e1)) & (e2 = op(e1, op(e1, e1)))) & (e3 = op(op(e1, op(e1, e1)), op(e1, e1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax8')).
% 0.49/0.68 tff(1514,plain,
% 0.49/0.68 (~((e0 = op(e1, e1)) & (e2 = op(e1, op(e1, e1))) & (e3 = op(op(e1, op(e1, e1)), op(e1, e1))))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1513, 1512])).
% 0.49/0.68 tff(1515,plain,
% 0.49/0.68 (~((e0 = op(e1, e1)) & (e2 = op(e1, op(e1, e1))) & (e3 = op(op(e1, op(e1, e1)), op(e1, e1))))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1514, 1511])).
% 0.49/0.68 tff(1516,plain,
% 0.49/0.68 ((~(e0 = op(e1, e1))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e3 = op(op(e1, op(e1, e1)), op(e1, e1))))),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1515, 1510])).
% 0.49/0.68 tff(1517,plain,
% 0.49/0.68 (~(e3 = op(op(e1, op(e1, e1)), op(e1, e1)))),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1516, 1506, 1503])).
% 0.49/0.68 tff(1518,plain,
% 0.49/0.68 ($false),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1517, 1500])).
% 0.49/0.68 tff(1519,plain,(((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))) | (~(op(e0, e1) = e2)) | (op(e2, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.68 tff(1520,plain,
% 0.49/0.68 ((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1519, 74, 14])).
% 0.49/0.68 tff(1521,plain,
% 0.49/0.68 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[681, 1520, 1336, 1321])).
% 0.49/0.68 tff(1522,plain,
% 0.49/0.68 (op(e2, op(e2, e2)) = e2),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[473, 1521])).
% 0.49/0.68 tff(1523,plain,
% 0.49/0.68 (~(op(e2, e2) = e1)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[488, 1522, 62])).
% 0.49/0.68 tff(1524,plain,
% 0.49/0.68 (op(e3, op(e2, e3)) = e3),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[471, 1521])).
% 0.49/0.68 tff(1525,plain,
% 0.49/0.68 (~(op(e2, e2) = e0)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[481, 1522, 74])).
% 0.49/0.68 tff(1526,plain,
% 0.49/0.68 ($false),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[515, 1525, 1524, 1459, 1523])).
% 0.49/0.68 tff(1527,plain,((op(e2, e0) = e2) | (~(op(e0, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.68 tff(1528,plain,
% 0.49/0.68 (op(e2, e0) = e2),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1527, 14])).
% 0.49/0.68 tff(1529,plain,
% 0.49/0.68 ((op(e2, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1528])).
% 0.49/0.68 tff(1530,plain,
% 0.49/0.68 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 0.49/0.68 inference(transitivity,[status(thm)],[1529, 1223])).
% 0.49/0.68 tff(1531,plain,
% 0.49/0.68 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1530])).
% 0.49/0.68 tff(1532,plain,
% 0.49/0.68 (~(op(e3, e0) = e2)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[1229, 1531])).
% 0.49/0.68 tff(1533,plain,
% 0.49/0.68 (op(e3, e2) = e2),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[537, 1532, 333, 1294])).
% 0.49/0.68 tff(1534,plain,
% 0.49/0.68 ((op(e2, e0) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1528])).
% 0.49/0.68 tff(1535,plain,
% 0.49/0.68 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.49/0.68 inference(transitivity,[status(thm)],[1534, 72])).
% 0.49/0.68 tff(1536,plain,
% 0.49/0.68 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1535])).
% 0.49/0.68 tff(1537,plain,
% 0.49/0.68 (~(op(e2, e3) = e2)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[979, 1536])).
% 0.49/0.68 tff(1538,plain,
% 0.49/0.68 (op(e1, e3) = e2),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[147, 1537, 92, 1294])).
% 0.49/0.68 tff(1539,plain,
% 0.49/0.68 (op(e3, op(e1, e3)) = op(e3, e2)),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1538])).
% 0.49/0.68 tff(1540,plain,
% 0.49/0.68 (op(e3, op(e1, e3)) = e2),
% 0.49/0.68 inference(transitivity,[status(thm)],[1539, 1533])).
% 0.49/0.68 tff(1541,plain,
% 0.49/0.68 ((op(e3, op(e1, e3)) = e3) <=> (e2 = e3)),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1540])).
% 0.49/0.68 tff(1542,plain,
% 0.49/0.68 ((e2 = e3) <=> (op(e3, op(e1, e3)) = e3)),
% 0.49/0.68 inference(symmetry,[status(thm)],[1541])).
% 0.49/0.68 tff(1543,plain,
% 0.49/0.68 ((~(e2 = e3)) <=> (~(op(e3, op(e1, e3)) = e3))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1542])).
% 0.49/0.68 tff(1544,plain,
% 0.49/0.68 (~(op(e3, op(e1, e3)) = e3)),
% 0.49/0.68 inference(modus_ponens,[status(thm)],[462, 1543])).
% 0.49/0.68 tff(1545,plain,
% 0.49/0.68 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[80, 1544])).
% 0.49/0.68 tff(1546,plain,
% 0.49/0.68 (~(op(e0, e2) = e3)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[908, 9, 1537])).
% 0.49/0.68 tff(1547,assumption,(op(e0, e0) = e3), introduced(assumption)).
% 0.49/0.68 tff(1548,plain,
% 0.49/0.68 (e3 = op(e0, e0)),
% 0.49/0.68 inference(symmetry,[status(thm)],[1547])).
% 0.49/0.68 tff(1549,plain,
% 0.49/0.68 (op(e0, e3) = op(e0, op(e0, e0))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1548])).
% 0.49/0.68 tff(1550,plain,
% 0.49/0.68 (op(e0, op(e0, e0)) = op(e0, e3)),
% 0.49/0.68 inference(symmetry,[status(thm)],[1549])).
% 0.49/0.68 tff(1551,plain,
% 0.49/0.68 (e0 = e1),
% 0.49/0.68 inference(transitivity,[status(thm)],[689, 1550, 1143])).
% 0.49/0.68 tff(1552,plain,
% 0.49/0.68 ($false),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[625, 1551])).
% 0.49/0.68 tff(1553,plain,((~(op(e0, e0) = e3)) | (~(op(e0, e3) = e1)) | (~(op(e0, op(e0, e0)) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.68 tff(1554,plain,
% 0.49/0.68 (~(op(e0, e0) = e3)),
% 0.49/0.68 inference(unit_resolution,[status(thm)],[1553, 1474, 7])).
% 0.49/0.68 tff(1555,plain,
% 0.49/0.68 (((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))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1556,plain,
% 0.49/0.68 ((((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))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1557,plain,
% 0.49/0.68 ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) <=> ((op(e0, e0) = e3) | (op(e0, e1) = e3) | (op(e0, e2) = e3))),
% 0.49/0.68 inference(rewrite,[status(thm)],[])).
% 0.49/0.68 tff(1558,plain,
% 0.49/0.68 (((((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))),
% 0.49/0.68 inference(monotonicity,[status(thm)],[1557])).
% 0.49/0.68 tff(1559,plain,
% 0.49/0.68 (((((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))),
% 0.49/0.68 inference(transitivity,[status(thm)],[1558, 1556])).
% 0.49/0.69 tff(1560,plain,
% 0.49/0.69 ((((op(e0, e0) = e3) | (op(e0, e1) = e3)) | (op(e0, e2) = e3)) | (op(e0, e3) = e3)),
% 0.49/0.69 inference(and_elim,[status(thm)],[711])).
% 0.49/0.69 tff(1561,plain,
% 0.49/0.69 ((op(e0, e0) = e3) | (op(e0, e1) = e3) | (op(e0, e2) = e3) | (op(e0, e3) = e3)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1560, 1559])).
% 0.49/0.69 tff(1562,plain,
% 0.49/0.69 ((op(e0, e0) = e3) | (op(e0, e1) = e3) | (op(e0, e2) = e3) | (op(e0, e3) = e3)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1561, 1555])).
% 0.49/0.69 tff(1563,plain,
% 0.49/0.69 (op(e0, e3) = e3),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1562, 1554, 463, 1546])).
% 0.49/0.69 tff(1564,plain,
% 0.49/0.69 (op(e1, e2) = e3),
% 0.49/0.69 inference(transitivity,[status(thm)],[1338, 5, 1475, 1563])).
% 0.49/0.69 tff(1565,plain,
% 0.49/0.69 ((e1 = e3) <=> (op(e1, e2) = e3)),
% 0.49/0.69 inference(monotonicity,[status(thm)],[983])).
% 0.49/0.69 tff(1566,plain,
% 0.49/0.69 ((~(e1 = e3)) <=> (~(op(e1, e2) = e3))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1565])).
% 0.49/0.69 tff(1567,plain,
% 0.49/0.69 (~(op(e1, e2) = e3)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[591, 1566])).
% 0.49/0.69 tff(1568,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1567, 1564])).
% 0.49/0.69 tff(1569,plain,(((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))) | (~(op(e0, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(1570,plain,
% 0.49/0.69 ((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1569, 14])).
% 0.49/0.69 tff(1571,plain,
% 0.49/0.69 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[681, 1570, 1336, 1545])).
% 0.49/0.69 tff(1572,plain,
% 0.49/0.69 (op(e2, op(e2, e2)) = e2),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[473, 1571])).
% 0.49/0.69 tff(1573,plain,
% 0.49/0.69 (~(op(e2, e2) = e1)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[488, 1572, 62])).
% 0.49/0.69 tff(1574,plain,
% 0.49/0.69 ((op(e3, e2) = e1) <=> (e2 = e1)),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1533])).
% 0.49/0.69 tff(1575,plain,
% 0.49/0.69 ((op(e3, e2) = e1) <=> (e1 = e2)),
% 0.49/0.69 inference(transitivity,[status(thm)],[1574, 317])).
% 0.49/0.69 tff(1576,plain,
% 0.49/0.69 ((e1 = e2) <=> (op(e3, e2) = e1)),
% 0.49/0.69 inference(symmetry,[status(thm)],[1575])).
% 0.49/0.69 tff(1577,plain,
% 0.49/0.69 ((~(e1 = e2)) <=> (~(op(e3, e2) = e1))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1576])).
% 0.49/0.69 tff(1578,plain,
% 0.49/0.69 (~(op(e3, e2) = e1)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[324, 1577])).
% 0.49/0.69 tff(1579,plain,
% 0.49/0.69 (op(e0, op(e2, e0)) = e0),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[967, 1571])).
% 0.49/0.69 tff(1580,plain,
% 0.49/0.69 (e2 = op(e2, e0)),
% 0.49/0.69 inference(symmetry,[status(thm)],[1528])).
% 0.49/0.69 tff(1581,plain,
% 0.49/0.69 (op(e0, e2) = op(e0, op(e2, e0))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1580])).
% 0.49/0.69 tff(1582,plain,
% 0.49/0.69 (op(e0, e2) = e0),
% 0.49/0.69 inference(transitivity,[status(thm)],[1581, 1579])).
% 0.49/0.69 tff(1583,plain,
% 0.49/0.69 ((op(e0, e2) = e1) <=> (e0 = e1)),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1582])).
% 0.49/0.69 tff(1584,plain,
% 0.49/0.69 ((e0 = e1) <=> (op(e0, e2) = e1)),
% 0.49/0.69 inference(symmetry,[status(thm)],[1583])).
% 0.49/0.69 tff(1585,plain,
% 0.49/0.69 ((~(e0 = e1)) <=> (~(op(e0, e2) = e1))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1584])).
% 0.49/0.69 tff(1586,plain,
% 0.49/0.69 (~(op(e0, e2) = e1)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[625, 1585])).
% 0.49/0.69 tff(1587,plain,
% 0.49/0.69 ((e1 = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 0.49/0.69 inference(commutativity,[status(thm)],[])).
% 0.49/0.69 tff(1588,plain,
% 0.49/0.69 (op(e1, op(e2, e1)) = e1),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[546, 1571])).
% 0.49/0.69 tff(1589,plain,
% 0.49/0.69 (~(op(e2, e1) = e3)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[555, 1588, 1538])).
% 0.49/0.69 tff(1590,plain,
% 0.49/0.69 (op(e2, e1) = e0),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[931, 1589, 62, 468, 1588, 463])).
% 0.49/0.69 tff(1591,plain,
% 0.49/0.69 (op(e1, e0) = e1),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[642, 1590, 1588])).
% 0.49/0.69 tff(1592,plain,
% 0.49/0.69 ((op(e1, e0) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1591])).
% 0.49/0.69 tff(1593,plain,
% 0.49/0.69 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 0.49/0.69 inference(transitivity,[status(thm)],[1592, 1587])).
% 0.49/0.69 tff(1594,plain,
% 0.49/0.69 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1593])).
% 0.49/0.69 tff(1595,plain,
% 0.49/0.69 (~(op(e1, e2) = e1)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1428, 1594])).
% 0.49/0.69 tff(1596,plain,
% 0.49/0.69 (((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1) | (op(e3, e2) = e1)) <=> ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1) | (op(e3, e2) = e1))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1597,plain,
% 0.49/0.69 ((((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1)) | (op(e3, e2) = e1)) <=> ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1) | (op(e3, e2) = e1))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1598,plain,
% 0.49/0.69 ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) <=> ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1599,plain,
% 0.49/0.69 (((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1)) <=> (((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1)) | (op(e3, e2) = e1))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1598])).
% 0.49/0.69 tff(1600,plain,
% 0.49/0.69 (((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1)) <=> ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1) | (op(e3, e2) = e1))),
% 0.49/0.69 inference(transitivity,[status(thm)],[1599, 1597])).
% 0.49/0.69 tff(1601,plain,
% 0.49/0.69 ((((op(e0, e2) = e1) | (op(e1, e2) = e1)) | (op(e2, e2) = e1)) | (op(e3, e2) = e1)),
% 0.49/0.69 inference(and_elim,[status(thm)],[125])).
% 0.49/0.69 tff(1602,plain,
% 0.49/0.69 ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1) | (op(e3, e2) = e1)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1601, 1600])).
% 0.49/0.69 tff(1603,plain,
% 0.49/0.69 ((op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e2, e2) = e1) | (op(e3, e2) = e1)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1602, 1596])).
% 0.49/0.69 tff(1604,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1603, 1595, 1586, 1578, 1573])).
% 0.49/0.69 tff(1605,plain,(~(op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(1606,plain,
% 0.49/0.69 ((op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e3, e1) = e2)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1018, 1605])).
% 0.49/0.69 tff(1607,plain,
% 0.49/0.69 (op(e3, e1) = e2),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1606, 12, 10])).
% 0.49/0.69 tff(1608,plain,
% 0.49/0.69 (op(e1, op(e3, e1)) = op(e1, e2)),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1607])).
% 0.49/0.69 tff(1609,plain,
% 0.49/0.69 (e1 = op(e1, op(e3, e1))),
% 0.49/0.69 inference(symmetry,[status(thm)],[338])).
% 0.49/0.69 tff(1610,plain,
% 0.49/0.69 (e1 = op(e1, e2)),
% 0.49/0.69 inference(transitivity,[status(thm)],[1609, 1608])).
% 0.49/0.69 tff(1611,plain,
% 0.49/0.69 ((op(e1, e1) = e1) <=> (op(e1, e1) = op(e1, e2))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1610])).
% 0.49/0.69 tff(1612,plain,
% 0.49/0.69 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e1)),
% 0.49/0.69 inference(symmetry,[status(thm)],[1611])).
% 0.49/0.69 tff(1613,plain,
% 0.49/0.69 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e1))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1612])).
% 0.49/0.69 tff(1614,plain,
% 0.49/0.69 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = op(e1, e2)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1615,plain,
% 0.49/0.69 (~(op(e1, e1) = op(e1, e2))),
% 0.49/0.69 inference(and_elim,[status(thm)],[33])).
% 0.49/0.69 tff(1616,plain,
% 0.49/0.69 (~(op(e1, e1) = op(e1, e2))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1615, 1614])).
% 0.49/0.69 tff(1617,plain,
% 0.49/0.69 (~(op(e1, e1) = e1)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1616, 1613])).
% 0.49/0.69 tff(1618,plain,
% 0.49/0.69 ((e1 = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.49/0.69 inference(commutativity,[status(thm)],[])).
% 0.49/0.69 tff(1619,plain,
% 0.49/0.69 (op(e1, e2) = op(e1, op(e3, e1))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1147])).
% 0.49/0.69 tff(1620,plain,
% 0.49/0.69 (op(e1, e2) = e1),
% 0.49/0.69 inference(transitivity,[status(thm)],[1619, 338])).
% 0.49/0.69 tff(1621,plain,
% 0.49/0.69 ((op(e1, e2) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1620])).
% 0.49/0.69 tff(1622,plain,
% 0.49/0.69 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.49/0.69 inference(transitivity,[status(thm)],[1621, 1618])).
% 0.49/0.69 tff(1623,plain,
% 0.49/0.69 ((op(e3, e2) = e1) <=> (op(e1, e2) = op(e3, e2))),
% 0.49/0.69 inference(symmetry,[status(thm)],[1622])).
% 0.49/0.69 tff(1624,plain,
% 0.49/0.69 ((op(e3, e1) = e1) <=> (e2 = e1)),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1146])).
% 0.49/0.69 tff(1625,plain,
% 0.49/0.69 ((op(e3, e1) = e1) <=> (e1 = e2)),
% 0.49/0.69 inference(transitivity,[status(thm)],[1624, 317])).
% 0.49/0.69 tff(1626,plain,
% 0.49/0.69 ((e1 = e2) <=> (op(e3, e1) = e1)),
% 0.49/0.69 inference(symmetry,[status(thm)],[1625])).
% 0.49/0.69 tff(1627,plain,
% 0.49/0.69 ((~(e1 = e2)) <=> (~(op(e3, e1) = e1))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1626])).
% 0.49/0.69 tff(1628,plain,
% 0.49/0.69 (~(op(e3, e1) = e1)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[324, 1627])).
% 0.49/0.69 tff(1629,plain,
% 0.49/0.69 (op(e3, e2) = e1),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[429, 372, 1414, 1628])).
% 0.49/0.69 tff(1630,plain,
% 0.49/0.69 (op(e1, e2) = op(e3, e2)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1629, 1623])).
% 0.49/0.69 tff(1631,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[165, 1630])).
% 0.49/0.69 tff(1632,plain,(((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (~(op(e3, e1) = e2)) | (op(e3, e0) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(1633,plain,
% 0.49/0.69 (op(e3, e0) = e1),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1632, 334, 1607])).
% 0.49/0.69 tff(1634,plain,
% 0.49/0.69 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e1)),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1633])).
% 0.49/0.69 tff(1635,plain,
% 0.49/0.69 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e1))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1634])).
% 0.49/0.69 tff(1636,plain,
% 0.49/0.69 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = op(e3, e0)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(1637,plain,
% 0.49/0.69 (~(op(e0, e0) = op(e3, e0))),
% 0.49/0.69 inference(and_elim,[status(thm)],[1053])).
% 0.49/0.69 tff(1638,plain,
% 0.49/0.69 (~(op(e0, e0) = op(e3, e0))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1637, 1636])).
% 0.49/0.69 tff(1639,plain,
% 0.49/0.69 (~(op(e0, e0) = e1)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1638, 1635])).
% 0.49/0.69 tff(1640,plain,
% 0.49/0.69 ((e1 = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 0.49/0.69 inference(commutativity,[status(thm)],[])).
% 0.49/0.69 tff(1641,plain,
% 0.49/0.69 ((op(e0, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1132])).
% 0.49/0.69 tff(1642,plain,
% 0.49/0.69 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 0.49/0.69 inference(transitivity,[status(thm)],[1641, 1640])).
% 0.49/0.69 tff(1643,plain,
% 0.49/0.69 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1642])).
% 0.49/0.69 tff(1644,plain,
% 0.49/0.69 (~(op(e3, e1) = e1)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[332, 1643])).
% 0.49/0.69 tff(1645,plain,
% 0.49/0.69 (~(op(e3, e3) = e1)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[371, 338, 354])).
% 0.49/0.69 tff(1646,plain,
% 0.49/0.69 (op(e3, e2) = e1),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[429, 1645, 1414, 1068])).
% 0.49/0.69 tff(1647,plain,
% 0.49/0.69 (e1 = op(e3, e2)),
% 0.49/0.69 inference(symmetry,[status(thm)],[1646])).
% 0.49/0.69 tff(1648,plain,
% 0.49/0.69 (op(e2, e1) = op(e2, op(e3, e2))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1647])).
% 0.49/0.69 tff(1649,plain,
% 0.49/0.69 (op(e2, e1) = e2),
% 0.49/0.69 inference(transitivity,[status(thm)],[1648, 336])).
% 0.49/0.69 tff(1650,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[10, 1649])).
% 0.49/0.69 tff(1651,plain,(((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (op(e2, e1) = e2) | (op(e3, e0) = e1) | (op(e3, e1) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(1652,plain,
% 0.49/0.69 (op(e3, e0) = e1),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1651, 334, 1644, 10])).
% 0.49/0.69 tff(1653,plain,
% 0.49/0.69 (op(e0, op(e3, e0)) = op(e0, e1)),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1652])).
% 0.49/0.69 tff(1654,plain,
% 0.49/0.69 (((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (op(e0, op(e3, e0)) = e0)),
% 0.49/0.69 inference(tautology,[status(thm)],[])).
% 0.49/0.69 tff(1655,plain,
% 0.49/0.69 (op(e0, op(e3, e0)) = e0),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1654, 334])).
% 0.49/0.69 tff(1656,plain,
% 0.49/0.69 (e0 = op(e0, op(e3, e0))),
% 0.49/0.69 inference(symmetry,[status(thm)],[1655])).
% 0.49/0.69 tff(1657,plain,
% 0.49/0.69 (e0 = e1),
% 0.49/0.69 inference(transitivity,[status(thm)],[1656, 1653, 1132])).
% 0.49/0.69 tff(1658,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[625, 1657])).
% 0.49/0.69 tff(1659,plain,(((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (~(op(e0, e1) = e1)) | (op(e2, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(1660,plain,
% 0.49/0.69 (~(op(e0, e1) = e1)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1659, 334, 10])).
% 0.49/0.69 tff(1661,plain,
% 0.49/0.69 (e3 = op(e3, op(e3, e3))),
% 0.49/0.69 inference(symmetry,[status(thm)],[354])).
% 0.49/0.69 tff(1662,plain,
% 0.49/0.69 (e3 = op(e3, e0)),
% 0.49/0.69 inference(transitivity,[status(thm)],[1661, 1328])).
% 0.49/0.69 tff(1663,plain,
% 0.49/0.69 (op(e0, e3) = op(e0, op(e3, e0))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1662])).
% 0.49/0.69 tff(1664,plain,
% 0.49/0.69 (op(e0, e3) = e0),
% 0.49/0.69 inference(transitivity,[status(thm)],[1663, 1655])).
% 0.49/0.69 tff(1665,plain,
% 0.49/0.69 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e0)),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1322])).
% 0.49/0.69 tff(1666,plain,
% 0.49/0.69 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e0))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1665])).
% 0.49/0.69 tff(1667,plain,
% 0.49/0.69 (~(op(e0, e3) = e0)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[725, 1666])).
% 0.49/0.69 tff(1668,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1667, 1664])).
% 0.49/0.69 tff(1669,plain,(((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (~(op(e3, e3) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(1670,plain,
% 0.49/0.69 (~(op(e3, e3) = e0)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1669, 334])).
% 0.49/0.69 tff(1671,plain,
% 0.49/0.69 (op(e3, e1) = e2),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[455, 334, 63, 433])).
% 0.49/0.69 tff(1672,plain,
% 0.49/0.69 (op(e3, e0) = e1),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1632, 1671, 334])).
% 0.49/0.69 tff(1673,plain,
% 0.49/0.69 (op(e0, op(e3, e0)) = op(e0, e1)),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1672])).
% 0.49/0.69 tff(1674,plain,
% 0.49/0.69 (e0 = e3),
% 0.49/0.69 inference(transitivity,[status(thm)],[1656, 1673, 840])).
% 0.49/0.69 tff(1675,plain,
% 0.49/0.69 ($false),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[286, 1674])).
% 0.49/0.69 tff(1676,plain,(((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (~(op(e0, e1) = e3)) | (op(e3, e3) = e0) | (op(e0, e1) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.69 tff(1677,plain,
% 0.49/0.69 (~(op(e0, e1) = e3)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1676, 334, 1670, 1660])).
% 0.49/0.69 tff(1678,plain,
% 0.49/0.69 ((op(e0, e1) = e0) | (op(e0, e1) = e1) | (op(e0, e1) = e3)),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[860, 1605])).
% 0.49/0.69 tff(1679,plain,
% 0.49/0.69 (op(e0, e1) = e0),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[1678, 1677, 1660])).
% 0.49/0.69 tff(1680,plain,
% 0.49/0.69 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e0)),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1679])).
% 0.49/0.69 tff(1681,plain,
% 0.49/0.69 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e0))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1680])).
% 0.49/0.69 tff(1682,plain,
% 0.49/0.69 (~(op(e0, e0) = e0)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[745, 1681])).
% 0.49/0.69 tff(1683,plain,
% 0.49/0.69 ((op(e3, e1) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1607])).
% 0.49/0.69 tff(1684,plain,
% 0.49/0.69 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.49/0.69 inference(transitivity,[status(thm)],[1683, 1024])).
% 0.49/0.69 tff(1685,plain,
% 0.49/0.69 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1684])).
% 0.49/0.69 tff(1686,plain,
% 0.49/0.69 (~(op(e3, e3) = e2)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[399, 1685])).
% 0.49/0.69 tff(1687,plain,
% 0.49/0.69 (op(e3, e3) = e3),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[266, 1670, 1686, 1645])).
% 0.49/0.69 tff(1688,plain,
% 0.49/0.69 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1687])).
% 0.49/0.69 tff(1689,plain,
% 0.49/0.69 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1688])).
% 0.49/0.69 tff(1690,plain,
% 0.49/0.69 (~(op(e3, e2) = e3)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[1111, 1689])).
% 0.49/0.69 tff(1691,plain,
% 0.49/0.69 (op(e1, op(e0, e1)) = op(e1, e0)),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1679])).
% 0.49/0.69 tff(1692,plain,
% 0.49/0.69 ((op(e1, op(e0, e1)) = e1) <=> (op(e1, e0) = op(e1, e2))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[1691, 1610])).
% 0.49/0.69 tff(1693,plain,
% 0.49/0.69 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, op(e0, e1)) = e1)),
% 0.49/0.69 inference(symmetry,[status(thm)],[1692])).
% 0.49/0.69 tff(1694,plain,
% 0.49/0.70 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, op(e0, e1)) = e1))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1693])).
% 0.49/0.70 tff(1695,plain,
% 0.49/0.70 (~(op(e1, op(e0, e1)) = e1)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1428, 1694])).
% 0.49/0.70 tff(1696,plain,
% 0.49/0.70 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1146])).
% 0.49/0.70 tff(1697,plain,
% 0.49/0.70 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1696])).
% 0.49/0.70 tff(1698,plain,
% 0.49/0.70 (~(op(e3, e0) = e2)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1333, 1697])).
% 0.49/0.70 tff(1699,assumption,(~(op(e3, e0) = e2)), introduced(assumption)).
% 0.49/0.70 tff(1700,plain,
% 0.49/0.70 (op(e3, e2) = e2),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[537, 374, 75, 1699])).
% 0.49/0.70 tff(1701,plain,
% 0.49/0.70 (e2 = op(e3, e2)),
% 0.49/0.70 inference(symmetry,[status(thm)],[1700])).
% 0.49/0.70 tff(1702,plain,
% 0.49/0.70 (op(e2, e2) = op(e2, op(e3, e2))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1701])).
% 0.49/0.70 tff(1703,plain,
% 0.49/0.70 (op(e2, e2) = e2),
% 0.49/0.70 inference(transitivity,[status(thm)],[1702, 376])).
% 0.49/0.70 tff(1704,plain,
% 0.49/0.70 (op(e2, e1) = e2),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1018, 374, 12, 830])).
% 0.49/0.70 tff(1705,plain,
% 0.49/0.70 ((op(e2, e1) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1704])).
% 0.49/0.70 tff(1706,plain,
% 0.49/0.70 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.49/0.70 inference(transitivity,[status(thm)],[1705, 810])).
% 0.49/0.70 tff(1707,plain,
% 0.49/0.70 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1706])).
% 0.49/0.70 tff(1708,plain,
% 0.49/0.70 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e1) = op(e2, e2)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(1709,plain,
% 0.49/0.70 (~(op(e2, e1) = op(e2, e2))),
% 0.49/0.70 inference(and_elim,[status(thm)],[27])).
% 0.49/0.70 tff(1710,plain,
% 0.49/0.70 (~(op(e2, e1) = op(e2, e2))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1709, 1708])).
% 0.49/0.70 tff(1711,plain,
% 0.49/0.70 (~(op(e2, e2) = e2)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1710, 1707])).
% 0.49/0.70 tff(1712,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1711, 1703])).
% 0.49/0.70 tff(1713,plain,((op(e3, e1) = e2) | (~(op(e2, op(e3, e2)) = e2)) | (op(e3, e3) = e2) | (op(e3, e0) = e2) | (op(e1, e1) = e2) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(1714,plain,
% 0.49/0.70 (op(e3, e1) = e2),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1713, 336, 393, 1699, 12, 830])).
% 0.49/0.70 tff(1715,plain,
% 0.49/0.70 (op(e3, e0) = e1),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1632, 1714, 334])).
% 0.49/0.70 tff(1716,plain,
% 0.49/0.70 (op(e0, op(e3, e0)) = op(e0, e1)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1715])).
% 0.49/0.70 tff(1717,plain,
% 0.49/0.70 (e0 = e1),
% 0.49/0.70 inference(transitivity,[status(thm)],[1656, 1716, 1132])).
% 0.49/0.70 tff(1718,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[625, 1717])).
% 0.49/0.70 tff(1719,plain,(((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (~(op(e0, e1) = e1)) | (op(e3, e0) = e2) | (op(e1, e1) = e2) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(1720,plain,
% 0.49/0.70 (((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (~(op(e0, e1) = e1)) | (op(e3, e0) = e2) | (op(e1, e1) = e2)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1719, 1605])).
% 0.49/0.70 tff(1721,plain,
% 0.49/0.70 (~(op(e0, e1) = e1)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1720, 334, 1698, 12])).
% 0.49/0.70 tff(1722,assumption,(~(op(e0, e3) = e1)), introduced(assumption)).
% 0.49/0.70 tff(1723,plain,
% 0.49/0.70 (op(e1, op(e3, e1)) = op(e1, e2)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1146])).
% 0.49/0.70 tff(1724,plain,
% 0.49/0.70 (e1 = op(e1, e2)),
% 0.49/0.70 inference(transitivity,[status(thm)],[1609, 1723])).
% 0.49/0.70 tff(1725,plain,
% 0.49/0.70 ((op(e0, e2) = e1) <=> (op(e0, e2) = op(e1, e2))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1724])).
% 0.49/0.70 tff(1726,plain,
% 0.49/0.70 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e1)),
% 0.49/0.70 inference(symmetry,[status(thm)],[1725])).
% 0.49/0.70 tff(1727,plain,
% 0.49/0.70 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e1))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1726])).
% 0.49/0.70 tff(1728,plain,
% 0.49/0.70 (~(op(e0, e2) = e1)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[703, 1727])).
% 0.49/0.70 tff(1729,plain,
% 0.49/0.70 (op(e3, e0) = e1),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1632, 334, 1146])).
% 0.49/0.70 tff(1730,plain,
% 0.49/0.70 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e1)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1729])).
% 0.49/0.70 tff(1731,plain,
% 0.49/0.70 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e1))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1730])).
% 0.49/0.70 tff(1732,plain,
% 0.49/0.70 (~(op(e0, e0) = e1)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1638, 1731])).
% 0.49/0.70 tff(1733,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[718, 1732, 1728, 1722, 1721])).
% 0.49/0.70 tff(1734,plain,(((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (op(e0, e3) = e1) | (~(op(e3, e1) = e2)) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(1735,plain,
% 0.49/0.70 (op(e0, e3) = e1),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1734, 334, 1607, 12])).
% 0.49/0.70 tff(1736,plain,
% 0.49/0.70 ((op(e3, e3) = e2) <=> (e2 = op(e3, e3))),
% 0.49/0.70 inference(symmetry,[status(thm)],[1024])).
% 0.49/0.70 tff(1737,plain,
% 0.49/0.70 (op(e2, e2) = e2),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[524, 767, 10, 74])).
% 0.49/0.70 tff(1738,plain,
% 0.49/0.70 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e2)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1737])).
% 0.49/0.70 tff(1739,plain,
% 0.49/0.70 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e2))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1738])).
% 0.49/0.70 tff(1740,plain,
% 0.49/0.70 (~(op(e1, e2) = e2)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[764, 1739])).
% 0.49/0.70 tff(1741,plain,
% 0.49/0.70 (~(op(e1, e0) = e2)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[790, 79, 10, 767, 1740])).
% 0.49/0.70 tff(1742,plain,
% 0.49/0.70 (op(e1, e3) = e2),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[147, 104, 75, 767])).
% 0.49/0.70 tff(1743,plain,
% 0.49/0.70 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e1) = e2)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1742])).
% 0.49/0.70 tff(1744,plain,
% 0.49/0.70 ((op(e1, e1) = e2) <=> (op(e1, e1) = op(e1, e3))),
% 0.49/0.70 inference(symmetry,[status(thm)],[1743])).
% 0.49/0.70 tff(1745,plain,
% 0.49/0.70 (op(e1, e1) = e2),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[205, 104, 10, 74, 79, 75, 1741])).
% 0.49/0.70 tff(1746,plain,
% 0.49/0.70 (op(e1, e1) = op(e1, e3)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1745, 1744])).
% 0.49/0.70 tff(1747,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[838, 1746])).
% 0.49/0.70 tff(1748,plain,((op(e0, e3) = e2) | (op(e2, e1) = e2) | (op(e2, e0) = e2) | ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))) | (op(e3, e3) = e2) | (op(e2, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(1749,plain,
% 0.49/0.70 (op(e0, e3) = e2),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1748, 79, 74, 10, 75, 767])).
% 0.49/0.70 tff(1750,plain,
% 0.49/0.70 ((op(e0, e3) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1749])).
% 0.49/0.70 tff(1751,plain,
% 0.49/0.70 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.49/0.70 inference(transitivity,[status(thm)],[1750, 218])).
% 0.49/0.70 tff(1752,plain,
% 0.49/0.70 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1751])).
% 0.49/0.70 tff(1753,plain,
% 0.49/0.70 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = op(e1, e3)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(1754,plain,
% 0.49/0.70 (~(op(e0, e3) = op(e1, e3))),
% 0.49/0.70 inference(and_elim,[status(thm)],[48])).
% 0.49/0.70 tff(1755,plain,
% 0.49/0.70 (~(op(e0, e3) = op(e1, e3))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1754, 1753])).
% 0.49/0.70 tff(1756,plain,
% 0.49/0.70 (~(op(e1, e3) = e2)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1755, 1752])).
% 0.49/0.70 tff(1757,plain,
% 0.49/0.70 (op(e1, e1) = e2),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[135, 1756, 1740, 1741])).
% 0.49/0.70 tff(1758,plain,
% 0.49/0.70 (e2 = op(e1, e1)),
% 0.49/0.70 inference(symmetry,[status(thm)],[1757])).
% 0.49/0.70 tff(1759,plain,
% 0.49/0.70 (op(e1, e2) = op(e1, op(e1, e1))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1758])).
% 0.49/0.70 tff(1760,plain,
% 0.49/0.70 (op(e1, op(e1, e1)) = op(e1, e2)),
% 0.49/0.70 inference(symmetry,[status(thm)],[1759])).
% 0.49/0.70 tff(1761,plain,
% 0.49/0.70 (e1 = op(e1, e2)),
% 0.49/0.70 inference(transitivity,[status(thm)],[1317, 1760])).
% 0.49/0.70 tff(1762,plain,
% 0.49/0.70 (op(e2, e1) = op(e2, op(e1, e2))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1761])).
% 0.49/0.70 tff(1763,plain,
% 0.49/0.70 (op(e2, e1) = e2),
% 0.49/0.70 inference(transitivity,[status(thm)],[1762, 103])).
% 0.49/0.70 tff(1764,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[10, 1763])).
% 0.49/0.70 tff(1765,plain,(((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))) | (op(e2, e1) = e2) | (op(e2, e0) = e2) | (op(e3, e3) = e2) | (op(e2, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(1766,plain,
% 0.49/0.70 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1765, 767, 74, 75, 10])).
% 0.49/0.70 tff(1767,plain,
% 0.49/0.70 (~(op(e0, e0) = e1)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1130, 7, 5])).
% 0.49/0.70 tff(1768,plain,
% 0.49/0.70 ((~(op(e1, e1) = e1)) | (~(op(e1, op(e0, e1)) = e1))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1066, 1605])).
% 0.49/0.70 tff(1769,plain,
% 0.49/0.70 (~(op(e1, e1) = e1)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1768, 5])).
% 0.49/0.70 tff(1770,plain,
% 0.49/0.70 (~(op(e0, e1) = e1)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1137, 1769, 5])).
% 0.49/0.70 tff(1771,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[10, 802])).
% 0.49/0.70 tff(1772,plain,((~(op(e0, e2) = e1)) | (op(e2, e1) = e2) | (~(op(e2, op(e0, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(1773,plain,
% 0.49/0.70 (~(op(e0, e2) = e1)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1772, 9, 10])).
% 0.49/0.70 tff(1774,plain,
% 0.49/0.70 (op(e0, e3) = e1),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[718, 1773, 1770, 1767])).
% 0.49/0.70 tff(1775,plain,
% 0.49/0.70 ((op(e0, e3) = e3) <=> (e1 = e3)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1774])).
% 0.49/0.70 tff(1776,plain,
% 0.49/0.70 ((e1 = e3) <=> (op(e0, e3) = e3)),
% 0.49/0.70 inference(symmetry,[status(thm)],[1775])).
% 0.49/0.70 tff(1777,plain,
% 0.49/0.70 ((~(e1 = e3)) <=> (~(op(e0, e3) = e3))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1776])).
% 0.49/0.70 tff(1778,plain,
% 0.49/0.70 (~(op(e0, e3) = e3)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[591, 1777])).
% 0.49/0.70 tff(1779,plain,
% 0.49/0.70 (~(op(e0, e0) = e3)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1553, 1774, 7])).
% 0.49/0.70 tff(1780,plain,
% 0.49/0.70 (e1 = op(e0, e3)),
% 0.49/0.70 inference(symmetry,[status(thm)],[1774])).
% 0.49/0.70 tff(1781,plain,
% 0.49/0.70 (op(e3, e1) = op(e3, op(e0, e3))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1780])).
% 0.49/0.70 tff(1782,plain,
% 0.49/0.70 (op(e3, e1) = e3),
% 0.49/0.70 inference(transitivity,[status(thm)],[1781, 3])).
% 0.49/0.70 tff(1783,plain,
% 0.49/0.70 ((op(e0, e1) = op(e3, e1)) <=> (op(e0, e1) = e3)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1782])).
% 0.49/0.70 tff(1784,plain,
% 0.49/0.70 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e0, e1) = e3))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1783])).
% 0.49/0.70 tff(1785,plain,
% 0.49/0.70 (~(op(e0, e1) = e3)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[332, 1784])).
% 0.49/0.70 tff(1786,plain,
% 0.49/0.70 (op(e0, e2) = e3),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1562, 1785, 1779, 1778])).
% 0.49/0.70 tff(1787,plain,
% 0.49/0.70 (~(op(e0, e2) = e2)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[819, 9])).
% 0.49/0.70 tff(1788,plain,
% 0.49/0.70 ((op(e0, e3) = e2) <=> (e1 = e2)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1774])).
% 0.49/0.70 tff(1789,plain,
% 0.49/0.70 ((e1 = e2) <=> (op(e0, e3) = e2)),
% 0.49/0.70 inference(symmetry,[status(thm)],[1788])).
% 0.49/0.70 tff(1790,plain,
% 0.49/0.70 ((~(e1 = e2)) <=> (~(op(e0, e3) = e2))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1789])).
% 0.49/0.70 tff(1791,plain,
% 0.49/0.70 (~(op(e0, e3) = e2)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[324, 1790])).
% 0.49/0.70 tff(1792,plain,
% 0.49/0.70 ((op(e0, e0) = e2) | (op(e0, e2) = e2) | (op(e0, e3) = e2)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[887, 1605])).
% 0.49/0.70 tff(1793,plain,
% 0.49/0.70 (op(e0, e0) = e2),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1792, 1791, 1787])).
% 0.49/0.70 tff(1794,plain,
% 0.49/0.70 (op(e0, op(e0, e0)) = op(e0, e2)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1793])).
% 0.49/0.70 tff(1795,plain,
% 0.49/0.70 (e0 = e3),
% 0.49/0.70 inference(transitivity,[status(thm)],[1180, 1794, 1786])).
% 0.49/0.70 tff(1796,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[286, 1795])).
% 0.49/0.70 tff(1797,plain,(((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))) | (op(e2, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(1798,plain,
% 0.49/0.70 ((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1797, 10])).
% 0.49/0.70 tff(1799,plain,
% 0.49/0.70 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e2)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1737])).
% 0.49/0.70 tff(1800,plain,
% 0.49/0.70 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e2))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1799])).
% 0.49/0.70 tff(1801,plain,
% 0.49/0.70 (~(op(e0, e2) = e2)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[816, 1800])).
% 0.49/0.70 tff(1802,plain,
% 0.49/0.70 ((op(e2, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1737])).
% 0.49/0.70 tff(1803,plain,
% 0.49/0.70 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.49/0.70 inference(transitivity,[status(thm)],[1802, 469])).
% 0.49/0.70 tff(1804,plain,
% 0.49/0.70 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1803])).
% 0.49/0.70 tff(1805,plain,
% 0.49/0.70 (~(op(e3, e2) = e2)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[504, 1804])).
% 0.49/0.70 tff(1806,plain,
% 0.49/0.70 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e1) = e2))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1743])).
% 0.49/0.70 tff(1807,plain,
% 0.49/0.70 (~(op(e1, e1) = e2)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[838, 1806])).
% 0.49/0.70 tff(1808,plain,
% 0.49/0.70 (op(e0, e0) = e2),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1792, 104, 796])).
% 0.49/0.70 tff(1809,plain,
% 0.49/0.70 ((op(e0, e0) = e0) <=> (e2 = e0)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1808])).
% 0.49/0.70 tff(1810,plain,
% 0.49/0.70 ((op(e0, e0) = e0) <=> (e0 = e2)),
% 0.49/0.70 inference(transitivity,[status(thm)],[1809, 217])).
% 0.49/0.70 tff(1811,plain,
% 0.49/0.70 ((e0 = e2) <=> (op(e0, e0) = e0)),
% 0.49/0.70 inference(symmetry,[status(thm)],[1810])).
% 0.49/0.70 tff(1812,plain,
% 0.49/0.70 ((~(e0 = e2)) <=> (~(op(e0, e0) = e0))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1811])).
% 0.49/0.70 tff(1813,plain,
% 0.49/0.70 (~(op(e0, e0) = e0)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[238, 1812])).
% 0.49/0.70 tff(1814,assumption,(~(op(e1, op(e0, e1)) = e1)), introduced(assumption)).
% 0.49/0.70 tff(1815,plain,
% 0.49/0.70 ((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1183, 989, 12, 63])).
% 0.49/0.70 tff(1816,plain,
% 0.49/0.70 ((e2 = op(e1, e0)) <=> (op(e1, e0) = e2)),
% 0.49/0.70 inference(commutativity,[status(thm)],[])).
% 0.49/0.70 tff(1817,plain,
% 0.49/0.70 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e1)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1132])).
% 0.49/0.70 tff(1818,plain,
% 0.49/0.70 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e1))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1817])).
% 0.49/0.70 tff(1819,plain,
% 0.49/0.70 (~(op(e0, e0) = e1)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[745, 1818])).
% 0.49/0.70 tff(1820,assumption,(~(op(e0, e0) = e2)), introduced(assumption)).
% 0.49/0.70 tff(1821,plain,
% 0.49/0.70 (op(e0, e0) = e3),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1100, 1820, 989, 1819])).
% 0.49/0.70 tff(1822,plain,
% 0.49/0.70 ((op(e0, e0) = op(e2, e0)) <=> (e3 = op(e2, e0))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1821])).
% 0.49/0.70 tff(1823,plain,
% 0.49/0.70 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 0.49/0.70 inference(transitivity,[status(thm)],[1822, 1337])).
% 0.49/0.70 tff(1824,plain,
% 0.49/0.70 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1823])).
% 0.49/0.70 tff(1825,plain,
% 0.49/0.70 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = op(e2, e0)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(1826,plain,
% 0.49/0.70 (~(op(e0, e0) = op(e2, e0))),
% 0.49/0.70 inference(and_elim,[status(thm)],[1054])).
% 0.49/0.70 tff(1827,plain,
% 0.49/0.70 (~(op(e0, e0) = op(e2, e0))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1826, 1825])).
% 0.49/0.70 tff(1828,plain,
% 0.49/0.70 (~(op(e2, e0) = e3)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[1827, 1824])).
% 0.49/0.70 tff(1829,plain,
% 0.49/0.70 (op(e0, e2) = e2),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[887, 1820, 830, 104])).
% 0.49/0.70 tff(1830,plain,
% 0.49/0.70 (op(e1, e0) = e2),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[757, 1820, 74, 1699])).
% 0.49/0.70 tff(1831,plain,
% 0.49/0.70 (op(e0, op(e1, e0)) = op(e0, e2)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1830])).
% 0.49/0.70 tff(1832,assumption,(op(e0, op(e1, e0)) = e0), introduced(assumption)).
% 0.49/0.70 tff(1833,plain,
% 0.49/0.70 (e0 = op(e0, op(e1, e0))),
% 0.49/0.70 inference(symmetry,[status(thm)],[1832])).
% 0.49/0.70 tff(1834,plain,
% 0.49/0.70 (e0 = e2),
% 0.49/0.70 inference(transitivity,[status(thm)],[1833, 1831, 1829])).
% 0.49/0.70 tff(1835,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[238, 1834])).
% 0.49/0.70 tff(1836,plain,((op(e0, e0) = e2) | (~(op(e0, op(e1, e0)) = e0)) | (op(e2, e0) = e2) | (op(e3, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.70 tff(1837,plain,
% 0.49/0.70 (~(op(e0, op(e1, e0)) = e0)),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[1836, 1820, 104, 74, 830, 1699])).
% 0.49/0.70 tff(1838,plain,
% 0.49/0.70 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[83, 1837])).
% 0.49/0.70 tff(1839,plain,
% 0.49/0.70 ((op(e0, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1829])).
% 0.49/0.70 tff(1840,plain,
% 0.49/0.70 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.49/0.70 inference(transitivity,[status(thm)],[1839, 469])).
% 0.49/0.70 tff(1841,plain,
% 0.49/0.70 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1840])).
% 0.49/0.70 tff(1842,plain,
% 0.49/0.70 (~(op(e3, e2) = e2)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[277, 1841])).
% 0.49/0.70 tff(1843,plain,
% 0.49/0.70 ((op(e1, e0) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1830])).
% 0.49/0.70 tff(1844,plain,
% 0.49/0.70 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.49/0.70 inference(transitivity,[status(thm)],[1843, 218])).
% 0.49/0.70 tff(1845,plain,
% 0.49/0.70 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1844])).
% 0.49/0.70 tff(1846,plain,
% 0.49/0.70 (~(op(e1, e3) = e2)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[224, 1845])).
% 0.49/0.70 tff(1847,plain,
% 0.49/0.70 ((e1 = op(e0, e3)) <=> (op(e0, e3) = e1)),
% 0.49/0.70 inference(commutativity,[status(thm)],[])).
% 0.49/0.70 tff(1848,plain,
% 0.49/0.70 ((op(e0, e1) = op(e0, e3)) <=> (e1 = op(e0, e3))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1132])).
% 0.49/0.70 tff(1849,plain,
% 0.49/0.70 ((op(e0, e1) = op(e0, e3)) <=> (op(e0, e3) = e1)),
% 0.49/0.70 inference(transitivity,[status(thm)],[1848, 1847])).
% 0.49/0.70 tff(1850,plain,
% 0.49/0.70 ((~(op(e0, e1) = op(e0, e3))) <=> (~(op(e0, e3) = e1))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1849])).
% 0.49/0.70 tff(1851,plain,
% 0.49/0.70 (~(op(e0, e3) = e1)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[91, 1850])).
% 0.49/0.70 tff(1852,assumption,((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))), introduced(assumption)).
% 0.49/0.70 tff(1853,plain,
% 0.49/0.70 (op(e2, e3) = e2),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[147, 75, 107, 104])).
% 0.49/0.70 tff(1854,plain,
% 0.49/0.70 ((op(e2, e3) = e1) <=> (e2 = e1)),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1853])).
% 0.49/0.70 tff(1855,plain,
% 0.49/0.70 ((op(e2, e3) = e1) <=> (e1 = e2)),
% 0.49/0.70 inference(transitivity,[status(thm)],[1854, 317])).
% 0.49/0.70 tff(1856,plain,
% 0.49/0.70 ((e1 = e2) <=> (op(e2, e3) = e1)),
% 0.49/0.70 inference(symmetry,[status(thm)],[1855])).
% 0.49/0.70 tff(1857,plain,
% 0.49/0.70 ((~(e1 = e2)) <=> (~(op(e2, e3) = e1))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1856])).
% 0.49/0.70 tff(1858,plain,
% 0.49/0.70 (~(op(e2, e3) = e1)),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[324, 1857])).
% 0.49/0.70 tff(1859,assumption,(~(op(e3, e2) = e2)), introduced(assumption)).
% 0.49/0.70 tff(1860,plain,
% 0.49/0.70 (op(e3, e1) = e2),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[537, 75, 1859, 1699])).
% 0.49/0.70 tff(1861,plain,
% 0.49/0.70 ((op(e1, e2) = op(e1, e3)) <=> (e1 = op(e1, e3))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[1620])).
% 0.49/0.70 tff(1862,plain,
% 0.49/0.70 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 0.49/0.70 inference(transitivity,[status(thm)],[1861, 831])).
% 0.49/0.70 tff(1863,plain,
% 0.49/0.70 ((op(e1, e3) = e1) <=> (op(e1, e2) = op(e1, e3))),
% 0.49/0.70 inference(symmetry,[status(thm)],[1862])).
% 0.49/0.70 tff(1864,assumption,(~(op(e2, e3) = e1)), introduced(assumption)).
% 0.49/0.70 tff(1865,plain,
% 0.49/0.70 (((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1) | (op(e3, e3) = e1)) <=> ((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1) | (op(e3, e3) = e1))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(1866,plain,
% 0.49/0.70 ((((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1)) | (op(e3, e3) = e1)) <=> ((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1) | (op(e3, e3) = e1))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(1867,plain,
% 0.49/0.70 ((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) <=> ((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(1868,plain,
% 0.49/0.71 (((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) | (op(e3, e3) = e1)) <=> (((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1)) | (op(e3, e3) = e1))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[1867])).
% 0.49/0.71 tff(1869,plain,
% 0.49/0.71 (((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) | (op(e3, e3) = e1)) <=> ((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1) | (op(e3, e3) = e1))),
% 0.49/0.71 inference(transitivity,[status(thm)],[1868, 1866])).
% 0.49/0.71 tff(1870,plain,
% 0.49/0.71 ((((op(e0, e3) = e1) | (op(e1, e3) = e1)) | (op(e2, e3) = e1)) | (op(e3, e3) = e1)),
% 0.49/0.71 inference(and_elim,[status(thm)],[117])).
% 0.49/0.71 tff(1871,plain,
% 0.49/0.71 ((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1) | (op(e3, e3) = e1)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[1870, 1869])).
% 0.49/0.71 tff(1872,plain,
% 0.49/0.71 ((op(e0, e3) = e1) | (op(e1, e3) = e1) | (op(e2, e3) = e1) | (op(e3, e3) = e1)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[1871, 1865])).
% 0.49/0.71 tff(1873,plain,
% 0.49/0.71 (op(e1, e3) = e1),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[1872, 372, 1722, 1864])).
% 0.49/0.71 tff(1874,plain,
% 0.49/0.71 (op(e1, e2) = op(e1, e3)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[1873, 1863])).
% 0.49/0.71 tff(1875,plain,
% 0.49/0.71 ($false),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[174, 1874])).
% 0.49/0.71 tff(1876,plain,(((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (~(op(e3, e1) = e2)) | (op(e0, e3) = e1) | (op(e2, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.71 tff(1877,plain,
% 0.49/0.71 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[1876, 1860, 1722, 1858])).
% 0.49/0.71 tff(1878,plain,
% 0.49/0.71 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[681, 1877, 1221, 1852])).
% 0.49/0.71 tff(1879,plain,
% 0.49/0.71 (op(e3, op(e2, e3)) = e3),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[471, 1878])).
% 0.49/0.71 tff(1880,plain,
% 0.49/0.71 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e2)),
% 0.49/0.71 inference(monotonicity,[status(thm)],[1860])).
% 0.49/0.71 tff(1881,plain,
% 0.49/0.71 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e2))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[1880])).
% 0.49/0.71 tff(1882,plain,
% 0.49/0.71 (~(op(e2, e1) = e2)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[576, 1881])).
% 0.49/0.71 tff(1883,plain,
% 0.49/0.71 (op(e2, op(e2, e2)) = e2),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[473, 1878])).
% 0.49/0.71 tff(1884,plain,
% 0.49/0.71 (~(op(e2, e2) = e1)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[488, 1883, 1882])).
% 0.49/0.71 tff(1885,plain,
% 0.49/0.71 (~(op(e2, e2) = e0)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[481, 1883, 74])).
% 0.49/0.71 tff(1886,plain,
% 0.49/0.71 ($false),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[515, 1885, 1884, 1853, 1879])).
% 0.49/0.71 tff(1887,plain,((op(e3, e3) = e2) | (op(e2, e0) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))) | (op(e0, e3) = e1) | (op(e1, e3) = e2) | (op(e0, e3) = e2) | (op(e3, e2) = e2) | (op(e3, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.71 tff(1888,plain,
% 0.49/0.71 (op(e3, e3) = e2),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[1887, 1838, 1221, 74, 1851, 1846, 104, 1842, 1699])).
% 0.49/0.71 tff(1889,plain,
% 0.49/0.71 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[392, 1888])).
% 0.49/0.71 tff(1890,plain,
% 0.49/0.71 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[681, 1889, 1221, 1838])).
% 0.49/0.71 tff(1891,plain,
% 0.49/0.71 (op(e0, op(e2, e0)) = e0),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[967, 1890])).
% 0.49/0.71 tff(1892,assumption,(op(e2, e0) = e0), introduced(assumption)).
% 0.49/0.71 tff(1893,plain,
% 0.49/0.71 (e0 = op(e2, e0)),
% 0.49/0.71 inference(symmetry,[status(thm)],[1892])).
% 0.49/0.71 tff(1894,plain,
% 0.49/0.71 (op(e0, e0) = op(e0, op(e2, e0))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[1893])).
% 0.49/0.71 tff(1895,plain,
% 0.49/0.71 (op(e0, op(e2, e0)) = op(e0, e0)),
% 0.49/0.71 inference(symmetry,[status(thm)],[1894])).
% 0.49/0.71 tff(1896,assumption,(op(e0, op(e2, e0)) = e0), introduced(assumption)).
% 0.49/0.71 tff(1897,plain,
% 0.49/0.71 (e0 = op(e0, op(e2, e0))),
% 0.49/0.71 inference(symmetry,[status(thm)],[1896])).
% 0.49/0.71 tff(1898,plain,
% 0.49/0.71 (e0 = e3),
% 0.49/0.71 inference(transitivity,[status(thm)],[1897, 1895, 1547])).
% 0.49/0.71 tff(1899,plain,
% 0.49/0.71 ($false),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[286, 1898])).
% 0.49/0.71 tff(1900,plain,((~(op(e2, e0) = e0)) | (~(op(e0, e0) = e3)) | (~(op(e0, op(e2, e0)) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.71 tff(1901,plain,
% 0.49/0.71 (~(op(e2, e0) = e0)),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[1900, 1891, 1821])).
% 0.49/0.71 tff(1902,plain,
% 0.49/0.71 (((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))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(1903,plain,
% 0.49/0.71 ((((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))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(1904,plain,
% 0.49/0.71 ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) <=> ((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e2))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(1905,plain,
% 0.49/0.71 (((((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))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[1904])).
% 0.49/0.71 tff(1906,plain,
% 0.49/0.71 (((((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))),
% 0.49/0.71 inference(transitivity,[status(thm)],[1905, 1903])).
% 0.49/0.71 tff(1907,plain,
% 0.49/0.71 ((((op(e2, e0) = e0) | (op(e2, e0) = e1)) | (op(e2, e0) = e2)) | (op(e2, e0) = e3)),
% 0.49/0.71 inference(and_elim,[status(thm)],[188])).
% 0.49/0.71 tff(1908,plain,
% 0.49/0.71 ((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e2) | (op(e2, e0) = e3)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[1907, 1906])).
% 0.49/0.71 tff(1909,plain,
% 0.49/0.71 ((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e2) | (op(e2, e0) = e3)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[1908, 1902])).
% 0.49/0.71 tff(1910,plain,
% 0.49/0.71 (op(e2, e0) = e1),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[1909, 1901, 74, 1828])).
% 0.49/0.71 tff(1911,plain,
% 0.49/0.71 (e1 = op(e2, e0)),
% 0.49/0.71 inference(symmetry,[status(thm)],[1910])).
% 0.49/0.71 tff(1912,plain,
% 0.49/0.71 (op(e0, e1) = op(e0, op(e2, e0))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[1911])).
% 0.49/0.71 tff(1913,plain,
% 0.49/0.71 (op(e0, op(e2, e0)) = op(e0, e1)),
% 0.49/0.71 inference(symmetry,[status(thm)],[1912])).
% 0.49/0.71 tff(1914,plain,
% 0.49/0.71 (e0 = op(e0, op(e2, e0))),
% 0.49/0.71 inference(symmetry,[status(thm)],[1891])).
% 0.49/0.71 tff(1915,plain,
% 0.49/0.71 ((op(e0, e1) = e0) <=> (e1 = e0)),
% 0.49/0.71 inference(monotonicity,[status(thm)],[1132])).
% 0.49/0.71 tff(1916,plain,
% 0.49/0.71 ((op(e0, e1) = e0) <=> (e0 = e1)),
% 0.49/0.71 inference(transitivity,[status(thm)],[1915, 635])).
% 0.49/0.71 tff(1917,plain,
% 0.49/0.71 ((e0 = e1) <=> (op(e0, e1) = e0)),
% 0.49/0.71 inference(symmetry,[status(thm)],[1916])).
% 0.49/0.71 tff(1918,plain,
% 0.49/0.71 ((~(e0 = e1)) <=> (~(op(e0, e1) = e0))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[1917])).
% 0.49/0.71 tff(1919,plain,
% 0.49/0.71 (~(op(e0, e1) = e0)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[625, 1918])).
% 0.49/0.71 tff(1920,plain,
% 0.49/0.71 ((op(e0, e2) = e0) <=> (e2 = e0)),
% 0.49/0.71 inference(monotonicity,[status(thm)],[1829])).
% 0.49/0.71 tff(1921,plain,
% 0.49/0.71 ((op(e0, e2) = e0) <=> (e0 = e2)),
% 0.49/0.71 inference(transitivity,[status(thm)],[1920, 217])).
% 0.49/0.71 tff(1922,plain,
% 0.49/0.71 ((e0 = e2) <=> (op(e0, e2) = e0)),
% 0.49/0.71 inference(symmetry,[status(thm)],[1921])).
% 0.49/0.71 tff(1923,plain,
% 0.49/0.71 ((~(e0 = e2)) <=> (~(op(e0, e2) = e0))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[1922])).
% 0.49/0.71 tff(1924,plain,
% 0.49/0.71 (~(op(e0, e2) = e0)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[238, 1923])).
% 0.56/0.71 tff(1925,plain,
% 0.56/0.71 (op(e0, e3) = e0),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[1357, 1924, 989, 1919])).
% 0.56/0.71 tff(1926,plain,
% 0.56/0.71 (op(e0, e3) = e1),
% 0.56/0.71 inference(transitivity,[status(thm)],[1925, 1914, 1913, 1132])).
% 0.56/0.71 tff(1927,plain,
% 0.56/0.71 ($false),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[1851, 1926])).
% 0.56/0.71 tff(1928,plain,((op(e0, e0) = e2) | (~(op(e0, e1) = e1)) | (op(e2, e0) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e0, e3) = e2) | (op(e3, e0) = e2) | (op(e0, e0) = e0) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.71 tff(1929,plain,
% 0.56/0.71 (op(e0, e0) = e2),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[1928, 1699, 74, 1221, 104, 1132, 989, 830])).
% 0.56/0.71 tff(1930,plain,
% 0.56/0.71 ((op(e0, e0) = op(e1, e0)) <=> (e2 = op(e1, e0))),
% 0.56/0.71 inference(monotonicity,[status(thm)],[1929])).
% 0.56/0.71 tff(1931,plain,
% 0.56/0.71 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e2)),
% 0.56/0.71 inference(transitivity,[status(thm)],[1930, 1816])).
% 0.56/0.71 tff(1932,plain,
% 0.56/0.71 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e2))),
% 0.56/0.71 inference(monotonicity,[status(thm)],[1931])).
% 0.56/0.71 tff(1933,plain,
% 0.56/0.71 (~(op(e1, e0) = e2)),
% 0.56/0.71 inference(modus_ponens,[status(thm)],[1056, 1932])).
% 0.56/0.71 tff(1934,plain,
% 0.56/0.71 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[1719, 1699, 1132, 12, 830])).
% 0.56/0.71 tff(1935,plain,
% 0.56/0.71 ((op(e2, e1) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 0.56/0.71 inference(monotonicity,[status(thm)],[1704])).
% 0.56/0.71 tff(1936,plain,
% 0.56/0.71 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.56/0.71 inference(transitivity,[status(thm)],[1935, 72])).
% 0.56/0.71 tff(1937,plain,
% 0.56/0.71 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.56/0.71 inference(monotonicity,[status(thm)],[1936])).
% 0.56/0.71 tff(1938,plain,
% 0.56/0.71 (~(op(e2, e3) = e2)),
% 0.56/0.71 inference(modus_ponens,[status(thm)],[1005, 1937])).
% 0.56/0.71 tff(1939,plain,
% 0.56/0.71 (op(e1, e3) = e2),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[147, 1938, 75, 104])).
% 0.56/0.71 tff(1940,plain,
% 0.56/0.71 (op(e3, op(e1, e3)) = op(e3, e2)),
% 0.56/0.71 inference(monotonicity,[status(thm)],[1939])).
% 0.56/0.71 tff(1941,plain,
% 0.56/0.71 (op(e3, op(e1, e3)) = e2),
% 0.56/0.71 inference(transitivity,[status(thm)],[1940, 1700])).
% 0.56/0.71 tff(1942,plain,
% 0.56/0.71 ((op(e3, op(e1, e3)) = e3) <=> (e2 = e3)),
% 0.56/0.71 inference(monotonicity,[status(thm)],[1941])).
% 0.56/0.71 tff(1943,plain,
% 0.56/0.71 ((e2 = e3) <=> (op(e3, op(e1, e3)) = e3)),
% 0.56/0.71 inference(symmetry,[status(thm)],[1942])).
% 0.56/0.71 tff(1944,plain,
% 0.56/0.71 ((~(e2 = e3)) <=> (~(op(e3, op(e1, e3)) = e3))),
% 0.56/0.71 inference(monotonicity,[status(thm)],[1943])).
% 0.56/0.71 tff(1945,plain,
% 0.56/0.71 (~(op(e3, op(e1, e3)) = e3)),
% 0.56/0.71 inference(modus_ponens,[status(thm)],[462, 1944])).
% 0.56/0.71 tff(1946,plain,
% 0.56/0.71 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[80, 1945])).
% 0.56/0.71 tff(1947,plain,
% 0.56/0.71 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[681, 1946, 1221, 1222])).
% 0.56/0.71 tff(1948,plain,
% 0.56/0.71 (op(e2, op(e2, e2)) = e2),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[473, 1947])).
% 0.56/0.71 tff(1949,plain,
% 0.56/0.71 ((e1 = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 0.56/0.71 inference(commutativity,[status(thm)],[])).
% 0.56/0.71 tff(1950,plain,
% 0.56/0.71 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e2)),
% 0.56/0.71 inference(monotonicity,[status(thm)],[375])).
% 0.56/0.71 tff(1951,plain,
% 0.56/0.71 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e2))),
% 0.56/0.71 inference(monotonicity,[status(thm)],[1950])).
% 0.56/0.71 tff(1952,plain,
% 0.56/0.71 (~(op(e3, e1) = e2)),
% 0.56/0.71 inference(modus_ponens,[status(thm)],[399, 1951])).
% 0.56/0.71 tff(1953,plain,
% 0.56/0.71 (op(e2, e1) = e2),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[1018, 1952, 12, 830])).
% 0.56/0.71 tff(1954,plain,
% 0.56/0.71 (op(e1, op(e2, e1)) = op(e1, e2)),
% 0.56/0.71 inference(monotonicity,[status(thm)],[1953])).
% 0.56/0.71 tff(1955,plain,
% 0.56/0.71 ((op(e1, op(e2, e1)) = e1) <=> (op(e1, e2) = e1)),
% 0.56/0.71 inference(monotonicity,[status(thm)],[1954])).
% 0.56/0.71 tff(1956,plain,
% 0.56/0.71 ((op(e1, e2) = e1) <=> (op(e1, op(e2, e1)) = e1)),
% 0.56/0.71 inference(symmetry,[status(thm)],[1955])).
% 0.56/0.71 tff(1957,plain,
% 0.56/0.71 ((~(op(e1, e2) = e1)) <=> (~(op(e1, op(e2, e1)) = e1))),
% 0.56/0.71 inference(monotonicity,[status(thm)],[1956])).
% 0.56/0.71 tff(1958,plain,
% 0.56/0.71 (~(op(e1, op(e2, e1)) = e1)),
% 0.56/0.71 inference(modus_ponens,[status(thm)],[168, 1957])).
% 0.56/0.71 tff(1959,plain,
% 0.56/0.71 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[546, 1958])).
% 0.56/0.71 tff(1960,plain,
% 0.56/0.71 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[392, 375])).
% 0.56/0.71 tff(1961,plain,
% 0.56/0.71 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[681, 1960, 1221, 1959])).
% 0.56/0.71 tff(1962,plain,
% 0.56/0.71 (op(e2, op(e1, e2)) = e2),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[102, 1961])).
% 0.56/0.71 tff(1963,plain,
% 0.56/0.71 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e2)),
% 0.56/0.71 inference(monotonicity,[status(thm)],[375])).
% 0.56/0.71 tff(1964,plain,
% 0.56/0.71 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e2))),
% 0.56/0.71 inference(monotonicity,[status(thm)],[1963])).
% 0.56/0.71 tff(1965,plain,
% 0.56/0.71 (~(op(e1, e3) = e2)),
% 0.56/0.71 inference(modus_ponens,[status(thm)],[368, 1964])).
% 0.56/0.71 tff(1966,plain,
% 0.56/0.71 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e2)),
% 0.56/0.71 inference(monotonicity,[status(thm)],[375])).
% 0.56/0.71 tff(1967,plain,
% 0.56/0.71 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e2))),
% 0.56/0.71 inference(monotonicity,[status(thm)],[1966])).
% 0.56/0.71 tff(1968,plain,
% 0.56/0.71 (~(op(e3, e0) = e2)),
% 0.56/0.71 inference(modus_ponens,[status(thm)],[257, 1967])).
% 0.56/0.71 tff(1969,plain,
% 0.56/0.71 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e0) = e2)),
% 0.56/0.71 inference(monotonicity,[status(thm)],[1953])).
% 0.56/0.71 tff(1970,plain,
% 0.56/0.71 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = e2))),
% 0.56/0.71 inference(monotonicity,[status(thm)],[1969])).
% 0.56/0.71 tff(1971,plain,
% 0.56/0.71 (~(op(e2, e0) = e2)),
% 0.56/0.71 inference(modus_ponens,[status(thm)],[997, 1970])).
% 0.56/0.71 tff(1972,plain,
% 0.56/0.71 (op(e0, op(e1, e0)) = e0),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[83, 1961])).
% 0.56/0.71 tff(1973,plain,
% 0.56/0.71 (op(e0, e0) = e2),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[1836, 1972, 1971, 1968, 830, 104])).
% 0.56/0.71 tff(1974,plain,
% 0.56/0.71 ((op(e0, e0) = op(e1, e0)) <=> (e2 = op(e1, e0))),
% 0.56/0.71 inference(monotonicity,[status(thm)],[1973])).
% 0.56/0.71 tff(1975,plain,
% 0.56/0.71 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e2)),
% 0.56/0.71 inference(transitivity,[status(thm)],[1974, 1816])).
% 0.56/0.71 tff(1976,plain,
% 0.56/0.71 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e2))),
% 0.56/0.71 inference(monotonicity,[status(thm)],[1975])).
% 0.56/0.71 tff(1977,plain,
% 0.56/0.71 (~(op(e1, e0) = e2)),
% 0.56/0.71 inference(modus_ponens,[status(thm)],[1056, 1976])).
% 0.56/0.71 tff(1978,plain,
% 0.56/0.71 (op(e1, e2) = e2),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[135, 1977, 12, 1965])).
% 0.56/0.71 tff(1979,plain,
% 0.56/0.71 (e2 = op(e1, e2)),
% 0.56/0.71 inference(symmetry,[status(thm)],[1978])).
% 0.56/0.71 tff(1980,plain,
% 0.56/0.71 (op(e2, e2) = op(e2, op(e1, e2))),
% 0.56/0.71 inference(monotonicity,[status(thm)],[1979])).
% 0.56/0.72 tff(1981,plain,
% 0.56/0.72 (op(e2, e2) = e2),
% 0.56/0.72 inference(transitivity,[status(thm)],[1980, 1962])).
% 0.56/0.72 tff(1982,plain,
% 0.56/0.72 ((op(e2, e1) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[1953])).
% 0.56/0.72 tff(1983,plain,
% 0.56/0.72 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.56/0.72 inference(transitivity,[status(thm)],[1982, 810])).
% 0.56/0.72 tff(1984,plain,
% 0.56/0.72 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[1983])).
% 0.56/0.72 tff(1985,plain,
% 0.56/0.72 (~(op(e2, e2) = e2)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[1710, 1984])).
% 0.56/0.72 tff(1986,plain,
% 0.56/0.72 ($false),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[1985, 1981])).
% 0.56/0.72 tff(1987,plain,((~(op(e3, e3) = e2)) | (op(e1, e1) = e2) | (op(e0, e1) = e2) | (op(e0, e3) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e1, e2) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.72 tff(1988,plain,
% 0.56/0.72 (~(op(e3, e3) = e2)),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[1987, 168, 830, 104, 1221, 12])).
% 0.56/0.72 tff(1989,plain,
% 0.56/0.72 (op(e3, e1) = e2),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[1713, 336, 75, 1699, 12, 830])).
% 0.56/0.72 tff(1990,plain,
% 0.56/0.72 (e2 = op(e3, e1)),
% 0.56/0.72 inference(symmetry,[status(thm)],[1989])).
% 0.56/0.72 tff(1991,plain,
% 0.56/0.72 (op(e1, e2) = op(e1, op(e3, e1))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[1990])).
% 0.56/0.72 tff(1992,plain,
% 0.56/0.72 (op(e1, e2) = e1),
% 0.56/0.72 inference(transitivity,[status(thm)],[1991, 338])).
% 0.56/0.72 tff(1993,plain,
% 0.56/0.72 ($false),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[168, 1992])).
% 0.56/0.72 tff(1994,plain,(((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (op(e1, e2) = e1) | (op(e3, e3) = e2) | (op(e3, e0) = e2) | (op(e1, e1) = e2) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.72 tff(1995,plain,
% 0.56/0.72 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[1994, 168, 1988, 1699, 12, 830])).
% 0.56/0.72 tff(1996,plain,
% 0.56/0.72 (op(e1, op(e2, e1)) = op(e1, e2)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[1704])).
% 0.56/0.72 tff(1997,plain,
% 0.56/0.72 ((op(e1, op(e2, e1)) = e1) <=> (op(e1, e2) = e1)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[1996])).
% 0.56/0.72 tff(1998,plain,
% 0.56/0.72 ((op(e1, e2) = e1) <=> (op(e1, op(e2, e1)) = e1)),
% 0.56/0.72 inference(symmetry,[status(thm)],[1997])).
% 0.56/0.72 tff(1999,plain,
% 0.56/0.72 ((~(op(e1, e2) = e1)) <=> (~(op(e1, op(e2, e1)) = e1))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[1998])).
% 0.56/0.72 tff(2000,plain,
% 0.56/0.72 (~(op(e1, op(e2, e1)) = e1)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[168, 1999])).
% 0.56/0.72 tff(2001,plain,
% 0.56/0.72 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[546, 2000])).
% 0.56/0.72 tff(2002,plain,
% 0.56/0.72 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[681, 2001, 1221, 1995])).
% 0.56/0.72 tff(2003,plain,
% 0.56/0.72 (op(e3, op(e1, e3)) = e3),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[80, 2002])).
% 0.56/0.72 tff(2004,plain,
% 0.56/0.72 (op(e1, e3) = e2),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[147, 1938, 1988, 104])).
% 0.56/0.72 tff(2005,plain,
% 0.56/0.72 (e2 = op(e1, e3)),
% 0.56/0.72 inference(symmetry,[status(thm)],[2004])).
% 0.56/0.72 tff(2006,plain,
% 0.56/0.72 (op(e3, e2) = op(e3, op(e1, e3))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2005])).
% 0.56/0.72 tff(2007,plain,
% 0.56/0.72 (op(e3, e2) = e2),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[537, 374, 1988, 1699])).
% 0.56/0.72 tff(2008,plain,
% 0.56/0.72 (e2 = op(e3, e2)),
% 0.56/0.72 inference(symmetry,[status(thm)],[2007])).
% 0.56/0.72 tff(2009,plain,
% 0.56/0.72 (e2 = e3),
% 0.56/0.72 inference(transitivity,[status(thm)],[2008, 2006, 2003])).
% 0.56/0.72 tff(2010,plain,
% 0.56/0.72 ($false),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[462, 2009])).
% 0.56/0.72 tff(2011,plain,((op(e3, e1) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e0, e3) = e2) | (op(e1, e2) = e1) | (op(e3, e0) = e2) | (op(e1, e1) = e2) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.72 tff(2012,plain,
% 0.56/0.72 (op(e1, e2) = e1),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[2011, 374, 1221, 104, 1699, 12, 830])).
% 0.56/0.72 tff(2013,plain,
% 0.56/0.72 ((op(e1, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2012])).
% 0.56/0.72 tff(2014,plain,
% 0.56/0.72 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 0.56/0.72 inference(transitivity,[status(thm)],[2013, 1949])).
% 0.56/0.72 tff(2015,plain,
% 0.56/0.72 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2014])).
% 0.56/0.72 tff(2016,plain,
% 0.56/0.72 (~(op(e2, e2) = e1)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[764, 2015])).
% 0.56/0.72 tff(2017,plain,
% 0.56/0.72 (~(op(e2, e2) = e0)),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[481, 1948, 74])).
% 0.56/0.72 tff(2018,plain,
% 0.56/0.72 (op(e2, e2) = e3),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[513, 2017, 1711, 2016])).
% 0.56/0.72 tff(2019,plain,
% 0.56/0.72 (e3 = op(e2, e2)),
% 0.56/0.72 inference(symmetry,[status(thm)],[2018])).
% 0.56/0.72 tff(2020,plain,
% 0.56/0.72 (op(e2, e3) = op(e2, op(e2, e2))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2019])).
% 0.56/0.72 tff(2021,plain,
% 0.56/0.72 (op(e2, e3) = e2),
% 0.56/0.72 inference(transitivity,[status(thm)],[2020, 1948])).
% 0.56/0.72 tff(2022,plain,
% 0.56/0.72 ($false),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[1938, 2021])).
% 0.56/0.72 tff(2023,plain,((op(e3, e1) = e2) | (op(e2, e0) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (~((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3)))) | (op(e3, e3) = e2) | (op(e0, e3) = e2) | (op(e3, e0) = e2) | (op(e1, e1) = e2) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.72 tff(2024,plain,
% 0.56/0.72 (op(e3, e1) = e2),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[2023, 75, 1221, 1934, 74, 104, 1699, 12, 830])).
% 0.56/0.72 tff(2025,plain,
% 0.56/0.72 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e2)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2024])).
% 0.56/0.72 tff(2026,plain,
% 0.56/0.72 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e2))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2025])).
% 0.56/0.72 tff(2027,plain,
% 0.56/0.72 (~(op(e2, e1) = e2)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[576, 2026])).
% 0.56/0.72 tff(2028,plain,
% 0.56/0.72 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[205, 2027, 74, 12, 105, 75, 104])).
% 0.56/0.72 tff(2029,plain,
% 0.56/0.72 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[681, 2028, 1221, 1934])).
% 0.56/0.72 tff(2030,plain,
% 0.56/0.72 (op(e2, op(e2, e2)) = e2),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[473, 2029])).
% 0.56/0.72 tff(2031,plain,
% 0.56/0.72 (~(op(e2, e2) = e1)),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[488, 2030, 2027])).
% 0.56/0.72 tff(2032,plain,
% 0.56/0.72 ((e1 = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 0.56/0.72 inference(commutativity,[status(thm)],[])).
% 0.56/0.72 tff(2033,plain,
% 0.56/0.72 ((op(e0, e1) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[1132])).
% 0.56/0.72 tff(2034,plain,
% 0.56/0.72 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 0.56/0.72 inference(transitivity,[status(thm)],[2033, 2032])).
% 0.56/0.72 tff(2035,plain,
% 0.56/0.72 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2034])).
% 0.56/0.72 tff(2036,plain,
% 0.56/0.72 (~(op(e2, e1) = e1)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[61, 2035])).
% 0.56/0.72 tff(2037,plain,
% 0.56/0.72 (op(e3, op(e2, e3)) = e3),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[471, 2029])).
% 0.56/0.72 tff(2038,assumption,(op(e2, e3) = e1), introduced(assumption)).
% 0.56/0.72 tff(2039,plain,
% 0.56/0.72 (op(e3, op(e2, e3)) = op(e3, e1)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2038])).
% 0.56/0.72 tff(2040,plain,
% 0.56/0.72 (op(e3, e1) = op(e3, op(e2, e3))),
% 0.56/0.72 inference(symmetry,[status(thm)],[2039])).
% 0.56/0.72 tff(2041,plain,
% 0.56/0.72 (e2 = e3),
% 0.56/0.72 inference(transitivity,[status(thm)],[1147, 2040, 496])).
% 0.56/0.72 tff(2042,plain,
% 0.56/0.72 ($false),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[462, 2041])).
% 0.56/0.72 tff(2043,plain,((~(op(e2, e3) = e1)) | (~(op(e3, op(e2, e3)) = e3)) | (~(op(e3, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.72 tff(2044,plain,
% 0.56/0.72 (~(op(e2, e3) = e1)),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[2043, 2037, 2024])).
% 0.56/0.72 tff(2045,plain,
% 0.56/0.72 (op(e2, e0) = e1),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[964, 2044, 2036, 2031])).
% 0.56/0.72 tff(2046,plain,
% 0.56/0.72 (op(e0, op(e2, e0)) = op(e0, e1)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2045])).
% 0.56/0.72 tff(2047,plain,
% 0.56/0.72 (op(e0, op(e2, e0)) = e0),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[967, 2029])).
% 0.56/0.72 tff(2048,plain,
% 0.56/0.72 (e0 = op(e0, op(e2, e0))),
% 0.56/0.72 inference(symmetry,[status(thm)],[2047])).
% 0.56/0.72 tff(2049,plain,
% 0.56/0.72 (e0 = e1),
% 0.56/0.72 inference(transitivity,[status(thm)],[2048, 2046, 1132])).
% 0.56/0.72 tff(2050,plain,
% 0.56/0.72 ($false),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[625, 2049])).
% 0.56/0.72 tff(2051,plain,((op(e3, e3) = e2) | (~(op(e0, e1) = e1)) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e2, e0) = e2) | (op(e1, e1) = e2) | (op(e1, e0) = e2) | (op(e0, e3) = e2) | (op(e3, e0) = e2) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.72 tff(2052,plain,
% 0.56/0.72 (op(e3, e3) = e2),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[2051, 1933, 1221, 74, 12, 1132, 104, 1699, 830])).
% 0.56/0.72 tff(2053,plain,
% 0.56/0.72 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e2)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2052])).
% 0.56/0.72 tff(2054,plain,
% 0.56/0.72 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e2))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2053])).
% 0.56/0.72 tff(2055,plain,
% 0.56/0.72 (~(op(e1, e3) = e2)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[368, 2054])).
% 0.56/0.72 tff(2056,plain,
% 0.56/0.72 (op(e1, e2) = e1),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[1987, 2052, 830, 104, 1221, 12])).
% 0.56/0.72 tff(2057,plain,
% 0.56/0.72 ((op(e1, e2) = e2) <=> (e1 = e2)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2056])).
% 0.56/0.72 tff(2058,plain,
% 0.56/0.72 ((e1 = e2) <=> (op(e1, e2) = e2)),
% 0.56/0.72 inference(symmetry,[status(thm)],[2057])).
% 0.56/0.72 tff(2059,plain,
% 0.56/0.72 ((~(e1 = e2)) <=> (~(op(e1, e2) = e2))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2058])).
% 0.56/0.72 tff(2060,plain,
% 0.56/0.72 (~(op(e1, e2) = e2)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[324, 2059])).
% 0.56/0.72 tff(2061,plain,
% 0.56/0.72 ($false),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[135, 2060, 2055, 12, 1933])).
% 0.56/0.72 tff(2062,plain,((op(e3, e0) = e2) | (op(e1, e1) = e2) | (op(e0, e1) = e2) | (op(e0, e3) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e2, e0) = e2) | (~(op(e0, e1) = e1)) | (op(e0, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.72 tff(2063,plain,
% 0.56/0.72 (op(e3, e0) = e2),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[2062, 104, 830, 12, 1221, 74, 1132, 989])).
% 0.56/0.72 tff(2064,plain,
% 0.56/0.72 (op(e0, op(e3, e0)) = op(e0, e2)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2063])).
% 0.56/0.72 tff(2065,plain,
% 0.56/0.72 ((op(e0, op(e3, e0)) = e0) <=> (op(e0, e2) = e0)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2064])).
% 0.56/0.72 tff(2066,plain,
% 0.56/0.72 ((op(e0, e2) = e0) <=> (op(e0, op(e3, e0)) = e0)),
% 0.56/0.72 inference(symmetry,[status(thm)],[2065])).
% 0.56/0.72 tff(2067,plain,
% 0.56/0.72 ((op(e0, e0) = op(e3, e0)) <=> (op(e0, e0) = e2)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2063])).
% 0.56/0.72 tff(2068,plain,
% 0.56/0.72 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e0, e0) = e2))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2067])).
% 0.56/0.72 tff(2069,plain,
% 0.56/0.72 (~(op(e0, e0) = e2)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[1638, 2068])).
% 0.56/0.72 tff(2070,plain,
% 0.56/0.72 (op(e0, e2) = e2),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[887, 2069, 830, 104])).
% 0.56/0.72 tff(2071,plain,
% 0.56/0.72 ((op(e0, e2) = e0) <=> (e2 = e0)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2070])).
% 0.56/0.72 tff(2072,plain,
% 0.56/0.72 ((op(e0, e2) = e0) <=> (e0 = e2)),
% 0.56/0.72 inference(transitivity,[status(thm)],[2071, 217])).
% 0.56/0.72 tff(2073,plain,
% 0.56/0.72 ((e0 = e2) <=> (op(e0, e2) = e0)),
% 0.56/0.72 inference(symmetry,[status(thm)],[2072])).
% 0.56/0.72 tff(2074,plain,
% 0.56/0.72 ((e0 = e2) <=> (op(e0, op(e3, e0)) = e0)),
% 0.56/0.72 inference(transitivity,[status(thm)],[2073, 2066])).
% 0.56/0.72 tff(2075,plain,
% 0.56/0.72 ((~(e0 = e2)) <=> (~(op(e0, op(e3, e0)) = e0))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2074])).
% 0.56/0.72 tff(2076,plain,
% 0.56/0.72 (~(op(e0, op(e3, e0)) = e0)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[238, 2075])).
% 0.56/0.72 tff(2077,plain,
% 0.56/0.72 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[1654, 2076])).
% 0.56/0.72 tff(2078,plain,
% 0.56/0.72 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e2)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2063])).
% 0.56/0.72 tff(2079,plain,
% 0.56/0.72 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e2))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2078])).
% 0.56/0.72 tff(2080,plain,
% 0.56/0.72 (~(op(e1, e0) = e2)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[420, 2079])).
% 0.56/0.72 tff(2081,plain,
% 0.56/0.72 ((e2 = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 0.56/0.72 inference(commutativity,[status(thm)],[])).
% 0.56/0.72 tff(2082,plain,
% 0.56/0.72 ((op(e0, e2) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2070])).
% 0.56/0.72 tff(2083,plain,
% 0.56/0.72 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 0.56/0.72 inference(transitivity,[status(thm)],[2082, 2081])).
% 0.56/0.72 tff(2084,plain,
% 0.56/0.72 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2083])).
% 0.56/0.72 tff(2085,plain,
% 0.56/0.72 (~(op(e1, e2) = e2)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[703, 2084])).
% 0.56/0.72 tff(2086,plain,
% 0.56/0.72 (op(e1, e3) = e2),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[135, 2085, 12, 2080])).
% 0.56/0.72 tff(2087,plain,
% 0.56/0.72 ((e3 = op(e1, e0)) <=> (op(e1, e0) = e3)),
% 0.56/0.72 inference(commutativity,[status(thm)],[])).
% 0.56/0.72 tff(2088,plain,
% 0.56/0.72 (op(e0, e0) = e3),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[1100, 2069, 989, 1819])).
% 0.56/0.72 tff(2089,plain,
% 0.56/0.72 ((op(e0, e0) = op(e1, e0)) <=> (e3 = op(e1, e0))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2088])).
% 0.56/0.72 tff(2090,plain,
% 0.56/0.72 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e3)),
% 0.56/0.72 inference(transitivity,[status(thm)],[2089, 2087])).
% 0.56/0.72 tff(2091,plain,
% 0.56/0.72 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e3))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2090])).
% 0.56/0.72 tff(2092,plain,
% 0.56/0.72 (~(op(e1, e0) = e3)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[1056, 2091])).
% 0.56/0.72 tff(2093,plain,
% 0.56/0.72 ((op(e1, e3) = e3) <=> (e2 = e3)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2086])).
% 0.56/0.72 tff(2094,plain,
% 0.56/0.72 ((e2 = e3) <=> (op(e1, e3) = e3)),
% 0.56/0.72 inference(symmetry,[status(thm)],[2093])).
% 0.56/0.72 tff(2095,plain,
% 0.56/0.72 ((~(e2 = e3)) <=> (~(op(e1, e3) = e3))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2094])).
% 0.56/0.72 tff(2096,plain,
% 0.56/0.72 (~(op(e1, e3) = e3)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[462, 2095])).
% 0.56/0.72 tff(2097,plain,
% 0.56/0.72 ((op(e3, e0) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2063])).
% 0.56/0.72 tff(2098,plain,
% 0.56/0.72 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 0.56/0.72 inference(transitivity,[status(thm)],[2097, 326])).
% 0.56/0.72 tff(2099,plain,
% 0.56/0.72 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2098])).
% 0.56/0.72 tff(2100,plain,
% 0.56/0.72 (~(op(e3, e1) = e2)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[1333, 2099])).
% 0.56/0.72 tff(2101,plain,
% 0.56/0.72 (op(e2, e1) = e2),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[1018, 2100, 12, 830])).
% 0.56/0.72 tff(2102,plain,
% 0.56/0.72 (op(e1, op(e2, e1)) = op(e1, e2)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[992])).
% 0.56/0.72 tff(2103,plain,
% 0.56/0.72 ((op(e1, op(e2, e1)) = e1) <=> (op(e1, e2) = e1)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2102])).
% 0.56/0.72 tff(2104,plain,
% 0.56/0.72 ((op(e1, e2) = e1) <=> (op(e1, op(e2, e1)) = e1)),
% 0.56/0.72 inference(symmetry,[status(thm)],[2103])).
% 0.56/0.72 tff(2105,plain,
% 0.56/0.72 ((~(op(e1, e2) = e1)) <=> (~(op(e1, op(e2, e1)) = e1))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2104])).
% 0.56/0.72 tff(2106,plain,
% 0.56/0.72 (~(op(e1, op(e2, e1)) = e1)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[168, 2105])).
% 0.56/0.72 tff(2107,plain,
% 0.56/0.72 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[546, 2106])).
% 0.56/0.72 tff(2108,plain,
% 0.56/0.72 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[681, 2107, 1221, 1222])).
% 0.56/0.72 tff(2109,plain,
% 0.56/0.72 (op(e2, op(e1, e2)) = e2),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[102, 2108])).
% 0.56/0.72 tff(2110,plain,
% 0.56/0.72 (op(e3, op(e1, e3)) = op(e3, e2)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[548])).
% 0.56/0.72 tff(2111,plain,
% 0.56/0.72 (op(e3, op(e1, e3)) = e3),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[80, 2108])).
% 0.56/0.72 tff(2112,plain,
% 0.56/0.72 (e3 = op(e3, op(e1, e3))),
% 0.56/0.72 inference(symmetry,[status(thm)],[2111])).
% 0.56/0.72 tff(2113,plain,
% 0.56/0.72 (e3 = op(e3, e2)),
% 0.56/0.72 inference(transitivity,[status(thm)],[2112, 2110])).
% 0.56/0.72 tff(2114,plain,
% 0.56/0.72 ((op(e1, e2) = e3) <=> (op(e1, e2) = op(e3, e2))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2113])).
% 0.56/0.72 tff(2115,plain,
% 0.56/0.72 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e3)),
% 0.56/0.72 inference(symmetry,[status(thm)],[2114])).
% 0.56/0.72 tff(2116,plain,
% 0.56/0.72 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e3))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[2115])).
% 0.56/0.72 tff(2117,plain,
% 0.56/0.72 (~(op(e1, e2) = e3)),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[165, 2116])).
% 0.56/0.72 tff(2118,plain,
% 0.56/0.72 (op(e1, e2) = e0),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[193, 2117, 766, 168])).
% 0.56/0.72 tff(2119,plain,
% 0.56/0.72 (e0 = op(e1, e2)),
% 0.56/0.72 inference(symmetry,[status(thm)],[2118])).
% 0.56/0.73 tff(2120,plain,
% 0.56/0.73 (op(e2, e0) = op(e2, op(e1, e2))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2119])).
% 0.56/0.73 tff(2121,plain,
% 0.56/0.73 (op(e2, e0) = e2),
% 0.56/0.73 inference(transitivity,[status(thm)],[2120, 2109])).
% 0.56/0.73 tff(2122,plain,
% 0.56/0.73 ($false),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[998, 2121])).
% 0.56/0.73 tff(2123,plain,((op(e1, e2) = e1) | (op(e1, e2) = e2) | (~(op(e1, e3) = e2)) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (~((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3)))) | (~(op(e2, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.73 tff(2124,plain,
% 0.56/0.73 (op(e1, e2) = e1),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[2123, 2086, 2101, 1221, 2077, 2085])).
% 0.56/0.73 tff(2125,plain,
% 0.56/0.73 ((op(e1, e2) = e3) <=> (e1 = e3)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2124])).
% 0.56/0.73 tff(2126,plain,
% 0.56/0.73 ((e1 = e3) <=> (op(e1, e2) = e3)),
% 0.56/0.73 inference(symmetry,[status(thm)],[2125])).
% 0.56/0.73 tff(2127,plain,
% 0.56/0.73 ((~(e1 = e3)) <=> (~(op(e1, e2) = e3))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2126])).
% 0.56/0.73 tff(2128,plain,
% 0.56/0.73 (~(op(e1, e2) = e3)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[591, 2127])).
% 0.56/0.73 tff(2129,plain,
% 0.56/0.73 (((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))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(2130,plain,
% 0.56/0.73 ((((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))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(2131,plain,
% 0.56/0.73 ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) <=> ((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(2132,plain,
% 0.56/0.73 (((((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))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2131])).
% 0.56/0.73 tff(2133,plain,
% 0.56/0.73 (((((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))),
% 0.56/0.73 inference(transitivity,[status(thm)],[2132, 2130])).
% 0.56/0.73 tff(2134,plain,
% 0.56/0.73 ((((op(e1, e0) = e3) | (op(e1, e1) = e3)) | (op(e1, e2) = e3)) | (op(e1, e3) = e3)),
% 0.56/0.73 inference(and_elim,[status(thm)],[130])).
% 0.56/0.73 tff(2135,plain,
% 0.56/0.73 ((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3) | (op(e1, e3) = e3)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[2134, 2133])).
% 0.56/0.73 tff(2136,plain,
% 0.56/0.73 ((op(e1, e0) = e3) | (op(e1, e1) = e3) | (op(e1, e2) = e3) | (op(e1, e3) = e3)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[2135, 2129])).
% 0.56/0.73 tff(2137,plain,
% 0.56/0.73 (op(e1, e1) = e3),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[2136, 2128, 2096, 2092])).
% 0.56/0.73 tff(2138,plain,
% 0.56/0.73 (op(e1, op(e1, e1)) = op(e1, e3)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2137])).
% 0.56/0.73 tff(2139,plain,
% 0.56/0.73 (op(e1, op(e1, e1)) = e2),
% 0.56/0.73 inference(transitivity,[status(thm)],[2138, 2086])).
% 0.56/0.73 tff(2140,plain,
% 0.56/0.73 ((op(e1, op(e1, e1)) = e1) <=> (e2 = e1)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2139])).
% 0.56/0.73 tff(2141,plain,
% 0.56/0.73 ((op(e1, op(e1, e1)) = e1) <=> (e1 = e2)),
% 0.56/0.73 inference(transitivity,[status(thm)],[2140, 317])).
% 0.56/0.73 tff(2142,plain,
% 0.56/0.73 ((e1 = e2) <=> (op(e1, op(e1, e1)) = e1)),
% 0.56/0.73 inference(symmetry,[status(thm)],[2141])).
% 0.56/0.73 tff(2143,plain,
% 0.56/0.73 ((~(e1 = e2)) <=> (~(op(e1, op(e1, e1)) = e1))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2142])).
% 0.56/0.73 tff(2144,plain,
% 0.56/0.73 (~(op(e1, op(e1, e1)) = e1)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[324, 2143])).
% 0.56/0.73 tff(2145,plain,
% 0.56/0.73 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[1315, 2144])).
% 0.56/0.73 tff(2146,plain,
% 0.56/0.73 ((~(e0 = e2)) <=> (~(op(e0, e2) = e0))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2073])).
% 0.56/0.73 tff(2147,plain,
% 0.56/0.73 (~(op(e0, e2) = e0)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[238, 2146])).
% 0.56/0.73 tff(2148,plain,
% 0.56/0.73 (op(e0, e3) = e0),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[1357, 2147, 989, 1919])).
% 0.56/0.73 tff(2149,plain,
% 0.56/0.73 (e0 = op(e0, e3)),
% 0.56/0.73 inference(symmetry,[status(thm)],[2148])).
% 0.56/0.73 tff(2150,plain,
% 0.56/0.73 ((op(e3, e0) = e1) <=> (e2 = e1)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2063])).
% 0.56/0.73 tff(2151,plain,
% 0.56/0.73 ((op(e3, e0) = e1) <=> (e1 = e2)),
% 0.56/0.73 inference(transitivity,[status(thm)],[2150, 317])).
% 0.56/0.73 tff(2152,plain,
% 0.56/0.73 ((e1 = e2) <=> (op(e3, e0) = e1)),
% 0.56/0.73 inference(symmetry,[status(thm)],[2151])).
% 0.56/0.73 tff(2153,plain,
% 0.56/0.73 ((~(e1 = e2)) <=> (~(op(e3, e0) = e1))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2152])).
% 0.56/0.73 tff(2154,plain,
% 0.56/0.73 (~(op(e3, e0) = e1)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[324, 2153])).
% 0.56/0.73 tff(2155,plain,
% 0.56/0.73 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e0) = e1)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2124])).
% 0.56/0.73 tff(2156,plain,
% 0.56/0.73 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = e1))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2155])).
% 0.56/0.73 tff(2157,plain,
% 0.56/0.73 (~(op(e1, e0) = e1)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[1428, 2156])).
% 0.56/0.73 tff(2158,plain,
% 0.56/0.73 (op(e2, e0) = e1),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[1423, 2157, 1819, 2154])).
% 0.56/0.73 tff(2159,plain,
% 0.56/0.73 (op(e0, op(e2, e0)) = op(e0, e1)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2158])).
% 0.56/0.73 tff(2160,plain,
% 0.56/0.73 (op(e0, op(e2, e0)) = e1),
% 0.56/0.73 inference(transitivity,[status(thm)],[2159, 1132])).
% 0.56/0.73 tff(2161,plain,
% 0.56/0.73 ((op(e0, op(e2, e0)) = e0) <=> (e1 = op(e0, e3))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2160, 2149])).
% 0.56/0.73 tff(2162,plain,
% 0.56/0.73 ((op(e0, op(e2, e0)) = e0) <=> (op(e0, e3) = e1)),
% 0.56/0.73 inference(transitivity,[status(thm)],[2161, 1847])).
% 0.56/0.73 tff(2163,plain,
% 0.56/0.73 ((op(e0, e3) = e1) <=> (op(e0, op(e2, e0)) = e0)),
% 0.56/0.73 inference(symmetry,[status(thm)],[2162])).
% 0.56/0.73 tff(2164,plain,
% 0.56/0.73 ((~(op(e0, e3) = e1)) <=> (~(op(e0, op(e2, e0)) = e0))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2163])).
% 0.56/0.73 tff(2165,plain,
% 0.56/0.73 (~(op(e0, op(e2, e0)) = e0)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[1851, 2164])).
% 0.56/0.73 tff(2166,plain,
% 0.56/0.73 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[967, 2165])).
% 0.56/0.73 tff(2167,plain,
% 0.56/0.73 ($false),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[681, 2166, 2145, 1221, 2077])).
% 0.56/0.73 tff(2168,plain,((op(e0, e3) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (~(op(e0, e1) = e1)) | (op(e1, e1) = e2) | (op(e0, e0) = e0) | (op(e0, e1) = e2) | (op(e2, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.73 tff(2169,plain,
% 0.56/0.73 (op(e0, e3) = e2),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[2168, 74, 1132, 12, 989, 830, 1815])).
% 0.56/0.73 tff(2170,plain,
% 0.56/0.73 ((op(e0, e3) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2169])).
% 0.56/0.73 tff(2171,plain,
% 0.56/0.73 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.56/0.73 inference(transitivity,[status(thm)],[2170, 1024])).
% 0.56/0.73 tff(2172,plain,
% 0.56/0.73 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2171])).
% 0.56/0.73 tff(2173,plain,
% 0.56/0.73 (~(op(e3, e3) = e2)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[725, 2172])).
% 0.56/0.73 tff(2174,plain,
% 0.56/0.73 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2169])).
% 0.56/0.73 tff(2175,plain,
% 0.56/0.73 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2174])).
% 0.56/0.73 tff(2176,plain,
% 0.56/0.73 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = op(e0, e3)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(2177,plain,
% 0.56/0.73 (~(op(e0, e0) = op(e0, e3))),
% 0.56/0.73 inference(and_elim,[status(thm)],[40])).
% 0.56/0.73 tff(2178,plain,
% 0.56/0.73 (~(op(e0, e0) = op(e0, e3))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[2177, 2176])).
% 0.56/0.73 tff(2179,plain,
% 0.56/0.73 (~(op(e0, e0) = e2)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[2178, 2175])).
% 0.56/0.73 tff(2180,plain,
% 0.56/0.73 ((op(e0, e3) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2169])).
% 0.56/0.73 tff(2181,plain,
% 0.56/0.73 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.56/0.73 inference(transitivity,[status(thm)],[2180, 218])).
% 0.56/0.73 tff(2182,plain,
% 0.56/0.73 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2181])).
% 0.56/0.73 tff(2183,plain,
% 0.56/0.73 (~(op(e1, e3) = e2)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[1755, 2182])).
% 0.56/0.73 tff(2184,plain,
% 0.56/0.73 ((op(e0, e3) = e0) <=> (e2 = e0)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2169])).
% 0.56/0.73 tff(2185,plain,
% 0.56/0.73 ((op(e0, e3) = e0) <=> (e0 = e2)),
% 0.56/0.73 inference(transitivity,[status(thm)],[2184, 217])).
% 0.56/0.73 tff(2186,plain,
% 0.56/0.73 ((e0 = e2) <=> (op(e0, e3) = e0)),
% 0.56/0.73 inference(symmetry,[status(thm)],[2185])).
% 0.56/0.73 tff(2187,plain,
% 0.56/0.73 ((~(e0 = e2)) <=> (~(op(e0, e3) = e0))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2186])).
% 0.56/0.73 tff(2188,plain,
% 0.56/0.73 (~(op(e0, e3) = e0)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[238, 2187])).
% 0.56/0.73 tff(2189,plain,
% 0.56/0.73 (op(e0, e2) = e0),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[1357, 2188, 989, 1919])).
% 0.56/0.73 tff(2190,plain,
% 0.56/0.73 ((op(e0, e2) = op(e2, e2)) <=> (e0 = op(e2, e2))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2189])).
% 0.56/0.73 tff(2191,plain,
% 0.56/0.73 ((op(e0, e2) = op(e2, e2)) <=> (op(e2, e2) = e0)),
% 0.56/0.73 inference(transitivity,[status(thm)],[2190, 1275])).
% 0.56/0.73 tff(2192,plain,
% 0.56/0.73 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e0))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2191])).
% 0.56/0.73 tff(2193,plain,
% 0.56/0.73 (~(op(e2, e2) = e0)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[816, 2192])).
% 0.56/0.73 tff(2194,plain,
% 0.56/0.73 (op(e0, e0) = e3),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[1100, 2179, 989, 1819])).
% 0.56/0.73 tff(2195,plain,
% 0.56/0.73 (op(e0, op(e0, e0)) = op(e0, e3)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2194])).
% 0.56/0.73 tff(2196,plain,
% 0.56/0.73 (op(e0, op(e0, e0)) = e2),
% 0.56/0.73 inference(transitivity,[status(thm)],[2195, 2169])).
% 0.56/0.73 tff(2197,plain,
% 0.56/0.73 (op(op(e0, op(e0, e0)), op(e0, e0)) = op(e2, e3)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2196, 2194])).
% 0.56/0.73 tff(2198,plain,
% 0.56/0.73 ((e1 = op(op(e0, op(e0, e0)), op(e0, e0))) <=> (e1 = op(e2, e3))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2197])).
% 0.56/0.73 tff(2199,plain,
% 0.56/0.73 ((e1 = op(op(e0, op(e0, e0)), op(e0, e0))) <=> (op(e2, e3) = e1)),
% 0.56/0.73 inference(transitivity,[status(thm)],[2198, 73])).
% 0.56/0.73 tff(2200,plain,
% 0.56/0.73 ((~(e1 = op(op(e0, op(e0, e0)), op(e0, e0)))) <=> (~(op(e2, e3) = e1))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2199])).
% 0.56/0.73 tff(2201,plain,
% 0.56/0.73 ((e3 = op(e0, e0)) <=> (op(e0, e0) = e3)),
% 0.56/0.73 inference(commutativity,[status(thm)],[])).
% 0.56/0.73 tff(2202,plain,
% 0.56/0.73 ((op(e0, e0) = e3) <=> (e3 = op(e0, e0))),
% 0.56/0.73 inference(symmetry,[status(thm)],[2201])).
% 0.56/0.73 tff(2203,plain,
% 0.56/0.73 (e3 = op(e0, e0)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[2194, 2202])).
% 0.56/0.73 tff(2204,plain,
% 0.56/0.73 (op(e0, e3) = op(e0, op(e0, e0))),
% 0.56/0.73 inference(symmetry,[status(thm)],[2195])).
% 0.56/0.73 tff(2205,plain,
% 0.56/0.73 (e2 = op(e0, e3)),
% 0.56/0.73 inference(symmetry,[status(thm)],[2169])).
% 0.56/0.73 tff(2206,plain,
% 0.56/0.73 (e2 = op(e0, op(e0, e0))),
% 0.56/0.73 inference(transitivity,[status(thm)],[2205, 2204])).
% 0.56/0.73 tff(2207,plain,
% 0.56/0.73 ((~(~((~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(op(e0, op(e0, e0)), op(e0, e0))))))) <=> ((~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(op(e0, op(e0, e0)), op(e0, e0)))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(2208,plain,
% 0.56/0.73 (((e3 = op(e0, e0)) & (e2 = op(e0, op(e0, e0))) & (e1 = op(op(e0, op(e0, e0)), op(e0, e0)))) <=> (~((~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(op(e0, op(e0, e0)), op(e0, e0))))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(2209,plain,
% 0.56/0.73 ((~((e3 = op(e0, e0)) & (e2 = op(e0, op(e0, e0))) & (e1 = op(op(e0, op(e0, e0)), op(e0, e0))))) <=> (~(~((~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(op(e0, op(e0, e0)), op(e0, e0)))))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2208])).
% 0.56/0.73 tff(2210,plain,
% 0.56/0.73 ((~((e3 = op(e0, e0)) & (e2 = op(e0, op(e0, e0))) & (e1 = op(op(e0, op(e0, e0)), op(e0, e0))))) <=> ((~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(op(e0, op(e0, e0)), op(e0, e0)))))),
% 0.56/0.73 inference(transitivity,[status(thm)],[2209, 2207])).
% 0.56/0.73 tff(2211,plain,
% 0.56/0.73 ((~((e3 = op(e0, e0)) & (e2 = op(e0, op(e0, e0))) & (e1 = op(op(e0, op(e0, e0)), op(e0, e0))))) <=> (~((e3 = op(e0, e0)) & (e2 = op(e0, op(e0, e0))) & (e1 = op(op(e0, op(e0, e0)), op(e0, e0)))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(2212,plain,
% 0.56/0.73 ((~(((e3 = op(e0, e0)) & (e2 = op(e0, op(e0, e0)))) & (e1 = op(op(e0, op(e0, e0)), op(e0, e0))))) <=> (~((e3 = op(e0, e0)) & (e2 = op(e0, op(e0, e0))) & (e1 = op(op(e0, op(e0, e0)), op(e0, e0)))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(2213,axiom,(~(((e3 = op(e0, e0)) & (e2 = op(e0, op(e0, e0)))) & (e1 = op(op(e0, op(e0, e0)), op(e0, e0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax28')).
% 0.56/0.73 tff(2214,plain,
% 0.56/0.73 (~((e3 = op(e0, e0)) & (e2 = op(e0, op(e0, e0))) & (e1 = op(op(e0, op(e0, e0)), op(e0, e0))))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[2213, 2212])).
% 0.56/0.73 tff(2215,plain,
% 0.56/0.73 (~((e3 = op(e0, e0)) & (e2 = op(e0, op(e0, e0))) & (e1 = op(op(e0, op(e0, e0)), op(e0, e0))))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[2214, 2211])).
% 0.56/0.73 tff(2216,plain,
% 0.56/0.73 ((~(e3 = op(e0, e0))) | (~(e2 = op(e0, op(e0, e0)))) | (~(e1 = op(op(e0, op(e0, e0)), op(e0, e0))))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[2215, 2210])).
% 0.56/0.73 tff(2217,plain,
% 0.56/0.73 (~(e1 = op(op(e0, op(e0, e0)), op(e0, e0)))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[2216, 2206, 2203])).
% 0.56/0.73 tff(2218,plain,
% 0.56/0.73 (~(op(e2, e3) = e1)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[2217, 2200])).
% 0.56/0.73 tff(2219,plain,
% 0.56/0.73 ((op(e0, e3) = e3) <=> (e2 = e3)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2169])).
% 0.56/0.73 tff(2220,plain,
% 0.56/0.73 ((e2 = e3) <=> (op(e0, e3) = e3)),
% 0.56/0.73 inference(symmetry,[status(thm)],[2219])).
% 0.56/0.73 tff(2221,plain,
% 0.56/0.73 ((~(e2 = e3)) <=> (~(op(e0, e3) = e3))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2220])).
% 0.56/0.73 tff(2222,plain,
% 0.56/0.73 (~(op(e0, e3) = e3)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[462, 2221])).
% 0.56/0.73 tff(2223,plain,
% 0.56/0.73 ((op(e0, e2) = op(e3, e2)) <=> (e0 = op(e3, e2))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2189])).
% 0.56/0.73 tff(2224,plain,
% 0.56/0.73 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 0.56/0.73 inference(transitivity,[status(thm)],[2223, 271])).
% 0.56/0.73 tff(2225,plain,
% 0.56/0.73 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2224])).
% 0.56/0.73 tff(2226,plain,
% 0.56/0.73 (~(op(e3, e2) = e0)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[277, 2225])).
% 0.56/0.73 tff(2227,plain,
% 0.56/0.73 ((op(e0, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2169])).
% 0.56/0.73 tff(2228,plain,
% 0.56/0.73 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.56/0.73 inference(transitivity,[status(thm)],[2227, 72])).
% 0.56/0.73 tff(2229,plain,
% 0.56/0.73 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2228])).
% 0.56/0.73 tff(2230,plain,
% 0.56/0.73 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = op(e2, e3)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(2231,plain,
% 0.56/0.73 (~(op(e0, e3) = op(e2, e3))),
% 0.56/0.73 inference(and_elim,[status(thm)],[47])).
% 0.56/0.73 tff(2232,plain,
% 0.56/0.73 (~(op(e0, e3) = op(e2, e3))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[2231, 2230])).
% 0.56/0.73 tff(2233,plain,
% 0.56/0.73 (~(op(e2, e3) = e2)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[2232, 2229])).
% 0.56/0.73 tff(2234,plain,
% 0.56/0.73 ((op(e0, e2) = op(e1, e2)) <=> (e0 = op(e1, e2))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2189])).
% 0.56/0.73 tff(2235,plain,
% 0.56/0.73 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 0.56/0.73 inference(transitivity,[status(thm)],[2234, 1299])).
% 0.56/0.73 tff(2236,plain,
% 0.56/0.73 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e0))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2235])).
% 0.56/0.73 tff(2237,plain,
% 0.56/0.73 (~(op(e1, e2) = e0)),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[703, 2236])).
% 0.56/0.73 tff(2238,plain,
% 0.56/0.73 (op(e1, e0) = e2),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[757, 1699, 74, 1820])).
% 0.56/0.73 tff(2239,plain,
% 0.56/0.73 ((op(e1, e0) = e1) <=> (e2 = e1)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2238])).
% 0.56/0.73 tff(2240,plain,
% 0.56/0.73 ((op(e1, e0) = e1) <=> (e1 = e2)),
% 0.56/0.73 inference(transitivity,[status(thm)],[2239, 317])).
% 0.56/0.73 tff(2241,plain,
% 0.56/0.73 ((e1 = e2) <=> (op(e1, e0) = e1)),
% 0.56/0.73 inference(symmetry,[status(thm)],[2240])).
% 0.56/0.73 tff(2242,plain,
% 0.56/0.73 ((~(e1 = e2)) <=> (~(op(e1, e0) = e1))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[2241])).
% 0.56/0.74 tff(2243,plain,
% 0.56/0.74 (~(op(e1, e0) = e1)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[324, 2242])).
% 0.56/0.74 tff(2244,assumption,(~(op(e3, e2) = e0)), introduced(assumption)).
% 0.56/0.74 tff(2245,assumption,(~(op(e0, e3) = e3)), introduced(assumption)).
% 0.56/0.74 tff(2246,plain,
% 0.56/0.74 (op(e0, op(e1, e0)) = e0),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[83, 2108])).
% 0.56/0.74 tff(2247,plain,
% 0.56/0.74 (~(op(e1, e2) = e3)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[773, 2109, 767])).
% 0.56/0.74 tff(2248,plain,
% 0.56/0.74 (op(e3, e2) = e2),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[537, 1699, 75, 374])).
% 0.56/0.74 tff(2249,plain,
% 0.56/0.74 ((op(e1, e2) = op(e3, e2)) <=> (op(e1, e2) = e2)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2248])).
% 0.56/0.74 tff(2250,plain,
% 0.56/0.74 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e1, e2) = e2))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2249])).
% 0.56/0.74 tff(2251,plain,
% 0.56/0.74 (~(op(e1, e2) = e2)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[165, 2250])).
% 0.56/0.74 tff(2252,plain,
% 0.56/0.74 (op(e1, e0) = e2),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[757, 1699, 1820, 74])).
% 0.56/0.74 tff(2253,plain,
% 0.56/0.74 (e2 = op(e1, e0)),
% 0.56/0.74 inference(symmetry,[status(thm)],[2252])).
% 0.56/0.74 tff(2254,plain,
% 0.56/0.74 (op(e0, e2) = op(e0, op(e1, e0))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2253])).
% 0.56/0.74 tff(2255,plain,
% 0.56/0.74 (op(e0, e2) = e0),
% 0.56/0.74 inference(transitivity,[status(thm)],[2254, 1832])).
% 0.56/0.74 tff(2256,plain,
% 0.56/0.74 ((op(e0, e2) = op(e1, e2)) <=> (e0 = op(e1, e2))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2255])).
% 0.56/0.74 tff(2257,plain,
% 0.56/0.74 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e0)),
% 0.56/0.74 inference(transitivity,[status(thm)],[2256, 1299])).
% 0.56/0.74 tff(2258,plain,
% 0.56/0.74 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e0))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2257])).
% 0.56/0.74 tff(2259,plain,
% 0.56/0.74 (~(op(e1, e2) = e0)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[703, 2258])).
% 0.56/0.74 tff(2260,plain,
% 0.56/0.74 ($false),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[193, 2259, 2251, 168, 167])).
% 0.56/0.74 tff(2261,plain,((op(e3, e0) = e2) | (op(e1, e2) = e1) | (op(e1, e2) = e3) | (~(op(e0, op(e1, e0)) = e0)) | (op(e0, e0) = e2) | (op(e2, e0) = e2) | (op(e3, e3) = e2) | (op(e3, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.74 tff(2262,plain,
% 0.56/0.74 (op(e3, e0) = e2),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[2261, 168, 2247, 2246, 1820, 998, 75, 374])).
% 0.56/0.74 tff(2263,plain,
% 0.56/0.74 ((op(e1, e0) = op(e3, e0)) <=> (op(e1, e0) = e2)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2262])).
% 0.56/0.74 tff(2264,plain,
% 0.56/0.74 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e1, e0) = e2))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2263])).
% 0.56/0.74 tff(2265,plain,
% 0.56/0.74 (~(op(e1, e0) = e2)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[420, 2264])).
% 0.56/0.74 tff(2266,plain,
% 0.56/0.74 (op(e1, e2) = e2),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[135, 2265, 12, 107])).
% 0.56/0.74 tff(2267,plain,
% 0.56/0.74 (e2 = op(e1, e2)),
% 0.56/0.74 inference(symmetry,[status(thm)],[2266])).
% 0.56/0.74 tff(2268,plain,
% 0.56/0.74 (op(e2, e2) = op(e2, op(e1, e2))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2267])).
% 0.56/0.74 tff(2269,plain,
% 0.56/0.74 (op(e2, e2) = e2),
% 0.56/0.74 inference(transitivity,[status(thm)],[2268, 2109])).
% 0.56/0.74 tff(2270,plain,
% 0.56/0.74 ((op(e2, e1) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[992])).
% 0.56/0.74 tff(2271,plain,
% 0.56/0.74 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.56/0.74 inference(transitivity,[status(thm)],[2270, 810])).
% 0.56/0.74 tff(2272,plain,
% 0.56/0.74 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2271])).
% 0.56/0.74 tff(2273,plain,
% 0.56/0.74 (~(op(e2, e2) = e2)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[1710, 2272])).
% 0.56/0.74 tff(2274,plain,
% 0.56/0.74 ($false),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[2273, 2269])).
% 0.56/0.74 tff(2275,plain,((op(e1, e2) = e1) | (op(e1, e1) = e2) | (op(e1, e3) = e2) | (op(e0, e0) = e2) | (op(e3, e3) = e2) | (op(e3, e1) = e2) | (op(e2, e3) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (~((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3)))) | (~(op(e2, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.74 tff(2276,plain,
% 0.56/0.74 (op(e1, e2) = e1),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[2275, 374, 107, 1820, 75, 12, 767, 1221, 1222, 1704])).
% 0.56/0.74 tff(2277,plain,
% 0.56/0.74 ((op(e1, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2276])).
% 0.56/0.74 tff(2278,plain,
% 0.56/0.74 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 0.56/0.74 inference(transitivity,[status(thm)],[2277, 1949])).
% 0.56/0.74 tff(2279,plain,
% 0.56/0.74 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2278])).
% 0.56/0.74 tff(2280,plain,
% 0.56/0.74 (~(op(e2, e2) = e1)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[764, 2279])).
% 0.56/0.74 tff(2281,plain,
% 0.56/0.74 (op(e2, e2) = e3),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[513, 1711, 491, 2280])).
% 0.56/0.74 tff(2282,plain,
% 0.56/0.74 (op(e2, op(e2, e2)) = op(e2, e3)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2281])).
% 0.56/0.74 tff(2283,plain,
% 0.56/0.74 ((op(e2, op(e2, e2)) = e2) <=> (op(e2, e3) = e2)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2282])).
% 0.56/0.74 tff(2284,plain,
% 0.56/0.74 ((op(e2, e3) = e2) <=> (op(e2, op(e2, e2)) = e2)),
% 0.56/0.74 inference(symmetry,[status(thm)],[2283])).
% 0.56/0.74 tff(2285,plain,
% 0.56/0.74 ((~(op(e2, e3) = e2)) <=> (~(op(e2, op(e2, e2)) = e2))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2284])).
% 0.56/0.74 tff(2286,plain,
% 0.56/0.74 (~(op(e2, op(e2, e2)) = e2)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[767, 2285])).
% 0.56/0.74 tff(2287,plain,
% 0.56/0.74 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[473, 2286])).
% 0.56/0.74 tff(2288,plain,
% 0.56/0.74 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[681, 2287, 1221, 1222])).
% 0.56/0.74 tff(2289,plain,
% 0.56/0.74 (op(e3, op(e1, e3)) = e3),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[80, 2288])).
% 0.56/0.74 tff(2290,plain,
% 0.56/0.74 ((e3 = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.56/0.74 inference(commutativity,[status(thm)],[])).
% 0.56/0.74 tff(2291,plain,
% 0.56/0.74 ((op(e2, e2) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2281])).
% 0.56/0.74 tff(2292,plain,
% 0.56/0.74 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.56/0.74 inference(transitivity,[status(thm)],[2291, 2290])).
% 0.56/0.74 tff(2293,plain,
% 0.56/0.74 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2292])).
% 0.56/0.74 tff(2294,plain,
% 0.56/0.74 (~(op(e2, e3) = e3)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[153, 2293])).
% 0.56/0.74 tff(2295,plain,
% 0.56/0.74 ((op(e1, e2) = op(e1, e3)) <=> (e1 = op(e1, e3))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2276])).
% 0.56/0.74 tff(2296,plain,
% 0.56/0.74 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 0.56/0.74 inference(transitivity,[status(thm)],[2295, 831])).
% 0.56/0.74 tff(2297,plain,
% 0.56/0.74 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e3) = e1))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2296])).
% 0.56/0.74 tff(2298,plain,
% 0.56/0.74 (~(op(e1, e3) = e1)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[174, 2297])).
% 0.56/0.74 tff(2299,plain,
% 0.56/0.74 (op(e3, e3) = e1),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1872, 2298, 1722, 1864])).
% 0.56/0.74 tff(2300,plain,
% 0.56/0.74 ((op(e3, e3) = e3) <=> (e1 = e3)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2299])).
% 0.56/0.74 tff(2301,plain,
% 0.56/0.74 ((e1 = e3) <=> (op(e3, e3) = e3)),
% 0.56/0.74 inference(symmetry,[status(thm)],[2300])).
% 0.56/0.74 tff(2302,plain,
% 0.56/0.74 ((~(e1 = e3)) <=> (~(op(e3, e3) = e3))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2301])).
% 0.56/0.74 tff(2303,plain,
% 0.56/0.74 (~(op(e3, e3) = e3)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[591, 2302])).
% 0.56/0.74 tff(2304,plain,
% 0.56/0.74 (((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))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(2305,plain,
% 0.56/0.74 ((((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))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(2306,plain,
% 0.56/0.74 ((((op(e0, e3) = e3) | (op(e1, e3) = e3)) | (op(e2, e3) = e3)) <=> ((op(e0, e3) = e3) | (op(e1, e3) = e3) | (op(e2, e3) = e3))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(2307,plain,
% 0.56/0.74 (((((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))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2306])).
% 0.56/0.74 tff(2308,plain,
% 0.56/0.74 (((((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))),
% 0.56/0.74 inference(transitivity,[status(thm)],[2307, 2305])).
% 0.56/0.74 tff(2309,plain,
% 0.56/0.74 ((((op(e0, e3) = e3) | (op(e1, e3) = e3)) | (op(e2, e3) = e3)) | (op(e3, e3) = e3)),
% 0.56/0.74 inference(and_elim,[status(thm)],[113])).
% 0.56/0.74 tff(2310,plain,
% 0.56/0.74 ((op(e0, e3) = e3) | (op(e1, e3) = e3) | (op(e2, e3) = e3) | (op(e3, e3) = e3)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[2309, 2308])).
% 0.56/0.74 tff(2311,plain,
% 0.56/0.74 ((op(e0, e3) = e3) | (op(e1, e3) = e3) | (op(e2, e3) = e3) | (op(e3, e3) = e3)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[2310, 2304])).
% 0.56/0.74 tff(2312,plain,
% 0.56/0.74 (op(e1, e3) = e3),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[2311, 2303, 2245, 2294])).
% 0.56/0.74 tff(2313,plain,
% 0.56/0.74 (e3 = op(e1, e3)),
% 0.56/0.74 inference(symmetry,[status(thm)],[2312])).
% 0.56/0.74 tff(2314,plain,
% 0.56/0.74 (op(e3, e3) = op(e3, op(e1, e3))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2313])).
% 0.56/0.74 tff(2315,plain,
% 0.56/0.74 (e1 = op(e3, e3)),
% 0.56/0.74 inference(symmetry,[status(thm)],[2299])).
% 0.56/0.74 tff(2316,plain,
% 0.56/0.74 (e1 = e3),
% 0.56/0.74 inference(transitivity,[status(thm)],[2315, 2314, 2289])).
% 0.56/0.74 tff(2317,plain,
% 0.56/0.74 ($false),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[591, 2316])).
% 0.56/0.74 tff(2318,plain,((op(e3, e1) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (~((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3)))) | (op(e0, e3) = e3) | (op(e2, e3) = e2) | (op(e0, e3) = e1) | (op(e2, e3) = e1) | (op(e2, e2) = e0) | (op(e1, e3) = e2) | (op(e0, e0) = e2) | (op(e3, e3) = e2) | (op(e1, e1) = e2) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.74 tff(2319,plain,
% 0.56/0.74 (op(e3, e1) = e2),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[2318, 1934, 1221, 2245, 767, 1851, 1864, 491, 107, 1820, 75, 12, 830])).
% 0.56/0.74 tff(2320,plain,
% 0.56/0.74 ((op(e3, e1) = e0) <=> (e2 = e0)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2319])).
% 0.56/0.74 tff(2321,plain,
% 0.56/0.74 ((op(e3, e1) = e0) <=> (e0 = e2)),
% 0.56/0.74 inference(transitivity,[status(thm)],[2320, 217])).
% 0.56/0.74 tff(2322,plain,
% 0.56/0.74 ((e0 = e2) <=> (op(e3, e1) = e0)),
% 0.56/0.74 inference(symmetry,[status(thm)],[2321])).
% 0.56/0.74 tff(2323,plain,
% 0.56/0.74 ((~(e0 = e2)) <=> (~(op(e3, e1) = e0))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2322])).
% 0.56/0.74 tff(2324,plain,
% 0.56/0.74 (~(op(e3, e1) = e0)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[238, 2323])).
% 0.56/0.74 tff(2325,plain,
% 0.56/0.74 (op(e3, e0) = e0),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[295, 2324, 2244, 63])).
% 0.56/0.74 tff(2326,plain,
% 0.56/0.74 ((op(e3, e0) = e1) <=> (e0 = e1)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2325])).
% 0.56/0.74 tff(2327,plain,
% 0.56/0.74 ((e0 = e1) <=> (op(e3, e0) = e1)),
% 0.56/0.74 inference(symmetry,[status(thm)],[2326])).
% 0.56/0.74 tff(2328,plain,
% 0.56/0.74 ((~(e0 = e1)) <=> (~(op(e3, e0) = e1))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2327])).
% 0.56/0.74 tff(2329,plain,
% 0.56/0.74 (~(op(e3, e0) = e1)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[625, 2328])).
% 0.56/0.74 tff(2330,plain,
% 0.56/0.74 (op(e2, e0) = e1),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1423, 2329, 1819, 2243])).
% 0.56/0.74 tff(2331,plain,
% 0.56/0.74 (op(e0, op(e2, e0)) = op(e0, e1)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2330])).
% 0.56/0.74 tff(2332,plain,
% 0.56/0.74 (op(e0, op(e2, e0)) = e1),
% 0.56/0.74 inference(transitivity,[status(thm)],[2331, 1132])).
% 0.56/0.74 tff(2333,plain,
% 0.56/0.74 ((op(e0, op(e2, e0)) = e0) <=> (e1 = e0)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2332])).
% 0.56/0.74 tff(2334,plain,
% 0.56/0.74 ((op(e0, op(e2, e0)) = e0) <=> (e0 = e1)),
% 0.56/0.74 inference(transitivity,[status(thm)],[2333, 635])).
% 0.56/0.74 tff(2335,plain,
% 0.56/0.74 ((e0 = e1) <=> (op(e0, op(e2, e0)) = e0)),
% 0.56/0.74 inference(symmetry,[status(thm)],[2334])).
% 0.56/0.74 tff(2336,plain,
% 0.56/0.74 ((~(e0 = e1)) <=> (~(op(e0, op(e2, e0)) = e0))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2335])).
% 0.56/0.74 tff(2337,plain,
% 0.56/0.74 (~(op(e0, op(e2, e0)) = e0)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[625, 2336])).
% 0.56/0.74 tff(2338,plain,
% 0.56/0.74 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[967, 2337])).
% 0.56/0.74 tff(2339,plain,
% 0.56/0.74 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[681, 2338, 1221, 1934])).
% 0.56/0.74 tff(2340,plain,
% 0.56/0.74 (op(e2, op(e1, e2)) = e2),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[102, 2339])).
% 0.56/0.74 tff(2341,assumption,(~(op(e1, e2) = e0)), introduced(assumption)).
% 0.56/0.74 tff(2342,plain,
% 0.56/0.74 ((op(e1, e0) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2238])).
% 0.56/0.74 tff(2343,plain,
% 0.56/0.74 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 0.56/0.74 inference(transitivity,[status(thm)],[2342, 2081])).
% 0.56/0.74 tff(2344,plain,
% 0.56/0.74 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2343])).
% 0.56/0.74 tff(2345,plain,
% 0.56/0.74 (~(op(e1, e2) = e2)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[1428, 2344])).
% 0.56/0.74 tff(2346,plain,
% 0.56/0.74 (~(op(e1, e2) = e3)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[773, 2340, 767])).
% 0.56/0.74 tff(2347,plain,
% 0.56/0.74 (op(e1, e2) = e1),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[193, 2346, 2345, 2341])).
% 0.56/0.74 tff(2348,plain,
% 0.56/0.74 (e1 = op(e1, e2)),
% 0.56/0.74 inference(symmetry,[status(thm)],[2347])).
% 0.56/0.74 tff(2349,plain,
% 0.56/0.74 (op(e2, e1) = op(e2, op(e1, e2))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2348])).
% 0.56/0.74 tff(2350,plain,
% 0.56/0.74 (op(e2, e1) = e2),
% 0.56/0.74 inference(transitivity,[status(thm)],[2349, 2340])).
% 0.56/0.74 tff(2351,plain,
% 0.56/0.74 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e2)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2319])).
% 0.56/0.74 tff(2352,plain,
% 0.56/0.74 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e2))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2351])).
% 0.56/0.74 tff(2353,plain,
% 0.56/0.74 (~(op(e2, e1) = e2)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[576, 2352])).
% 0.56/0.74 tff(2354,plain,
% 0.56/0.74 ($false),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[2353, 2350])).
% 0.56/0.74 tff(2355,plain,((op(e3, e0) = e2) | (op(e1, e2) = e0) | (op(e2, e3) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (~(op(e0, e1) = e1)) | (op(e3, e2) = e0) | (op(e3, e3) = e0) | (op(e0, e3) = e3) | (op(e2, e3) = e1) | (op(e2, e2) = e0) | (op(e1, e3) = e2) | (op(e0, e0) = e2) | (op(e3, e3) = e2) | (op(e1, e1) = e2) | (op(e0, e1) = e2) | (op(e2, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.74 tff(2356,plain,
% 0.56/0.74 (op(e3, e0) = e2),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[2355, 2237, 2233, 1815, 1132, 2226, 63, 2222, 2218, 2193, 2183, 2179, 2173, 12, 830, 74])).
% 0.56/0.74 tff(2357,plain,
% 0.56/0.74 ((op(e3, e0) = e1) <=> (e2 = e1)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2356])).
% 0.56/0.74 tff(2358,plain,
% 0.56/0.74 ((op(e3, e0) = e1) <=> (e1 = e2)),
% 0.56/0.74 inference(transitivity,[status(thm)],[2357, 317])).
% 0.56/0.74 tff(2359,plain,
% 0.56/0.74 ((e1 = e2) <=> (op(e3, e0) = e1)),
% 0.56/0.74 inference(symmetry,[status(thm)],[2358])).
% 0.56/0.74 tff(2360,plain,
% 0.56/0.74 ((~(e1 = e2)) <=> (~(op(e3, e0) = e1))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2359])).
% 0.56/0.74 tff(2361,plain,
% 0.56/0.74 (~(op(e3, e0) = e1)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[324, 2360])).
% 0.56/0.74 tff(2362,plain,
% 0.56/0.74 ((op(e3, e0) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2356])).
% 0.56/0.74 tff(2363,plain,
% 0.56/0.74 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 0.56/0.74 inference(transitivity,[status(thm)],[2362, 326])).
% 0.56/0.74 tff(2364,plain,
% 0.56/0.74 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[2363])).
% 0.56/0.74 tff(2365,plain,
% 0.56/0.74 (~(op(e3, e1) = e2)),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[1333, 2364])).
% 0.56/0.74 tff(2366,plain,
% 0.56/0.74 (~((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3)))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[2318, 2365, 1815, 2222, 2233, 1851, 2218, 2193, 2183, 2179, 2173, 12, 830])).
% 0.56/0.74 tff(2367,plain,
% 0.56/0.74 (op(e3, e0) = e2),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[1713, 336, 75, 374, 12, 830])).
% 0.56/0.74 tff(2368,plain,
% 0.56/0.75 ((op(e3, e0) = e0) <=> (e2 = e0)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2367])).
% 0.56/0.75 tff(2369,plain,
% 0.56/0.75 ((op(e3, e0) = e0) <=> (e0 = e2)),
% 0.56/0.75 inference(transitivity,[status(thm)],[2368, 217])).
% 0.56/0.75 tff(2370,plain,
% 0.56/0.75 ((e0 = e2) <=> (op(e3, e0) = e0)),
% 0.56/0.75 inference(symmetry,[status(thm)],[2369])).
% 0.56/0.75 tff(2371,plain,
% 0.56/0.75 ((~(e0 = e2)) <=> (~(op(e3, e0) = e0))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2370])).
% 0.56/0.75 tff(2372,plain,
% 0.56/0.75 (~(op(e3, e0) = e0)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[238, 2371])).
% 0.56/0.75 tff(2373,plain,
% 0.56/0.75 (op(e3, e2) = e1),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[429, 352, 1414, 372])).
% 0.56/0.75 tff(2374,plain,
% 0.56/0.75 ((op(e3, e2) = e0) <=> (e1 = e0)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2373])).
% 0.56/0.75 tff(2375,plain,
% 0.56/0.75 ((op(e3, e2) = e0) <=> (e0 = e1)),
% 0.56/0.75 inference(transitivity,[status(thm)],[2374, 635])).
% 0.56/0.75 tff(2376,plain,
% 0.56/0.75 ((e0 = e1) <=> (op(e3, e2) = e0)),
% 0.56/0.75 inference(symmetry,[status(thm)],[2375])).
% 0.56/0.75 tff(2377,plain,
% 0.56/0.75 ((~(e0 = e1)) <=> (~(op(e3, e2) = e0))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2376])).
% 0.56/0.75 tff(2378,plain,
% 0.56/0.75 (~(op(e3, e2) = e0)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[625, 2377])).
% 0.56/0.75 tff(2379,plain,
% 0.56/0.75 (op(e3, e1) = e0),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[295, 2378, 2372, 63])).
% 0.56/0.75 tff(2380,plain,
% 0.56/0.75 (e0 = op(e3, e1)),
% 0.56/0.75 inference(symmetry,[status(thm)],[2379])).
% 0.56/0.75 tff(2381,plain,
% 0.56/0.75 (op(e1, e0) = op(e1, op(e3, e1))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2380])).
% 0.56/0.75 tff(2382,plain,
% 0.56/0.75 (op(e1, e0) = e1),
% 0.56/0.75 inference(transitivity,[status(thm)],[2381, 338])).
% 0.56/0.75 tff(2383,plain,
% 0.56/0.75 ($false),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[640, 2382])).
% 0.56/0.75 tff(2384,plain,(((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (op(e1, e0) = e1) | (op(e3, e3) = e0) | (op(e3, e0) = e1) | (op(e3, e3) = e2) | (op(e3, e1) = e2) | (op(e1, e1) = e2) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.75 tff(2385,plain,
% 0.56/0.75 (op(e1, e0) = e1),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[2384, 2366, 63, 2365, 2173, 2361, 12, 830])).
% 0.56/0.75 tff(2386,plain,
% 0.56/0.75 ((op(e1, e0) = op(e1, e3)) <=> (e1 = op(e1, e3))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2385])).
% 0.56/0.75 tff(2387,plain,
% 0.56/0.75 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 0.56/0.75 inference(transitivity,[status(thm)],[2386, 831])).
% 0.56/0.75 tff(2388,plain,
% 0.56/0.75 ((op(e1, e3) = e1) <=> (op(e1, e0) = op(e1, e3))),
% 0.56/0.75 inference(symmetry,[status(thm)],[2387])).
% 0.56/0.75 tff(2389,plain,
% 0.56/0.75 (op(e1, op(e3, e1)) = e1),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[337, 2366])).
% 0.56/0.75 tff(2390,plain,
% 0.56/0.75 (op(e3, op(e3, e3)) = e3),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[353, 2366])).
% 0.56/0.75 tff(2391,plain,
% 0.56/0.75 (~(op(e3, e3) = e1)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[371, 2390, 2389])).
% 0.56/0.75 tff(2392,plain,
% 0.56/0.75 (op(e1, e3) = e1),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1872, 2391, 1851, 2218])).
% 0.56/0.75 tff(2393,plain,
% 0.56/0.75 (op(e1, e0) = op(e1, e3)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[2392, 2388])).
% 0.56/0.75 tff(2394,plain,
% 0.56/0.75 ($false),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[224, 2393])).
% 0.56/0.75 tff(2395,plain,((op(e2, e0) = e2) | (op(e3, e3) = e0) | (op(e1, e1) = e2) | (op(e0, e1) = e2) | (~(op(e0, e1) = e1)) | (op(e0, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.75 tff(2396,plain,
% 0.56/0.75 (op(e2, e0) = e2),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[2395, 1132, 12, 830, 63, 989])).
% 0.56/0.75 tff(2397,plain,
% 0.56/0.75 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e2)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2396])).
% 0.56/0.75 tff(2398,plain,
% 0.56/0.75 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e2))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2397])).
% 0.56/0.75 tff(2399,plain,
% 0.56/0.75 (~(op(e1, e0) = e2)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[1206, 2398])).
% 0.56/0.75 tff(2400,plain,
% 0.56/0.75 ((op(e2, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2396])).
% 0.56/0.75 tff(2401,plain,
% 0.56/0.75 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 0.56/0.75 inference(transitivity,[status(thm)],[2400, 1223])).
% 0.56/0.75 tff(2402,plain,
% 0.56/0.75 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2401])).
% 0.56/0.75 tff(2403,plain,
% 0.56/0.75 (~(op(e3, e0) = e2)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[1229, 2402])).
% 0.56/0.75 tff(2404,plain,
% 0.56/0.75 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1719, 2403, 1132, 12, 830])).
% 0.56/0.75 tff(2405,plain,
% 0.56/0.75 ((op(e2, e0) = op(e2, e1)) <=> (e2 = op(e2, e1))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2396])).
% 0.56/0.75 tff(2406,plain,
% 0.56/0.75 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e1) = e2)),
% 0.56/0.75 inference(transitivity,[status(thm)],[2405, 13])).
% 0.56/0.75 tff(2407,plain,
% 0.56/0.75 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e1) = e2))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2406])).
% 0.56/0.75 tff(2408,plain,
% 0.56/0.75 (~(op(e2, e1) = e2)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[997, 2407])).
% 0.56/0.75 tff(2409,plain,
% 0.56/0.75 (op(e3, e1) = e2),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1018, 2408, 12, 830])).
% 0.56/0.75 tff(2410,plain,
% 0.56/0.75 ((op(e2, e0) = e1) <=> (e2 = e1)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2396])).
% 0.56/0.75 tff(2411,plain,
% 0.56/0.75 ((op(e2, e0) = e1) <=> (e1 = e2)),
% 0.56/0.75 inference(transitivity,[status(thm)],[2410, 317])).
% 0.56/0.75 tff(2412,plain,
% 0.56/0.75 ((e1 = e2) <=> (op(e2, e0) = e1)),
% 0.56/0.75 inference(symmetry,[status(thm)],[2411])).
% 0.56/0.75 tff(2413,plain,
% 0.56/0.75 ((~(e1 = e2)) <=> (~(op(e2, e0) = e1))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2412])).
% 0.56/0.75 tff(2414,plain,
% 0.56/0.75 (~(op(e2, e0) = e1)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[324, 2413])).
% 0.56/0.75 tff(2415,plain,
% 0.56/0.75 (~(op(e2, e3) = e1)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[2043, 472, 1146])).
% 0.56/0.75 tff(2416,plain,
% 0.56/0.75 ($false),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[964, 2415, 489, 1069, 1413])).
% 0.56/0.75 tff(2417,plain,(((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))) | (op(e2, e1) = e1) | (op(e2, e0) = e1) | (~(op(e3, e1) = e2)) | (op(e2, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.75 tff(2418,plain,
% 0.56/0.75 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[2417, 2036, 2414, 2409, 2408])).
% 0.56/0.75 tff(2419,plain,
% 0.56/0.75 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[681, 2418, 1815, 2404])).
% 0.56/0.75 tff(2420,plain,
% 0.56/0.75 (op(e2, op(e1, e2)) = e2),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[102, 2419])).
% 0.56/0.75 tff(2421,plain,
% 0.56/0.75 ((op(e2, e0) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2396])).
% 0.56/0.75 tff(2422,plain,
% 0.56/0.75 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.56/0.75 inference(transitivity,[status(thm)],[2421, 810])).
% 0.56/0.75 tff(2423,plain,
% 0.56/0.75 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2422])).
% 0.56/0.75 tff(2424,plain,
% 0.56/0.75 (~(op(e2, e2) = e2)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[1200, 2423])).
% 0.56/0.75 tff(2425,plain,
% 0.56/0.75 (~(op(e1, e2) = e2)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1269, 2424, 2420])).
% 0.56/0.75 tff(2426,plain,
% 0.56/0.75 (op(e1, e3) = e2),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[135, 2425, 12, 2399])).
% 0.56/0.75 tff(2427,plain,
% 0.56/0.75 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e2)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2396])).
% 0.56/0.75 tff(2428,plain,
% 0.56/0.75 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e2))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2427])).
% 0.56/0.75 tff(2429,plain,
% 0.56/0.75 (~(op(e0, e0) = e2)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[1827, 2428])).
% 0.56/0.75 tff(2430,plain,
% 0.56/0.75 (op(e0, e0) = e3),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1100, 2429, 989, 1819])).
% 0.56/0.75 tff(2431,plain,
% 0.56/0.75 ((op(e0, e0) = op(e1, e0)) <=> (e3 = op(e1, e0))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2430])).
% 0.56/0.75 tff(2432,plain,
% 0.56/0.75 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e3)),
% 0.56/0.75 inference(transitivity,[status(thm)],[2431, 2087])).
% 0.56/0.75 tff(2433,plain,
% 0.56/0.75 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e3))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2432])).
% 0.56/0.75 tff(2434,plain,
% 0.56/0.75 (~(op(e1, e0) = e3)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[1056, 2433])).
% 0.56/0.75 tff(2435,plain,
% 0.56/0.75 ((op(e2, e0) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2396])).
% 0.56/0.75 tff(2436,plain,
% 0.56/0.75 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.56/0.75 inference(transitivity,[status(thm)],[2435, 72])).
% 0.56/0.75 tff(2437,plain,
% 0.56/0.75 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2436])).
% 0.56/0.75 tff(2438,plain,
% 0.56/0.75 (~(op(e2, e3) = e2)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[979, 2437])).
% 0.56/0.75 tff(2439,plain,
% 0.56/0.75 (~(op(e1, e2) = e3)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[773, 2420, 2438])).
% 0.56/0.75 tff(2440,plain,
% 0.56/0.75 ((op(e1, e3) = e3) <=> (e2 = e3)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2426])).
% 0.56/0.75 tff(2441,plain,
% 0.56/0.75 ((e2 = e3) <=> (op(e1, e3) = e3)),
% 0.56/0.75 inference(symmetry,[status(thm)],[2440])).
% 0.56/0.75 tff(2442,plain,
% 0.56/0.75 ((~(e2 = e3)) <=> (~(op(e1, e3) = e3))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2441])).
% 0.56/0.75 tff(2443,plain,
% 0.56/0.75 (~(op(e1, e3) = e3)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[462, 2442])).
% 0.56/0.75 tff(2444,plain,
% 0.56/0.75 (op(e1, e1) = e3),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[2136, 2443, 2439, 2434])).
% 0.56/0.75 tff(2445,plain,
% 0.56/0.75 (op(e1, op(e1, e1)) = op(e1, e3)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2444])).
% 0.56/0.75 tff(2446,plain,
% 0.56/0.75 (op(e1, op(e1, e1)) = e1),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1315, 2419])).
% 0.56/0.75 tff(2447,plain,
% 0.56/0.75 (e1 = op(e1, op(e1, e1))),
% 0.56/0.75 inference(symmetry,[status(thm)],[2446])).
% 0.56/0.75 tff(2448,plain,
% 0.56/0.75 (e1 = e2),
% 0.56/0.75 inference(transitivity,[status(thm)],[2447, 2445, 2426])).
% 0.56/0.75 tff(2449,plain,
% 0.56/0.75 ($false),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[324, 2448])).
% 0.56/0.75 tff(2450,plain,((~(op(e0, e1) = e1)) | (op(e1, e1) = e2) | (op(e0, e1) = e2) | (op(e0, e0) = e0) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.75 tff(2451,plain,
% 0.56/0.75 (~(op(e0, e1) = e1)),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[2450, 830, 12, 989, 63])).
% 0.56/0.75 tff(2452,assumption,(~(op(e2, op(e0, e2)) = e2)), introduced(assumption)).
% 0.56/0.75 tff(2453,plain,
% 0.56/0.75 (op(e0, e3) = e1),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[718, 1139, 991, 433])).
% 0.56/0.75 tff(2454,plain,
% 0.56/0.75 ((op(e0, e3) = e2) <=> (e1 = e2)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2453])).
% 0.56/0.75 tff(2455,plain,
% 0.56/0.75 ((e1 = e2) <=> (op(e0, e3) = e2)),
% 0.56/0.75 inference(symmetry,[status(thm)],[2454])).
% 0.56/0.75 tff(2456,plain,
% 0.56/0.75 ((~(e1 = e2)) <=> (~(op(e0, e3) = e2))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2455])).
% 0.56/0.75 tff(2457,plain,
% 0.56/0.75 (~(op(e0, e3) = e2)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[324, 2456])).
% 0.56/0.75 tff(2458,assumption,(~(op(e0, op(e0, e0)) = e0)), introduced(assumption)).
% 0.56/0.75 tff(2459,plain,
% 0.56/0.75 ((op(e0, e3) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2453])).
% 0.56/0.75 tff(2460,plain,
% 0.56/0.75 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 0.56/0.75 inference(transitivity,[status(thm)],[2459, 76])).
% 0.56/0.75 tff(2461,plain,
% 0.56/0.75 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2460])).
% 0.56/0.75 tff(2462,plain,
% 0.56/0.75 (~(op(e3, e3) = e1)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[725, 2461])).
% 0.56/0.75 tff(2463,plain,
% 0.56/0.75 ((e3 = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 0.56/0.75 inference(commutativity,[status(thm)],[])).
% 0.56/0.75 tff(2464,plain,
% 0.56/0.75 ((op(e1, e1) = e3) <=> (e3 = op(e1, e1))),
% 0.56/0.75 inference(symmetry,[status(thm)],[2463])).
% 0.56/0.75 tff(2465,plain,
% 0.56/0.75 ((op(e0, e3) = e0) <=> (e1 = e0)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[1143])).
% 0.56/0.75 tff(2466,plain,
% 0.56/0.75 ((op(e0, e3) = e0) <=> (e0 = e1)),
% 0.56/0.75 inference(transitivity,[status(thm)],[2465, 635])).
% 0.56/0.75 tff(2467,plain,
% 0.56/0.75 ((e0 = e1) <=> (op(e0, e3) = e0)),
% 0.56/0.75 inference(symmetry,[status(thm)],[2466])).
% 0.56/0.75 tff(2468,plain,
% 0.56/0.75 ((~(e0 = e1)) <=> (~(op(e0, e3) = e0))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2467])).
% 0.56/0.75 tff(2469,plain,
% 0.56/0.75 (~(op(e0, e3) = e0)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[625, 2468])).
% 0.56/0.75 tff(2470,assumption,(op(e3, e3) = e3), introduced(assumption)).
% 0.56/0.75 tff(2471,plain,
% 0.56/0.75 (e3 = op(e3, e3)),
% 0.56/0.75 inference(symmetry,[status(thm)],[2470])).
% 0.56/0.75 tff(2472,plain,
% 0.56/0.75 ((e2 = e3) <=> (e2 = op(e3, e3))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2471])).
% 0.56/0.75 tff(2473,plain,
% 0.56/0.75 ((e2 = e3) <=> (op(e3, e3) = e2)),
% 0.56/0.75 inference(transitivity,[status(thm)],[2472, 1024])).
% 0.56/0.75 tff(2474,plain,
% 0.56/0.75 ((~(e2 = e3)) <=> (~(op(e3, e3) = e2))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2473])).
% 0.56/0.75 tff(2475,plain,
% 0.56/0.75 (~(op(e3, e3) = e2)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[462, 2474])).
% 0.56/0.75 tff(2476,plain,
% 0.56/0.75 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e3)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2470])).
% 0.56/0.75 tff(2477,plain,
% 0.56/0.75 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e3))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2476])).
% 0.56/0.75 tff(2478,plain,
% 0.56/0.75 (~(op(e1, e3) = e3)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[368, 2477])).
% 0.56/0.75 tff(2479,plain,
% 0.56/0.75 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e3)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2470])).
% 0.56/0.75 tff(2480,plain,
% 0.56/0.75 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e3))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2479])).
% 0.56/0.75 tff(2481,plain,
% 0.56/0.75 (~(op(e3, e0) = e3)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[257, 2480])).
% 0.56/0.75 tff(2482,plain,
% 0.56/0.75 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2470])).
% 0.56/0.75 tff(2483,plain,
% 0.56/0.75 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2482])).
% 0.56/0.75 tff(2484,plain,
% 0.56/0.75 (~(op(e3, e2) = e3)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[1111, 2483])).
% 0.56/0.75 tff(2485,plain,
% 0.56/0.75 ((op(e0, e3) = e2) <=> (e1 = e2)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[1143])).
% 0.56/0.75 tff(2486,plain,
% 0.56/0.75 ((e1 = e2) <=> (op(e0, e3) = e2)),
% 0.56/0.75 inference(symmetry,[status(thm)],[2485])).
% 0.56/0.75 tff(2487,plain,
% 0.56/0.75 ((~(e1 = e2)) <=> (~(op(e0, e3) = e2))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2486])).
% 0.56/0.75 tff(2488,plain,
% 0.56/0.75 (~(op(e0, e3) = e2)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[324, 2487])).
% 0.56/0.75 tff(2489,plain,
% 0.56/0.75 (op(e0, e0) = e3),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[1100, 1820, 989, 1139])).
% 0.56/0.75 tff(2490,plain,
% 0.56/0.75 (op(e0, op(e0, e0)) = op(e0, e3)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2489])).
% 0.56/0.75 tff(2491,plain,
% 0.56/0.75 (op(e0, op(e0, e0)) = e1),
% 0.56/0.75 inference(transitivity,[status(thm)],[2490, 1143])).
% 0.56/0.75 tff(2492,plain,
% 0.56/0.75 (op(op(e0, op(e0, e0)), op(e0, e0)) = op(e1, e3)),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2491, 2489])).
% 0.56/0.75 tff(2493,plain,
% 0.56/0.75 ((e2 = op(op(e0, op(e0, e0)), op(e0, e0))) <=> (e2 = op(e1, e3))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2492])).
% 0.56/0.75 tff(2494,plain,
% 0.56/0.75 ((e2 = op(op(e0, op(e0, e0)), op(e0, e0))) <=> (op(e1, e3) = e2)),
% 0.56/0.75 inference(transitivity,[status(thm)],[2493, 218])).
% 0.56/0.75 tff(2495,plain,
% 0.56/0.75 ((~(e2 = op(op(e0, op(e0, e0)), op(e0, e0)))) <=> (~(op(e1, e3) = e2))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2494])).
% 0.56/0.75 tff(2496,plain,
% 0.56/0.75 (e3 = op(e0, e0)),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[2489, 2202])).
% 0.56/0.75 tff(2497,plain,
% 0.56/0.75 (op(e0, e3) = op(e0, op(e0, e0))),
% 0.56/0.75 inference(symmetry,[status(thm)],[2490])).
% 0.56/0.75 tff(2498,plain,
% 0.56/0.75 (e1 = op(e0, op(e0, e0))),
% 0.56/0.75 inference(transitivity,[status(thm)],[1144, 2497])).
% 0.56/0.75 tff(2499,plain,
% 0.56/0.75 ((~(~((~(e3 = op(e0, e0))) | (~(e1 = op(e0, op(e0, e0)))) | (~(e2 = op(op(e0, op(e0, e0)), op(e0, e0))))))) <=> ((~(e3 = op(e0, e0))) | (~(e1 = op(e0, op(e0, e0)))) | (~(e2 = op(op(e0, op(e0, e0)), op(e0, e0)))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(2500,plain,
% 0.56/0.75 (((e3 = op(e0, e0)) & (e1 = op(e0, op(e0, e0))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0)))) <=> (~((~(e3 = op(e0, e0))) | (~(e1 = op(e0, op(e0, e0)))) | (~(e2 = op(op(e0, op(e0, e0)), op(e0, e0))))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(2501,plain,
% 0.56/0.75 ((~((e3 = op(e0, e0)) & (e1 = op(e0, op(e0, e0))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0))))) <=> (~(~((~(e3 = op(e0, e0))) | (~(e1 = op(e0, op(e0, e0)))) | (~(e2 = op(op(e0, op(e0, e0)), op(e0, e0)))))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[2500])).
% 0.56/0.75 tff(2502,plain,
% 0.56/0.75 ((~((e3 = op(e0, e0)) & (e1 = op(e0, op(e0, e0))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0))))) <=> ((~(e3 = op(e0, e0))) | (~(e1 = op(e0, op(e0, e0)))) | (~(e2 = op(op(e0, op(e0, e0)), op(e0, e0)))))),
% 0.56/0.75 inference(transitivity,[status(thm)],[2501, 2499])).
% 0.56/0.75 tff(2503,plain,
% 0.56/0.75 ((~((e3 = op(e0, e0)) & (e1 = op(e0, op(e0, e0))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0))))) <=> (~((e3 = op(e0, e0)) & (e1 = op(e0, op(e0, e0))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0)))))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(2504,plain,
% 0.56/0.76 ((~(((e3 = op(e0, e0)) & (e1 = op(e0, op(e0, e0)))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0))))) <=> (~((e3 = op(e0, e0)) & (e1 = op(e0, op(e0, e0))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0)))))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(2505,axiom,(~(((e3 = op(e0, e0)) & (e1 = op(e0, op(e0, e0)))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax26')).
% 0.56/0.76 tff(2506,plain,
% 0.56/0.76 (~((e3 = op(e0, e0)) & (e1 = op(e0, op(e0, e0))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0))))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[2505, 2504])).
% 0.56/0.76 tff(2507,plain,
% 0.56/0.76 (~((e3 = op(e0, e0)) & (e1 = op(e0, op(e0, e0))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0))))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[2506, 2503])).
% 0.56/0.76 tff(2508,plain,
% 0.56/0.76 ((~(e3 = op(e0, e0))) | (~(e1 = op(e0, op(e0, e0)))) | (~(e2 = op(op(e0, op(e0, e0)), op(e0, e0))))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[2507, 2502])).
% 0.56/0.76 tff(2509,plain,
% 0.56/0.76 (~(e2 = op(op(e0, op(e0, e0)), op(e0, e0)))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[2508, 2498, 2496])).
% 0.56/0.76 tff(2510,plain,
% 0.56/0.76 (~(op(e1, e3) = e2)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[2509, 2495])).
% 0.56/0.76 tff(2511,plain,
% 0.56/0.76 (op(e2, e3) = e2),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[147, 2510, 75, 2488])).
% 0.56/0.76 tff(2512,plain,
% 0.56/0.76 (op(e3, op(e2, e3)) = op(e3, e2)),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2511])).
% 0.56/0.76 tff(2513,plain,
% 0.56/0.76 ((op(e3, op(e2, e3)) = e3) <=> (op(e3, e2) = e3)),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2512])).
% 0.56/0.76 tff(2514,plain,
% 0.56/0.76 ((op(e3, e2) = e3) <=> (op(e3, op(e2, e3)) = e3)),
% 0.56/0.76 inference(symmetry,[status(thm)],[2513])).
% 0.56/0.76 tff(2515,plain,
% 0.56/0.76 ((~(op(e3, e2) = e3)) <=> (~(op(e3, op(e2, e3)) = e3))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2514])).
% 0.56/0.76 tff(2516,plain,
% 0.56/0.76 (~(op(e3, op(e2, e3)) = e3)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[1118, 2515])).
% 0.56/0.76 tff(2517,plain,
% 0.56/0.76 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[471, 2516])).
% 0.56/0.76 tff(2518,plain,
% 0.56/0.76 ((op(e0, e3) = op(e1, e3)) <=> (e1 = op(e1, e3))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[1143])).
% 0.56/0.76 tff(2519,plain,
% 0.56/0.76 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 0.56/0.76 inference(transitivity,[status(thm)],[2518, 831])).
% 0.56/0.76 tff(2520,plain,
% 0.56/0.76 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e1))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2519])).
% 0.56/0.76 tff(2521,plain,
% 0.56/0.76 (~(op(e1, e3) = e1)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[1755, 2520])).
% 0.56/0.76 tff(2522,assumption,(~(op(e1, e3) = e3)), introduced(assumption)).
% 0.56/0.76 tff(2523,plain,
% 0.56/0.76 (((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))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(2524,plain,
% 0.56/0.76 ((((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))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(2525,plain,
% 0.56/0.76 ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) <=> ((op(e1, e3) = e0) | (op(e1, e3) = e1) | (op(e1, e3) = e2))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(2526,plain,
% 0.56/0.76 (((((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))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2525])).
% 0.56/0.76 tff(2527,plain,
% 0.56/0.76 (((((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))),
% 0.56/0.76 inference(transitivity,[status(thm)],[2526, 2524])).
% 0.56/0.76 tff(2528,plain,
% 0.56/0.76 ((((op(e1, e3) = e0) | (op(e1, e3) = e1)) | (op(e1, e3) = e2)) | (op(e1, e3) = e3)),
% 0.56/0.76 inference(and_elim,[status(thm)],[189])).
% 0.56/0.76 tff(2529,plain,
% 0.56/0.76 ((op(e1, e3) = e0) | (op(e1, e3) = e1) | (op(e1, e3) = e2) | (op(e1, e3) = e3)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[2528, 2527])).
% 0.56/0.76 tff(2530,plain,
% 0.56/0.76 ((op(e1, e3) = e0) | (op(e1, e3) = e1) | (op(e1, e3) = e2) | (op(e1, e3) = e3)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[2529, 2523])).
% 0.56/0.76 tff(2531,plain,
% 0.56/0.76 (op(e1, e3) = e0),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[2530, 2510, 2522, 2521])).
% 0.56/0.76 tff(2532,plain,
% 0.56/0.76 (op(e3, op(e1, e3)) = op(e3, e0)),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2531])).
% 0.56/0.76 tff(2533,plain,
% 0.56/0.76 ((op(e3, op(e1, e3)) = e3) <=> (op(e3, e0) = e3)),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2532])).
% 0.56/0.76 tff(2534,plain,
% 0.56/0.76 ((op(e3, e0) = e3) <=> (op(e3, op(e1, e3)) = e3)),
% 0.56/0.76 inference(symmetry,[status(thm)],[2533])).
% 0.56/0.76 tff(2535,plain,
% 0.56/0.76 ((~(op(e3, e0) = e3)) <=> (~(op(e3, op(e1, e3)) = e3))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2534])).
% 0.56/0.76 tff(2536,assumption,(~(op(e3, e0) = e3)), introduced(assumption)).
% 0.56/0.76 tff(2537,plain,
% 0.56/0.76 (~(op(e3, op(e1, e3)) = e3)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[2536, 2535])).
% 0.56/0.76 tff(2538,plain,
% 0.56/0.76 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[80, 2537])).
% 0.56/0.76 tff(2539,plain,
% 0.56/0.76 (~((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3)))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[681, 2538, 1221, 2517])).
% 0.56/0.76 tff(2540,plain,
% 0.56/0.76 (op(e2, op(e3, e2)) = e2),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[335, 2539])).
% 0.56/0.76 tff(2541,plain,
% 0.56/0.76 (op(e0, e2) = e2),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[887, 1820, 830, 2488])).
% 0.56/0.76 tff(2542,plain,
% 0.56/0.76 ((op(e0, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2541])).
% 0.56/0.76 tff(2543,plain,
% 0.56/0.76 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.56/0.76 inference(transitivity,[status(thm)],[2542, 469])).
% 0.56/0.76 tff(2544,plain,
% 0.56/0.76 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2543])).
% 0.56/0.76 tff(2545,plain,
% 0.56/0.76 (~(op(e3, e2) = e2)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[277, 2544])).
% 0.56/0.76 tff(2546,plain,
% 0.56/0.76 ((op(e0, e2) = e0) <=> (e2 = e0)),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2541])).
% 0.56/0.76 tff(2547,plain,
% 0.56/0.76 ((op(e0, e2) = e0) <=> (e0 = e2)),
% 0.56/0.76 inference(transitivity,[status(thm)],[2546, 217])).
% 0.56/0.76 tff(2548,plain,
% 0.56/0.76 ((e0 = e2) <=> (op(e0, e2) = e0)),
% 0.56/0.76 inference(symmetry,[status(thm)],[2547])).
% 0.56/0.76 tff(2549,plain,
% 0.56/0.76 ((~(e0 = e2)) <=> (~(op(e0, e2) = e0))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2548])).
% 0.56/0.76 tff(2550,plain,
% 0.56/0.76 (~(op(e0, e2) = e0)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[238, 2549])).
% 0.56/0.76 tff(2551,plain,
% 0.56/0.76 (op(e0, e1) = e0),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[1357, 2550, 989, 2469])).
% 0.56/0.76 tff(2552,plain,
% 0.56/0.76 (op(e1, op(e0, e1)) = op(e1, e0)),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2551])).
% 0.56/0.76 tff(2553,plain,
% 0.56/0.76 ((op(e1, op(e0, e1)) = e1) <=> (op(e1, e0) = e1)),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2552])).
% 0.56/0.76 tff(2554,plain,
% 0.56/0.76 ((~(op(e1, op(e0, e1)) = e1)) <=> (~(op(e1, e0) = e1))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2553])).
% 0.56/0.76 tff(2555,plain,
% 0.56/0.76 (~(op(e1, e0) = e1)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[1814, 2554])).
% 0.56/0.76 tff(2556,plain,
% 0.56/0.76 (((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))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(2557,plain,
% 0.56/0.76 ((((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))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(2558,plain,
% 0.56/0.76 ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) <=> ((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(2559,plain,
% 0.56/0.76 (((((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))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2558])).
% 0.56/0.76 tff(2560,plain,
% 0.56/0.76 (((((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))),
% 0.56/0.76 inference(transitivity,[status(thm)],[2559, 2557])).
% 0.56/0.76 tff(2561,plain,
% 0.56/0.76 ((((op(e1, e0) = e1) | (op(e1, e1) = e1)) | (op(e1, e2) = e1)) | (op(e1, e3) = e1)),
% 0.56/0.76 inference(and_elim,[status(thm)],[615])).
% 0.56/0.76 tff(2562,plain,
% 0.56/0.76 ((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1) | (op(e1, e3) = e1)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[2561, 2560])).
% 0.56/0.76 tff(2563,plain,
% 0.56/0.76 ((op(e1, e0) = e1) | (op(e1, e1) = e1) | (op(e1, e2) = e1) | (op(e1, e3) = e1)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[2562, 2556])).
% 0.56/0.76 tff(2564,plain,
% 0.56/0.76 (op(e1, e2) = e1),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[2563, 2555, 2521, 1070])).
% 0.56/0.76 tff(2565,plain,
% 0.56/0.76 ((op(e1, e2) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2564])).
% 0.56/0.76 tff(2566,plain,
% 0.56/0.76 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.56/0.76 inference(transitivity,[status(thm)],[2565, 1618])).
% 0.56/0.76 tff(2567,plain,
% 0.56/0.76 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2566])).
% 0.56/0.76 tff(2568,plain,
% 0.56/0.76 (~(op(e3, e2) = e1)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[165, 2567])).
% 0.56/0.76 tff(2569,plain,
% 0.56/0.76 (((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))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(2570,plain,
% 0.56/0.76 ((((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))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(2571,plain,
% 0.56/0.76 ((((op(e3, e2) = e0) | (op(e3, e2) = e1)) | (op(e3, e2) = e2)) <=> ((op(e3, e2) = e0) | (op(e3, e2) = e1) | (op(e3, e2) = e2))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(2572,plain,
% 0.56/0.76 (((((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))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2571])).
% 0.56/0.76 tff(2573,plain,
% 0.56/0.76 (((((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))),
% 0.56/0.76 inference(transitivity,[status(thm)],[2572, 2570])).
% 0.56/0.76 tff(2574,plain,
% 0.56/0.76 ((((op(e3, e2) = e0) | (op(e3, e2) = e1)) | (op(e3, e2) = e2)) | (op(e3, e2) = e3)),
% 0.56/0.76 inference(and_elim,[status(thm)],[182])).
% 0.56/0.76 tff(2575,plain,
% 0.56/0.76 ((op(e3, e2) = e0) | (op(e3, e2) = e1) | (op(e3, e2) = e2) | (op(e3, e2) = e3)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[2574, 2573])).
% 0.56/0.76 tff(2576,plain,
% 0.56/0.76 ((op(e3, e2) = e0) | (op(e3, e2) = e1) | (op(e3, e2) = e2) | (op(e3, e2) = e3)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[2575, 2569])).
% 0.56/0.76 tff(2577,plain,
% 0.56/0.76 (op(e3, e2) = e0),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[2576, 2568, 1118, 2545])).
% 0.56/0.76 tff(2578,plain,
% 0.56/0.76 (e0 = op(e3, e2)),
% 0.56/0.76 inference(symmetry,[status(thm)],[2577])).
% 0.56/0.76 tff(2579,plain,
% 0.56/0.76 (op(e2, e0) = op(e2, op(e3, e2))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2578])).
% 0.56/0.76 tff(2580,plain,
% 0.56/0.76 (op(e2, e0) = e2),
% 0.56/0.76 inference(transitivity,[status(thm)],[2579, 2540])).
% 0.56/0.76 tff(2581,plain,
% 0.56/0.76 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e0) = e2)),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2511])).
% 0.56/0.76 tff(2582,plain,
% 0.56/0.76 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e0) = e2))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[2581])).
% 0.56/0.76 tff(2583,plain,
% 0.56/0.76 (~(op(e2, e0) = e2)),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[979, 2582])).
% 0.56/0.76 tff(2584,plain,
% 0.56/0.76 ($false),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[2583, 2580])).
% 0.56/0.76 tff(2585,plain,((op(e0, e0) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e3, e2) = e3) | (op(e3, e0) = e3) | (op(e1, e1) = e1) | (op(e1, e3) = e3) | (op(e3, e3) = e2) | (op(e1, op(e0, e1)) = e1) | (~(op(e0, e3) = e1)) | (op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.76 tff(2586,plain,
% 0.61/0.76 (op(e0, e0) = e2),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[2585, 2484, 1221, 2481, 1070, 2478, 2475, 1814, 1143, 989, 1139, 830])).
% 0.61/0.76 tff(2587,plain,
% 0.61/0.76 (op(e0, op(e0, e0)) = op(e0, e2)),
% 0.61/0.76 inference(monotonicity,[status(thm)],[2586])).
% 0.61/0.76 tff(2588,plain,
% 0.61/0.76 ((op(e0, op(e0, e0)) = e0) <=> (op(e0, e2) = e0)),
% 0.61/0.76 inference(monotonicity,[status(thm)],[2587])).
% 0.61/0.76 tff(2589,plain,
% 0.61/0.76 ((~(op(e0, op(e0, e0)) = e0)) <=> (~(op(e0, e2) = e0))),
% 0.61/0.76 inference(monotonicity,[status(thm)],[2588])).
% 0.61/0.76 tff(2590,plain,
% 0.61/0.76 (~(op(e0, e2) = e0)),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[2458, 2589])).
% 0.61/0.76 tff(2591,plain,
% 0.61/0.76 (op(e0, e1) = e0),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[1357, 2590, 989, 2469])).
% 0.61/0.76 tff(2592,plain,
% 0.61/0.76 ((op(e0, e1) = op(e1, e1)) <=> (e0 = op(e1, e1))),
% 0.61/0.76 inference(monotonicity,[status(thm)],[2591])).
% 0.61/0.76 tff(2593,plain,
% 0.61/0.76 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e0)),
% 0.61/0.76 inference(transitivity,[status(thm)],[2592, 1501])).
% 0.61/0.76 tff(2594,plain,
% 0.61/0.76 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e0))),
% 0.61/0.76 inference(monotonicity,[status(thm)],[2593])).
% 0.61/0.76 tff(2595,plain,
% 0.61/0.76 (~(op(e1, e1) = e0)),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[100, 2594])).
% 0.61/0.76 tff(2596,plain,
% 0.61/0.76 (((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))),
% 0.61/0.76 inference(rewrite,[status(thm)],[])).
% 0.61/0.76 tff(2597,plain,
% 0.61/0.76 ((((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))),
% 0.61/0.76 inference(rewrite,[status(thm)],[])).
% 0.61/0.76 tff(2598,plain,
% 0.61/0.76 ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) <=> ((op(e1, e1) = e0) | (op(e1, e1) = e1) | (op(e1, e1) = e2))),
% 0.61/0.76 inference(rewrite,[status(thm)],[])).
% 0.61/0.76 tff(2599,plain,
% 0.61/0.76 (((((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))),
% 0.61/0.76 inference(monotonicity,[status(thm)],[2598])).
% 0.61/0.76 tff(2600,plain,
% 0.61/0.76 (((((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))),
% 0.61/0.76 inference(transitivity,[status(thm)],[2599, 2597])).
% 0.61/0.76 tff(2601,plain,
% 0.61/0.76 ((((op(e1, e1) = e0) | (op(e1, e1) = e1)) | (op(e1, e1) = e2)) | (op(e1, e1) = e3)),
% 0.61/0.76 inference(and_elim,[status(thm)],[853])).
% 0.61/0.76 tff(2602,plain,
% 0.61/0.76 ((op(e1, e1) = e0) | (op(e1, e1) = e1) | (op(e1, e1) = e2) | (op(e1, e1) = e3)),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[2601, 2600])).
% 0.61/0.76 tff(2603,plain,
% 0.61/0.76 ((op(e1, e1) = e0) | (op(e1, e1) = e1) | (op(e1, e1) = e2) | (op(e1, e1) = e3)),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[2602, 2596])).
% 0.61/0.76 tff(2604,plain,
% 0.61/0.76 (op(e1, e1) = e3),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[2603, 2595, 12, 1070])).
% 0.61/0.76 tff(2605,plain,
% 0.61/0.76 (e3 = op(e1, e1)),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[2604, 2464])).
% 0.61/0.76 tff(2606,plain,
% 0.61/0.76 (op(e1, op(e1, e1)) = op(e1, e3)),
% 0.61/0.76 inference(monotonicity,[status(thm)],[2604])).
% 0.61/0.76 tff(2607,plain,
% 0.61/0.76 (op(e1, e3) = op(e1, op(e1, e1))),
% 0.61/0.76 inference(symmetry,[status(thm)],[2606])).
% 0.61/0.76 tff(2608,plain,
% 0.61/0.76 ((op(e0, e0) = op(e0, e2)) <=> (e2 = op(e0, e2))),
% 0.61/0.76 inference(monotonicity,[status(thm)],[2586])).
% 0.61/0.76 tff(2609,plain,
% 0.61/0.76 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e2)),
% 0.61/0.76 inference(transitivity,[status(thm)],[2608, 64])).
% 0.61/0.76 tff(2610,plain,
% 0.61/0.76 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e2))),
% 0.61/0.76 inference(monotonicity,[status(thm)],[2609])).
% 0.61/0.76 tff(2611,plain,
% 0.61/0.76 (~(op(e0, e2) = e2)),
% 0.61/0.76 inference(modus_ponens,[status(thm)],[1190, 2610])).
% 0.61/0.76 tff(2612,plain,
% 0.61/0.76 (op(e0, e2) = e3),
% 0.61/0.76 inference(unit_resolution,[status(thm)],[917, 2611, 2590, 991])).
% 0.61/0.76 tff(2613,plain,
% 0.61/0.76 (op(e2, op(e0, e2)) = op(e2, e3)),
% 0.61/0.76 inference(monotonicity,[status(thm)],[2612])).
% 0.61/0.76 tff(2614,plain,
% 0.61/0.76 ((op(e2, op(e0, e2)) = e2) <=> (op(e2, e3) = e2)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2613])).
% 0.61/0.77 tff(2615,plain,
% 0.61/0.77 ((~(op(e2, op(e0, e2)) = e2)) <=> (~(op(e2, e3) = e2))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2614])).
% 0.61/0.77 tff(2616,plain,
% 0.61/0.77 (~(op(e2, e3) = e2)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[2452, 2615])).
% 0.61/0.77 tff(2617,plain,
% 0.61/0.77 (op(e1, e3) = e2),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[147, 2616, 2475, 2488])).
% 0.61/0.77 tff(2618,plain,
% 0.61/0.77 (e2 = op(e1, e3)),
% 0.61/0.77 inference(symmetry,[status(thm)],[2617])).
% 0.61/0.77 tff(2619,plain,
% 0.61/0.77 (e2 = op(e1, op(e1, e1))),
% 0.61/0.77 inference(transitivity,[status(thm)],[2618, 2607])).
% 0.61/0.77 tff(2620,plain,
% 0.61/0.77 (op(e1, op(e1, e1)) = e2),
% 0.61/0.77 inference(transitivity,[status(thm)],[2606, 2617])).
% 0.61/0.77 tff(2621,plain,
% 0.61/0.77 (op(op(e1, op(e1, e1)), op(e1, e1)) = op(e2, e3)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2620, 2604])).
% 0.61/0.77 tff(2622,plain,
% 0.61/0.77 (op(e2, e3) = op(op(e1, op(e1, e1)), op(e1, e1))),
% 0.61/0.77 inference(symmetry,[status(thm)],[2621])).
% 0.61/0.77 tff(2623,plain,
% 0.61/0.77 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e3)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2470])).
% 0.61/0.77 tff(2624,plain,
% 0.61/0.77 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e3))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2623])).
% 0.61/0.77 tff(2625,plain,
% 0.61/0.77 (~(op(e2, e3) = e3)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[387, 2624])).
% 0.61/0.77 tff(2626,plain,
% 0.61/0.77 ((op(e0, e3) = op(e2, e3)) <=> (e1 = op(e2, e3))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[1143])).
% 0.61/0.77 tff(2627,plain,
% 0.61/0.77 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e1)),
% 0.61/0.77 inference(transitivity,[status(thm)],[2626, 73])).
% 0.61/0.77 tff(2628,plain,
% 0.61/0.77 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e1))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2627])).
% 0.61/0.77 tff(2629,plain,
% 0.61/0.77 (~(op(e2, e3) = e1)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[2232, 2628])).
% 0.61/0.77 tff(2630,plain,
% 0.61/0.77 (((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))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(2631,plain,
% 0.61/0.77 ((((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))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(2632,plain,
% 0.61/0.77 ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) <=> ((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(2633,plain,
% 0.61/0.77 (((((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))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2632])).
% 0.61/0.77 tff(2634,plain,
% 0.61/0.77 (((((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))),
% 0.61/0.77 inference(transitivity,[status(thm)],[2633, 2631])).
% 0.61/0.77 tff(2635,plain,
% 0.61/0.77 ((((op(e2, e3) = e0) | (op(e2, e3) = e1)) | (op(e2, e3) = e2)) | (op(e2, e3) = e3)),
% 0.61/0.77 inference(and_elim,[status(thm)],[185])).
% 0.61/0.77 tff(2636,plain,
% 0.61/0.77 ((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2) | (op(e2, e3) = e3)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[2635, 2634])).
% 0.61/0.77 tff(2637,plain,
% 0.61/0.77 ((op(e2, e3) = e0) | (op(e2, e3) = e1) | (op(e2, e3) = e2) | (op(e2, e3) = e3)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[2636, 2630])).
% 0.61/0.77 tff(2638,plain,
% 0.61/0.77 (op(e2, e3) = e0),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[2637, 2616, 2629, 2625])).
% 0.61/0.77 tff(2639,plain,
% 0.61/0.77 (e0 = op(e2, e3)),
% 0.61/0.77 inference(symmetry,[status(thm)],[2638])).
% 0.61/0.77 tff(2640,plain,
% 0.61/0.77 (e0 = op(op(e1, op(e1, e1)), op(e1, e1))),
% 0.61/0.77 inference(transitivity,[status(thm)],[2639, 2622])).
% 0.61/0.77 tff(2641,plain,
% 0.61/0.77 ((~(~((~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e0 = op(op(e1, op(e1, e1)), op(e1, e1))))))) <=> ((~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e0 = op(op(e1, op(e1, e1)), op(e1, e1)))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(2642,plain,
% 0.61/0.77 (((e3 = op(e1, e1)) & (e2 = op(e1, op(e1, e1))) & (e0 = op(op(e1, op(e1, e1)), op(e1, e1)))) <=> (~((~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e0 = op(op(e1, op(e1, e1)), op(e1, e1))))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(2643,plain,
% 0.61/0.77 ((~((e3 = op(e1, e1)) & (e2 = op(e1, op(e1, e1))) & (e0 = op(op(e1, op(e1, e1)), op(e1, e1))))) <=> (~(~((~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e0 = op(op(e1, op(e1, e1)), op(e1, e1)))))))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2642])).
% 0.61/0.77 tff(2644,plain,
% 0.61/0.77 ((~((e3 = op(e1, e1)) & (e2 = op(e1, op(e1, e1))) & (e0 = op(op(e1, op(e1, e1)), op(e1, e1))))) <=> ((~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e0 = op(op(e1, op(e1, e1)), op(e1, e1)))))),
% 0.61/0.77 inference(transitivity,[status(thm)],[2643, 2641])).
% 0.61/0.77 tff(2645,plain,
% 0.61/0.77 ((~((e3 = op(e1, e1)) & (e2 = op(e1, op(e1, e1))) & (e0 = op(op(e1, op(e1, e1)), op(e1, e1))))) <=> (~((e3 = op(e1, e1)) & (e2 = op(e1, op(e1, e1))) & (e0 = op(op(e1, op(e1, e1)), op(e1, e1)))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(2646,plain,
% 0.61/0.77 ((~(((e3 = op(e1, e1)) & (e2 = op(e1, op(e1, e1)))) & (e0 = op(op(e1, op(e1, e1)), op(e1, e1))))) <=> (~((e3 = op(e1, e1)) & (e2 = op(e1, op(e1, e1))) & (e0 = op(op(e1, op(e1, e1)), op(e1, e1)))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(2647,axiom,(~(((e3 = op(e1, e1)) & (e2 = op(e1, op(e1, e1)))) & (e0 = op(op(e1, op(e1, e1)), op(e1, e1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax29')).
% 0.61/0.77 tff(2648,plain,
% 0.61/0.77 (~((e3 = op(e1, e1)) & (e2 = op(e1, op(e1, e1))) & (e0 = op(op(e1, op(e1, e1)), op(e1, e1))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[2647, 2646])).
% 0.61/0.77 tff(2649,plain,
% 0.61/0.77 (~((e3 = op(e1, e1)) & (e2 = op(e1, op(e1, e1))) & (e0 = op(op(e1, op(e1, e1)), op(e1, e1))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[2648, 2645])).
% 0.61/0.77 tff(2650,plain,
% 0.61/0.77 ((~(e3 = op(e1, e1))) | (~(e2 = op(e1, op(e1, e1)))) | (~(e0 = op(op(e1, op(e1, e1)), op(e1, e1))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[2649, 2644])).
% 0.61/0.77 tff(2651,plain,
% 0.61/0.77 ($false),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[2650, 2640, 2619, 2605])).
% 0.61/0.77 tff(2652,plain,((~(op(e3, e3) = e3)) | (op(e1, e1) = e2) | (op(e1, e1) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e0, e0) = e0) | (op(e0, e2) = e1) | (op(e0, op(e0, e0)) = e0) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e1, op(e0, e1)) = e1) | (~(op(e0, e3) = e1)) | (op(e0, e0) = e1) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.77 tff(2653,plain,
% 0.61/0.77 (~(op(e3, e3) = e3)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[2652, 1070, 12, 2452, 989, 991, 2458, 1815, 1814, 2453, 1139, 830])).
% 0.61/0.77 tff(2654,plain,
% 0.61/0.77 (op(e3, e3) = e2),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[266, 2653, 63, 2462])).
% 0.61/0.77 tff(2655,plain,
% 0.61/0.77 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e2)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2654])).
% 0.61/0.77 tff(2656,plain,
% 0.61/0.77 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e2))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2655])).
% 0.61/0.77 tff(2657,plain,
% 0.61/0.77 (~(op(e3, e1) = e2)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[399, 2656])).
% 0.61/0.77 tff(2658,plain,
% 0.61/0.77 (op(e2, e1) = e2),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[1018, 2657, 12, 830])).
% 0.61/0.77 tff(2659,plain,
% 0.61/0.77 ((op(e0, e3) = op(e1, e3)) <=> (e1 = op(e1, e3))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2453])).
% 0.61/0.77 tff(2660,plain,
% 0.61/0.77 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 0.61/0.77 inference(transitivity,[status(thm)],[2659, 831])).
% 0.61/0.77 tff(2661,plain,
% 0.61/0.77 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e1))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2660])).
% 0.61/0.77 tff(2662,plain,
% 0.61/0.77 (~(op(e1, e3) = e1)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[1755, 2661])).
% 0.61/0.77 tff(2663,plain,
% 0.61/0.77 ((op(e0, e3) = e0) <=> (e1 = e0)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2453])).
% 0.61/0.77 tff(2664,plain,
% 0.61/0.77 ((op(e0, e3) = e0) <=> (e0 = e1)),
% 0.61/0.77 inference(transitivity,[status(thm)],[2663, 635])).
% 0.61/0.77 tff(2665,plain,
% 0.61/0.77 ((e0 = e1) <=> (op(e0, e3) = e0)),
% 0.61/0.77 inference(symmetry,[status(thm)],[2664])).
% 0.61/0.77 tff(2666,plain,
% 0.61/0.77 ((~(e0 = e1)) <=> (~(op(e0, e3) = e0))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2665])).
% 0.61/0.77 tff(2667,plain,
% 0.61/0.77 (~(op(e0, e3) = e0)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[625, 2666])).
% 0.61/0.77 tff(2668,assumption,(~(op(e3, e3) = e1)), introduced(assumption)).
% 0.61/0.77 tff(2669,plain,
% 0.61/0.77 (op(e3, e3) = e2),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[266, 797, 63, 2668])).
% 0.61/0.77 tff(2670,plain,
% 0.61/0.77 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e2)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2669])).
% 0.61/0.77 tff(2671,plain,
% 0.61/0.77 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e2))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2670])).
% 0.61/0.77 tff(2672,plain,
% 0.61/0.77 (~(op(e1, e3) = e2)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[368, 2671])).
% 0.61/0.77 tff(2673,plain,
% 0.61/0.77 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e2)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2669])).
% 0.61/0.77 tff(2674,plain,
% 0.61/0.77 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e2))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2673])).
% 0.61/0.77 tff(2675,plain,
% 0.61/0.77 (~(op(e3, e0) = e2)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[257, 2674])).
% 0.61/0.77 tff(2676,plain,
% 0.61/0.77 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e2)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2669])).
% 0.61/0.77 tff(2677,plain,
% 0.61/0.77 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e2))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2676])).
% 0.61/0.77 tff(2678,plain,
% 0.61/0.77 (~(op(e3, e1) = e2)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[399, 2677])).
% 0.61/0.77 tff(2679,plain,
% 0.61/0.77 (op(e2, e1) = e2),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[1018, 2678, 12, 830])).
% 0.61/0.77 tff(2680,plain,
% 0.61/0.77 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e0) = e2)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2679])).
% 0.61/0.77 tff(2681,plain,
% 0.61/0.77 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = e2))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2680])).
% 0.61/0.77 tff(2682,plain,
% 0.61/0.77 (~(op(e2, e0) = e2)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[997, 2681])).
% 0.61/0.77 tff(2683,assumption,(~(op(e3, e1) = e3)), introduced(assumption)).
% 0.61/0.77 tff(2684,plain,
% 0.61/0.77 ((op(e2, e1) = e1) <=> (e2 = e1)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2679])).
% 0.61/0.77 tff(2685,plain,
% 0.61/0.77 ((op(e2, e1) = e1) <=> (e1 = e2)),
% 0.61/0.77 inference(transitivity,[status(thm)],[2684, 317])).
% 0.61/0.77 tff(2686,plain,
% 0.61/0.77 ((e1 = e2) <=> (op(e2, e1) = e1)),
% 0.61/0.77 inference(symmetry,[status(thm)],[2685])).
% 0.61/0.77 tff(2687,plain,
% 0.61/0.77 ((~(e1 = e2)) <=> (~(op(e2, e1) = e1))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2686])).
% 0.61/0.77 tff(2688,plain,
% 0.61/0.77 (~(op(e2, e1) = e1)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[324, 2687])).
% 0.61/0.77 tff(2689,plain,
% 0.61/0.77 (op(e3, e1) = e1),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[450, 2688, 433, 1070])).
% 0.61/0.77 tff(2690,plain,
% 0.61/0.77 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e1)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2689])).
% 0.61/0.77 tff(2691,plain,
% 0.61/0.77 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e1))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2690])).
% 0.61/0.77 tff(2692,plain,
% 0.61/0.77 (~(op(e3, e0) = e1)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[1333, 2691])).
% 0.61/0.77 tff(2693,plain,
% 0.61/0.77 (~(op(e1, op(e3, e1)) = e1)),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[351, 2689])).
% 0.61/0.77 tff(2694,plain,
% 0.61/0.77 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[337, 2693])).
% 0.61/0.77 tff(2695,plain,
% 0.61/0.77 (op(e0, op(e1, e0)) = e2),
% 0.61/0.77 inference(transitivity,[status(thm)],[1831, 1829])).
% 0.61/0.77 tff(2696,plain,
% 0.61/0.77 ((op(e0, op(e1, e0)) = e0) <=> (e2 = e0)),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2695])).
% 0.61/0.77 tff(2697,plain,
% 0.61/0.77 ((op(e0, op(e1, e0)) = e0) <=> (e0 = e2)),
% 0.61/0.77 inference(transitivity,[status(thm)],[2696, 217])).
% 0.61/0.77 tff(2698,plain,
% 0.61/0.77 ((e0 = e2) <=> (op(e0, op(e1, e0)) = e0)),
% 0.61/0.77 inference(symmetry,[status(thm)],[2697])).
% 0.61/0.77 tff(2699,plain,
% 0.61/0.77 ((~(e0 = e2)) <=> (~(op(e0, op(e1, e0)) = e0))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2698])).
% 0.61/0.77 tff(2700,plain,
% 0.61/0.77 (~(op(e0, op(e1, e0)) = e0)),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[238, 2699])).
% 0.61/0.77 tff(2701,plain,
% 0.61/0.77 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[83, 2700])).
% 0.61/0.77 tff(2702,plain,
% 0.61/0.77 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[681, 2701, 1221, 1222])).
% 0.61/0.78 tff(2703,plain,
% 0.61/0.78 (op(e2, op(e2, e2)) = e2),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[473, 2702])).
% 0.61/0.78 tff(2704,plain,
% 0.61/0.78 ((op(e1, e0) = e1) <=> (e2 = e1)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[1830])).
% 0.61/0.78 tff(2705,plain,
% 0.61/0.78 ((op(e1, e0) = e1) <=> (e1 = e2)),
% 0.61/0.78 inference(transitivity,[status(thm)],[2704, 317])).
% 0.61/0.78 tff(2706,plain,
% 0.61/0.78 ((e1 = e2) <=> (op(e1, e0) = e1)),
% 0.61/0.78 inference(symmetry,[status(thm)],[2705])).
% 0.61/0.78 tff(2707,plain,
% 0.61/0.78 ((~(e1 = e2)) <=> (~(op(e1, e0) = e1))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2706])).
% 0.61/0.78 tff(2708,plain,
% 0.61/0.78 (~(op(e1, e0) = e1)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[324, 2707])).
% 0.61/0.78 tff(2709,plain,
% 0.61/0.78 (op(e1, e2) = e1),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[2563, 2708, 844, 1070])).
% 0.61/0.78 tff(2710,plain,
% 0.61/0.78 ((op(e1, e2) = e0) <=> (e1 = e0)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2709])).
% 0.61/0.78 tff(2711,plain,
% 0.61/0.78 ((op(e1, e2) = e0) <=> (e0 = e1)),
% 0.61/0.78 inference(transitivity,[status(thm)],[2710, 635])).
% 0.61/0.78 tff(2712,plain,
% 0.61/0.78 ((e0 = e1) <=> (op(e1, e2) = e0)),
% 0.61/0.78 inference(symmetry,[status(thm)],[2711])).
% 0.61/0.78 tff(2713,plain,
% 0.61/0.78 ((~(e0 = e1)) <=> (~(op(e1, e2) = e0))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2712])).
% 0.61/0.78 tff(2714,plain,
% 0.61/0.78 (~(op(e1, e2) = e0)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[625, 2713])).
% 0.61/0.78 tff(2715,plain,
% 0.61/0.78 ((e3 = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 0.61/0.78 inference(commutativity,[status(thm)],[])).
% 0.61/0.78 tff(2716,plain,
% 0.61/0.78 ((op(e0, e0) = op(e3, e0)) <=> (e3 = op(e3, e0))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2489])).
% 0.61/0.78 tff(2717,plain,
% 0.61/0.78 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 0.61/0.78 inference(transitivity,[status(thm)],[2716, 2715])).
% 0.61/0.78 tff(2718,plain,
% 0.61/0.78 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e3))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2717])).
% 0.61/0.78 tff(2719,plain,
% 0.61/0.78 (~(op(e3, e0) = e3)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[1638, 2718])).
% 0.61/0.78 tff(2720,plain,
% 0.61/0.78 (((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))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(2721,plain,
% 0.61/0.78 ((((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))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(2722,plain,
% 0.61/0.78 ((((op(e3, e0) = e3) | (op(e3, e1) = e3)) | (op(e3, e2) = e3)) <=> ((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(2723,plain,
% 0.61/0.78 (((((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))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2722])).
% 0.61/0.78 tff(2724,plain,
% 0.61/0.78 (((((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))),
% 0.61/0.78 inference(transitivity,[status(thm)],[2723, 2721])).
% 0.61/0.78 tff(2725,plain,
% 0.61/0.78 ((((op(e3, e0) = e3) | (op(e3, e1) = e3)) | (op(e3, e2) = e3)) | (op(e3, e3) = e3)),
% 0.61/0.78 inference(and_elim,[status(thm)],[114])).
% 0.61/0.78 tff(2726,plain,
% 0.61/0.78 ((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3) | (op(e3, e3) = e3)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[2725, 2724])).
% 0.61/0.78 tff(2727,plain,
% 0.61/0.78 ((op(e3, e0) = e3) | (op(e3, e1) = e3) | (op(e3, e2) = e3) | (op(e3, e3) = e3)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[2726, 2720])).
% 0.61/0.78 tff(2728,plain,
% 0.61/0.78 (op(e3, e2) = e3),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[2727, 2719, 797, 2683])).
% 0.61/0.78 tff(2729,plain,
% 0.61/0.78 ((op(e3, e2) = e0) <=> (e3 = e0)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2728])).
% 0.61/0.78 tff(2730,plain,
% 0.61/0.78 ((op(e3, e2) = e0) <=> (e0 = e3)),
% 0.61/0.78 inference(transitivity,[status(thm)],[2729, 279])).
% 0.61/0.78 tff(2731,plain,
% 0.61/0.78 ((e0 = e3) <=> (op(e3, e2) = e0)),
% 0.61/0.78 inference(symmetry,[status(thm)],[2730])).
% 0.61/0.78 tff(2732,plain,
% 0.61/0.78 ((~(e0 = e3)) <=> (~(op(e3, e2) = e0))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2731])).
% 0.61/0.78 tff(2733,plain,
% 0.61/0.78 (~(op(e3, e2) = e0)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[286, 2732])).
% 0.61/0.78 tff(2734,plain,
% 0.61/0.78 (((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))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(2735,plain,
% 0.61/0.78 ((((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))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(2736,plain,
% 0.61/0.78 ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) <=> ((op(e0, e2) = e0) | (op(e1, e2) = e0) | (op(e2, e2) = e0))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(2737,plain,
% 0.61/0.78 (((((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))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2736])).
% 0.61/0.78 tff(2738,plain,
% 0.61/0.78 (((((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))),
% 0.61/0.78 inference(transitivity,[status(thm)],[2737, 2735])).
% 0.61/0.78 tff(2739,plain,
% 0.61/0.78 ((((op(e0, e2) = e0) | (op(e1, e2) = e0)) | (op(e2, e2) = e0)) | (op(e3, e2) = e0)),
% 0.61/0.78 inference(and_elim,[status(thm)],[127])).
% 0.61/0.78 tff(2740,plain,
% 0.61/0.78 ((op(e0, e2) = e0) | (op(e1, e2) = e0) | (op(e2, e2) = e0) | (op(e3, e2) = e0)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[2739, 2738])).
% 0.61/0.78 tff(2741,plain,
% 0.61/0.78 ((op(e0, e2) = e0) | (op(e1, e2) = e0) | (op(e2, e2) = e0) | (op(e3, e2) = e0)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[2740, 2734])).
% 0.61/0.78 tff(2742,plain,
% 0.61/0.78 (op(e2, e2) = e0),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[2741, 2733, 2714, 1924])).
% 0.61/0.78 tff(2743,plain,
% 0.61/0.78 (e0 = op(e2, e2)),
% 0.61/0.78 inference(symmetry,[status(thm)],[2742])).
% 0.61/0.78 tff(2744,plain,
% 0.61/0.78 (op(e2, e0) = op(e2, op(e2, e2))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2743])).
% 0.61/0.78 tff(2745,plain,
% 0.61/0.78 (op(e2, e0) = e1),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[1423, 2708, 1414, 1139])).
% 0.61/0.78 tff(2746,plain,
% 0.61/0.78 (e1 = op(e2, e0)),
% 0.61/0.78 inference(symmetry,[status(thm)],[2745])).
% 0.61/0.78 tff(2747,plain,
% 0.61/0.78 (e1 = e2),
% 0.61/0.78 inference(transitivity,[status(thm)],[2746, 2744, 2703])).
% 0.61/0.78 tff(2748,plain,
% 0.61/0.78 ($false),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[324, 2747])).
% 0.61/0.78 tff(2749,plain,((op(e0, e0) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (~((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3)))) | (op(e3, e0) = e1) | (op(e0, e0) = e1) | (op(e1, e3) = e1) | (op(e1, e1) = e1) | (op(e3, e3) = e3) | (op(e3, e1) = e3) | (op(e2, e0) = e2) | (op(e3, e0) = e2) | (op(e0, e0) = e0) | (op(e0, e1) = e2) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.78 tff(2750,plain,
% 0.61/0.78 (op(e0, e0) = e2),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[2749, 2694, 1815, 2692, 1139, 844, 1070, 797, 2683, 2682, 2675, 989, 830, 104])).
% 0.61/0.78 tff(2751,plain,
% 0.61/0.78 ((op(e0, e0) = op(e1, e0)) <=> (e2 = op(e1, e0))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2750])).
% 0.61/0.78 tff(2752,plain,
% 0.61/0.78 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e2)),
% 0.61/0.78 inference(transitivity,[status(thm)],[2751, 1816])).
% 0.61/0.78 tff(2753,plain,
% 0.61/0.78 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e2))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2752])).
% 0.61/0.78 tff(2754,plain,
% 0.61/0.78 (~(op(e1, e0) = e2)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[1056, 2753])).
% 0.61/0.78 tff(2755,plain,
% 0.61/0.78 (op(e1, e2) = e2),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[135, 2754, 12, 2672])).
% 0.61/0.78 tff(2756,plain,
% 0.61/0.78 ((op(e1, e2) = e1) <=> (e2 = e1)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2755])).
% 0.61/0.78 tff(2757,plain,
% 0.61/0.78 ((op(e1, e2) = e1) <=> (e1 = e2)),
% 0.61/0.78 inference(transitivity,[status(thm)],[2756, 317])).
% 0.61/0.78 tff(2758,plain,
% 0.61/0.78 ((e1 = e2) <=> (op(e1, e2) = e1)),
% 0.61/0.78 inference(symmetry,[status(thm)],[2757])).
% 0.61/0.78 tff(2759,plain,
% 0.61/0.78 ((~(e1 = e2)) <=> (~(op(e1, e2) = e1))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2758])).
% 0.61/0.78 tff(2760,plain,
% 0.61/0.78 (~(op(e1, e2) = e1)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[324, 2759])).
% 0.61/0.78 tff(2761,assumption,(~(op(e0, e3) = e0)), introduced(assumption)).
% 0.61/0.78 tff(2762,plain,
% 0.61/0.78 (op(e0, op(e0, e0)) = op(e0, e2)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2750])).
% 0.61/0.78 tff(2763,plain,
% 0.61/0.78 ((op(e0, op(e0, e0)) = e0) <=> (op(e0, e2) = e0)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2762])).
% 0.61/0.78 tff(2764,plain,
% 0.61/0.78 ((~(op(e0, op(e0, e0)) = e0)) <=> (~(op(e0, e2) = e0))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2763])).
% 0.61/0.78 tff(2765,plain,
% 0.61/0.78 (~(op(e0, e2) = e0)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[2458, 2764])).
% 0.61/0.78 tff(2766,plain,
% 0.61/0.78 (op(e0, e1) = e0),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[1357, 2765, 989, 2761])).
% 0.61/0.78 tff(2767,plain,
% 0.61/0.78 (op(e1, op(e0, e1)) = op(e1, e0)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2766])).
% 0.61/0.78 tff(2768,plain,
% 0.61/0.78 ((op(e1, op(e0, e1)) = e1) <=> (op(e1, e0) = e1)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2767])).
% 0.61/0.78 tff(2769,plain,
% 0.61/0.78 ((~(op(e1, op(e0, e1)) = e1)) <=> (~(op(e1, e0) = e1))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2768])).
% 0.61/0.78 tff(2770,plain,
% 0.61/0.78 (~(op(e1, e0) = e1)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[1814, 2769])).
% 0.61/0.78 tff(2771,plain,
% 0.61/0.78 ($false),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[2563, 2770, 2760, 844, 1070])).
% 0.61/0.78 tff(2772,plain,((op(e3, e3) = e3) | (op(e1, e3) = e1) | (op(e1, e1) = e1) | (op(e1, op(e0, e1)) = e1) | (op(e0, e0) = e0) | (op(e0, e3) = e0) | (op(e1, e1) = e2) | (op(e0, op(e0, e0)) = e0) | (op(e0, e0) = e1) | (op(e3, e1) = e3) | (op(e0, e1) = e2) | (op(e0, e3) = e2) | (op(e0, e1) = e1) | (op(e3, e3) = e0) | (op(e3, e3) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.78 tff(2773,plain,
% 0.61/0.78 (op(e3, e1) = e3),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[2772, 2653, 1070, 1814, 989, 2667, 12, 2458, 1139, 2662, 830, 2457, 433, 63, 2462])).
% 0.61/0.78 tff(2774,plain,
% 0.61/0.78 ((op(e3, e1) = e1) <=> (e3 = e1)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2773])).
% 0.61/0.78 tff(2775,plain,
% 0.61/0.78 ((op(e3, e1) = e1) <=> (e1 = e3)),
% 0.61/0.78 inference(transitivity,[status(thm)],[2774, 951])).
% 0.61/0.78 tff(2776,plain,
% 0.61/0.78 ((e1 = e3) <=> (op(e3, e1) = e1)),
% 0.61/0.78 inference(symmetry,[status(thm)],[2775])).
% 0.61/0.78 tff(2777,plain,
% 0.61/0.78 ((~(e1 = e3)) <=> (~(op(e3, e1) = e1))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2776])).
% 0.61/0.78 tff(2778,plain,
% 0.61/0.78 (~(op(e3, e1) = e1)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[591, 2777])).
% 0.61/0.78 tff(2779,plain,
% 0.61/0.78 (op(e2, e1) = e1),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[450, 2778, 433, 1070])).
% 0.61/0.78 tff(2780,plain,
% 0.61/0.78 (e1 = op(e2, e1)),
% 0.61/0.78 inference(symmetry,[status(thm)],[2779])).
% 0.61/0.78 tff(2781,plain,
% 0.61/0.78 (e1 = e2),
% 0.61/0.78 inference(transitivity,[status(thm)],[2780, 2658])).
% 0.61/0.78 tff(2782,plain,
% 0.61/0.78 ($false),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[324, 2781])).
% 0.61/0.78 tff(2783,plain,((op(e1, e1) = e1) | (op(e0, e1) = e1) | (op(e1, e1) = e2) | (op(e0, e1) = e2) | (op(e1, op(e0, e1)) = e1) | (op(e0, e0) = e0) | (op(e0, op(e0, e0)) = e0) | (op(e0, e0) = e1) | (op(e3, e3) = e0) | (op(e2, op(e0, e2)) = e2) | (op(e0, e2) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.78 tff(2784,plain,
% 0.61/0.78 (op(e1, e1) = e1),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[2783, 2458, 12, 830, 1814, 989, 433, 1139, 63, 2452, 991])).
% 0.61/0.78 tff(2785,plain,
% 0.61/0.78 ((op(e1, e1) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2784])).
% 0.61/0.78 tff(2786,plain,
% 0.61/0.78 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 0.61/0.78 inference(transitivity,[status(thm)],[2785, 1587])).
% 0.61/0.78 tff(2787,plain,
% 0.61/0.78 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2786])).
% 0.61/0.78 tff(2788,plain,
% 0.61/0.78 (~(op(e1, e2) = e1)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[1616, 2787])).
% 0.61/0.78 tff(2789,plain,
% 0.61/0.78 (~(op(e3, e3) = e2)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[1987, 2788, 830, 2457, 1815, 12])).
% 0.61/0.78 tff(2790,plain,
% 0.61/0.78 ((op(e1, e1) = e3) <=> (e1 = e3)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2784])).
% 0.61/0.78 tff(2791,plain,
% 0.61/0.78 ((e1 = e3) <=> (op(e1, e1) = e3)),
% 0.61/0.78 inference(symmetry,[status(thm)],[2790])).
% 0.61/0.78 tff(2792,plain,
% 0.61/0.78 ((~(e1 = e3)) <=> (~(op(e1, e1) = e3))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2791])).
% 0.61/0.78 tff(2793,plain,
% 0.61/0.78 (~(op(e1, e1) = e3)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[591, 2792])).
% 0.61/0.78 tff(2794,plain,
% 0.61/0.78 (op(e3, e3) = e3),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[266, 2789, 63, 2462])).
% 0.61/0.78 tff(2795,plain,
% 0.61/0.78 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e3)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2794])).
% 0.61/0.78 tff(2796,plain,
% 0.61/0.78 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e3))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2795])).
% 0.61/0.78 tff(2797,plain,
% 0.61/0.78 (~(op(e1, e3) = e3)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[368, 2796])).
% 0.61/0.78 tff(2798,plain,
% 0.61/0.78 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e3)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2794])).
% 0.61/0.78 tff(2799,plain,
% 0.61/0.78 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e3))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2798])).
% 0.61/0.78 tff(2800,plain,
% 0.61/0.78 (~(op(e3, e1) = e3)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[399, 2799])).
% 0.61/0.78 tff(2801,plain,
% 0.61/0.78 ((op(e1, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2784])).
% 0.61/0.78 tff(2802,plain,
% 0.61/0.78 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 0.61/0.78 inference(transitivity,[status(thm)],[2801, 1640])).
% 0.61/0.78 tff(2803,plain,
% 0.61/0.78 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2802])).
% 0.61/0.78 tff(2804,plain,
% 0.61/0.78 (~(op(e3, e1) = e1)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[348, 2803])).
% 0.61/0.78 tff(2805,plain,
% 0.61/0.78 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e3)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2794])).
% 0.61/0.78 tff(2806,plain,
% 0.61/0.78 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e3))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2805])).
% 0.61/0.78 tff(2807,plain,
% 0.61/0.78 (~(op(e3, e0) = e3)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[257, 2806])).
% 0.61/0.78 tff(2808,assumption,(~(op(e1, e1) = e3)), introduced(assumption)).
% 0.61/0.78 tff(2809,plain,
% 0.61/0.78 ((e3 = op(e0, e1)) <=> (op(e0, e1) = e3)),
% 0.61/0.78 inference(commutativity,[status(thm)],[])).
% 0.61/0.78 tff(2810,plain,
% 0.61/0.78 ((op(e0, e0) = op(e0, e1)) <=> (e3 = op(e0, e1))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2489])).
% 0.61/0.78 tff(2811,plain,
% 0.61/0.78 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e1) = e3)),
% 0.61/0.78 inference(transitivity,[status(thm)],[2810, 2809])).
% 0.61/0.78 tff(2812,plain,
% 0.61/0.78 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e1) = e3))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2811])).
% 0.61/0.78 tff(2813,plain,
% 0.61/0.78 (~(op(e0, e1) = e3)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[745, 2812])).
% 0.61/0.78 tff(2814,plain,
% 0.61/0.78 (op(e2, e1) = e3),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[570, 2813, 2808, 2683])).
% 0.61/0.78 tff(2815,plain,
% 0.61/0.78 (op(e1, op(e2, e1)) = op(e1, e3)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2814])).
% 0.61/0.78 tff(2816,plain,
% 0.61/0.78 ((op(e1, op(e2, e1)) = e1) <=> (op(e1, e3) = e1)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2815])).
% 0.61/0.78 tff(2817,plain,
% 0.61/0.78 ((op(e1, e3) = e1) <=> (op(e1, op(e2, e1)) = e1)),
% 0.61/0.78 inference(symmetry,[status(thm)],[2816])).
% 0.61/0.78 tff(2818,plain,
% 0.61/0.78 ((~(op(e1, e3) = e1)) <=> (~(op(e1, op(e2, e1)) = e1))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2817])).
% 0.61/0.78 tff(2819,plain,
% 0.61/0.78 (~(op(e1, op(e2, e1)) = e1)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[2521, 2818])).
% 0.61/0.78 tff(2820,plain,
% 0.61/0.78 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[546, 2819])).
% 0.61/0.78 tff(2821,plain,
% 0.61/0.78 (e0 = op(e1, e3)),
% 0.61/0.78 inference(symmetry,[status(thm)],[2531])).
% 0.61/0.78 tff(2822,plain,
% 0.61/0.78 (op(e3, e0) = op(e3, op(e1, e3))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2821])).
% 0.61/0.78 tff(2823,plain,
% 0.61/0.78 (op(e3, op(e1, e3)) = op(e3, e0)),
% 0.61/0.78 inference(symmetry,[status(thm)],[2822])).
% 0.61/0.78 tff(2824,plain,
% 0.61/0.78 ((op(e3, op(e1, e3)) = e3) <=> (op(e3, e0) = e3)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2823])).
% 0.61/0.78 tff(2825,plain,
% 0.61/0.78 ((op(e3, e0) = e3) <=> (op(e3, op(e1, e3)) = e3)),
% 0.61/0.78 inference(symmetry,[status(thm)],[2824])).
% 0.61/0.78 tff(2826,plain,
% 0.61/0.78 ((~(op(e3, e0) = e3)) <=> (~(op(e3, op(e1, e3)) = e3))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2825])).
% 0.61/0.78 tff(2827,plain,
% 0.61/0.78 (~(op(e3, op(e1, e3)) = e3)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[2536, 2826])).
% 0.61/0.78 tff(2828,plain,
% 0.61/0.78 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[80, 2827])).
% 0.61/0.78 tff(2829,plain,
% 0.61/0.78 ((op(e0, e0) = op(e1, e0)) <=> (e3 = op(e1, e0))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2489])).
% 0.61/0.78 tff(2830,plain,
% 0.61/0.78 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e3)),
% 0.61/0.78 inference(transitivity,[status(thm)],[2829, 2087])).
% 0.61/0.78 tff(2831,plain,
% 0.61/0.78 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e3))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2830])).
% 0.61/0.78 tff(2832,plain,
% 0.61/0.78 (~(op(e1, e0) = e3)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[1056, 2831])).
% 0.61/0.78 tff(2833,plain,
% 0.61/0.78 (op(e1, e2) = e3),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[2136, 2832, 2808, 2522])).
% 0.61/0.78 tff(2834,plain,
% 0.61/0.78 ((e0 = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 0.61/0.78 inference(commutativity,[status(thm)],[])).
% 0.61/0.78 tff(2835,plain,
% 0.61/0.78 ((op(e0, e1) = op(e3, e1)) <=> (e0 = op(e3, e1))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2551])).
% 0.61/0.78 tff(2836,plain,
% 0.61/0.78 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 0.61/0.78 inference(transitivity,[status(thm)],[2835, 2834])).
% 0.61/0.78 tff(2837,plain,
% 0.61/0.78 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2836])).
% 0.61/0.78 tff(2838,plain,
% 0.61/0.78 (~(op(e3, e1) = e0)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[332, 2837])).
% 0.61/0.78 tff(2839,plain,
% 0.61/0.78 (op(e3, e1) = e2),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[408, 2838, 1068, 2683])).
% 0.61/0.78 tff(2840,plain,
% 0.61/0.78 (op(e1, op(e3, e1)) = op(e1, e2)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2839])).
% 0.61/0.78 tff(2841,plain,
% 0.61/0.78 (op(e1, op(e3, e1)) = e3),
% 0.61/0.78 inference(transitivity,[status(thm)],[2840, 2833])).
% 0.61/0.78 tff(2842,plain,
% 0.61/0.78 ((op(e1, op(e3, e1)) = e1) <=> (e3 = e1)),
% 0.61/0.78 inference(monotonicity,[status(thm)],[2841])).
% 0.61/0.78 tff(2843,plain,
% 0.61/0.78 ((op(e1, op(e3, e1)) = e1) <=> (e1 = e3)),
% 0.61/0.78 inference(transitivity,[status(thm)],[2842, 951])).
% 0.61/0.78 tff(2844,plain,
% 0.61/0.78 ((e1 = e3) <=> (op(e1, op(e3, e1)) = e1)),
% 0.61/0.78 inference(symmetry,[status(thm)],[2843])).
% 0.61/0.79 tff(2845,plain,
% 0.61/0.79 ((~(e1 = e3)) <=> (~(op(e1, op(e3, e1)) = e1))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2844])).
% 0.61/0.79 tff(2846,plain,
% 0.61/0.79 (~(op(e1, op(e3, e1)) = e1)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[591, 2845])).
% 0.61/0.79 tff(2847,plain,
% 0.61/0.79 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[337, 2846])).
% 0.61/0.79 tff(2848,plain,
% 0.61/0.79 ($false),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[681, 2847, 2828, 1221, 2820])).
% 0.61/0.79 tff(2849,plain,((op(e0, e0) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e3, e0) = e3) | (op(e3, e1) = e1) | (op(e3, e1) = e3) | (op(e1, e3) = e3) | (~(op(e0, e3) = e1)) | (op(e1, e1) = e3) | (op(e0, e0) = e0) | (op(e0, e0) = e1) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.79 tff(2850,plain,
% 0.61/0.79 (op(e0, e0) = e2),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[2849, 2807, 1815, 2804, 2800, 2797, 2453, 2793, 989, 1139, 830])).
% 0.61/0.79 tff(2851,plain,
% 0.61/0.79 (op(e0, op(e0, e0)) = op(e0, e2)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2850])).
% 0.61/0.79 tff(2852,plain,
% 0.61/0.79 ((op(e0, op(e0, e0)) = e0) <=> (op(e0, e2) = e0)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2851])).
% 0.61/0.79 tff(2853,plain,
% 0.61/0.79 ((~(op(e0, op(e0, e0)) = e0)) <=> (~(op(e0, e2) = e0))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2852])).
% 0.61/0.79 tff(2854,plain,
% 0.61/0.79 (~(op(e0, e2) = e0)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[2458, 2853])).
% 0.61/0.79 tff(2855,plain,
% 0.61/0.79 ((op(e0, e0) = op(e0, e2)) <=> (e2 = op(e0, e2))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2850])).
% 0.61/0.79 tff(2856,plain,
% 0.61/0.79 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e2)),
% 0.61/0.79 inference(transitivity,[status(thm)],[2855, 64])).
% 0.61/0.79 tff(2857,plain,
% 0.61/0.79 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e2))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2856])).
% 0.61/0.79 tff(2858,plain,
% 0.61/0.79 (~(op(e0, e2) = e2)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[1190, 2857])).
% 0.61/0.79 tff(2859,plain,
% 0.61/0.79 (op(e0, e2) = e3),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[917, 2858, 2854, 991])).
% 0.61/0.79 tff(2860,plain,
% 0.61/0.79 (op(e2, op(e0, e2)) = op(e2, e3)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2859])).
% 0.61/0.79 tff(2861,plain,
% 0.61/0.79 ((op(e2, op(e0, e2)) = e2) <=> (op(e2, e3) = e2)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2860])).
% 0.61/0.79 tff(2862,plain,
% 0.61/0.79 ((~(op(e2, op(e0, e2)) = e2)) <=> (~(op(e2, e3) = e2))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2861])).
% 0.61/0.79 tff(2863,plain,
% 0.61/0.79 (~(op(e2, e3) = e2)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[2452, 2862])).
% 0.61/0.79 tff(2864,plain,
% 0.61/0.79 (op(e1, e3) = e2),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[147, 2863, 2789, 2457])).
% 0.61/0.79 tff(2865,plain,
% 0.61/0.79 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e3)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2859])).
% 0.61/0.79 tff(2866,plain,
% 0.61/0.79 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e3))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2865])).
% 0.61/0.79 tff(2867,plain,
% 0.61/0.79 (~(op(e0, e1) = e3)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[70, 2866])).
% 0.61/0.79 tff(2868,plain,
% 0.61/0.79 (op(e2, e1) = e3),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[570, 2867, 2793, 2800])).
% 0.61/0.79 tff(2869,plain,
% 0.61/0.79 (op(e1, op(e2, e1)) = op(e1, e3)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2868])).
% 0.61/0.79 tff(2870,plain,
% 0.61/0.79 (op(e1, op(e2, e1)) = e2),
% 0.61/0.79 inference(transitivity,[status(thm)],[2869, 2864])).
% 0.61/0.79 tff(2871,plain,
% 0.61/0.79 ((op(e1, op(e2, e1)) = e1) <=> (e2 = e1)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2870])).
% 0.61/0.79 tff(2872,plain,
% 0.61/0.79 ((op(e1, op(e2, e1)) = e1) <=> (e1 = e2)),
% 0.61/0.79 inference(transitivity,[status(thm)],[2871, 317])).
% 0.61/0.79 tff(2873,plain,
% 0.61/0.79 ((e1 = e2) <=> (op(e1, op(e2, e1)) = e1)),
% 0.61/0.79 inference(symmetry,[status(thm)],[2872])).
% 0.61/0.79 tff(2874,plain,
% 0.61/0.79 ((~(e1 = e2)) <=> (~(op(e1, op(e2, e1)) = e1))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2873])).
% 0.61/0.79 tff(2875,plain,
% 0.61/0.79 (~(op(e1, op(e2, e1)) = e1)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[324, 2874])).
% 0.61/0.79 tff(2876,plain,
% 0.61/0.79 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[546, 2875])).
% 0.61/0.79 tff(2877,plain,
% 0.61/0.79 ((e3 = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 0.61/0.79 inference(commutativity,[status(thm)],[])).
% 0.61/0.79 tff(2878,plain,
% 0.61/0.79 ((op(e0, e2) = op(e1, e2)) <=> (e3 = op(e1, e2))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2859])).
% 0.61/0.79 tff(2879,plain,
% 0.61/0.79 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e3)),
% 0.61/0.79 inference(transitivity,[status(thm)],[2878, 2877])).
% 0.61/0.79 tff(2880,plain,
% 0.61/0.79 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e3))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2879])).
% 0.61/0.79 tff(2881,plain,
% 0.61/0.79 (~(op(e1, e2) = e3)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[703, 2880])).
% 0.61/0.79 tff(2882,plain,
% 0.61/0.79 (op(e1, e0) = e3),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[2136, 2881, 2793, 2797])).
% 0.61/0.79 tff(2883,plain,
% 0.61/0.79 (op(e0, op(e1, e0)) = op(e0, e3)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2882])).
% 0.61/0.79 tff(2884,plain,
% 0.61/0.79 (op(e0, op(e1, e0)) = e1),
% 0.61/0.79 inference(transitivity,[status(thm)],[2883, 2453])).
% 0.61/0.79 tff(2885,plain,
% 0.61/0.79 ((op(e0, op(e1, e0)) = e0) <=> (e1 = e0)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2884])).
% 0.61/0.79 tff(2886,plain,
% 0.61/0.79 ((op(e0, op(e1, e0)) = e0) <=> (e0 = e1)),
% 0.61/0.79 inference(transitivity,[status(thm)],[2885, 635])).
% 0.61/0.79 tff(2887,plain,
% 0.61/0.79 ((e0 = e1) <=> (op(e0, op(e1, e0)) = e0)),
% 0.61/0.79 inference(symmetry,[status(thm)],[2886])).
% 0.61/0.79 tff(2888,plain,
% 0.61/0.79 ((~(e0 = e1)) <=> (~(op(e0, op(e1, e0)) = e0))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2887])).
% 0.61/0.79 tff(2889,plain,
% 0.61/0.79 (~(op(e0, op(e1, e0)) = e0)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[625, 2888])).
% 0.61/0.79 tff(2890,plain,
% 0.61/0.79 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[83, 2889])).
% 0.61/0.79 tff(2891,plain,
% 0.61/0.79 (op(e0, e1) = e0),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1357, 2854, 989, 2667])).
% 0.61/0.79 tff(2892,plain,
% 0.61/0.79 ((op(e0, e1) = op(e3, e1)) <=> (e0 = op(e3, e1))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2891])).
% 0.61/0.79 tff(2893,plain,
% 0.61/0.79 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 0.61/0.79 inference(transitivity,[status(thm)],[2892, 2834])).
% 0.61/0.79 tff(2894,plain,
% 0.61/0.79 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2893])).
% 0.61/0.79 tff(2895,plain,
% 0.61/0.79 (~(op(e3, e1) = e0)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[332, 2894])).
% 0.61/0.79 tff(2896,plain,
% 0.61/0.79 (op(e3, e1) = e2),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[408, 2895, 2804, 2800])).
% 0.61/0.79 tff(2897,plain,
% 0.61/0.79 (op(e1, op(e3, e1)) = op(e1, e2)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2896])).
% 0.61/0.79 tff(2898,plain,
% 0.61/0.79 ((op(e1, op(e3, e1)) = e1) <=> (op(e1, e2) = e1)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2897])).
% 0.61/0.79 tff(2899,plain,
% 0.61/0.79 ((op(e1, e2) = e1) <=> (op(e1, op(e3, e1)) = e1)),
% 0.61/0.79 inference(symmetry,[status(thm)],[2898])).
% 0.61/0.79 tff(2900,plain,
% 0.61/0.79 ((~(op(e1, e2) = e1)) <=> (~(op(e1, op(e3, e1)) = e1))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2899])).
% 0.61/0.79 tff(2901,plain,
% 0.61/0.79 (~(op(e1, op(e3, e1)) = e1)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[2788, 2900])).
% 0.61/0.79 tff(2902,plain,
% 0.61/0.79 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[337, 2901])).
% 0.61/0.79 tff(2903,plain,
% 0.61/0.79 ($false),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[681, 2902, 2890, 1815, 2876])).
% 0.61/0.79 tff(2904,plain,((op(e0, op(e0, e0)) = e0) | (op(e2, op(e0, e2)) = e2) | (op(e0, e0) = e0) | (op(e0, e2) = e1) | (op(e0, e0) = e1) | (op(e0, e1) = e2) | (op(e3, e3) = e0) | (op(e1, e1) = e2) | (op(e1, op(e0, e1)) = e1) | (op(e0, e1) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.79 tff(2905,plain,
% 0.61/0.79 (op(e0, op(e0, e0)) = e0),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[2904, 1139, 989, 991, 2452, 830, 63, 12, 1814, 433])).
% 0.61/0.79 tff(2906,plain,
% 0.61/0.79 (~(op(e0, e0) = e3)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1553, 2453, 2905])).
% 0.61/0.79 tff(2907,plain,
% 0.61/0.79 (op(e0, e0) = e2),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1100, 2906, 989, 1139])).
% 0.61/0.79 tff(2908,plain,
% 0.61/0.79 ((op(e0, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2907])).
% 0.61/0.79 tff(2909,plain,
% 0.61/0.79 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 0.61/0.79 inference(transitivity,[status(thm)],[2908, 1223])).
% 0.61/0.79 tff(2910,plain,
% 0.61/0.79 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2909])).
% 0.61/0.79 tff(2911,plain,
% 0.61/0.79 (~(op(e3, e0) = e2)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[1638, 2910])).
% 0.61/0.79 tff(2912,plain,
% 0.61/0.79 ((op(e0, e3) = e3) <=> (e1 = e3)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2453])).
% 0.61/0.79 tff(2913,plain,
% 0.61/0.79 ((e1 = e3) <=> (op(e0, e3) = e3)),
% 0.61/0.79 inference(symmetry,[status(thm)],[2912])).
% 0.61/0.79 tff(2914,plain,
% 0.61/0.79 ((~(e1 = e3)) <=> (~(op(e0, e3) = e3))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2913])).
% 0.61/0.79 tff(2915,plain,
% 0.61/0.79 (~(op(e0, e3) = e3)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[591, 2914])).
% 0.61/0.79 tff(2916,plain,
% 0.61/0.79 (e2 = op(e0, e0)),
% 0.61/0.79 inference(symmetry,[status(thm)],[2907])).
% 0.61/0.79 tff(2917,plain,
% 0.61/0.79 (op(e0, e2) = op(e0, op(e0, e0))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2916])).
% 0.61/0.79 tff(2918,plain,
% 0.61/0.79 (op(e0, e2) = e0),
% 0.61/0.79 inference(transitivity,[status(thm)],[2917, 2905])).
% 0.61/0.79 tff(2919,plain,
% 0.61/0.79 ((op(e0, e2) = e3) <=> (e0 = e3)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2918])).
% 0.61/0.79 tff(2920,plain,
% 0.61/0.79 ((e0 = e3) <=> (op(e0, e2) = e3)),
% 0.61/0.79 inference(symmetry,[status(thm)],[2919])).
% 0.61/0.79 tff(2921,plain,
% 0.61/0.79 ((~(e0 = e3)) <=> (~(op(e0, e2) = e3))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2920])).
% 0.61/0.79 tff(2922,plain,
% 0.61/0.79 (~(op(e0, e2) = e3)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[286, 2921])).
% 0.61/0.79 tff(2923,plain,
% 0.61/0.79 (op(e0, e1) = e3),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1562, 2922, 2915, 2906])).
% 0.61/0.79 tff(2924,plain,
% 0.61/0.79 ((op(e0, e1) = op(e1, e1)) <=> (e3 = op(e1, e1))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2923])).
% 0.61/0.79 tff(2925,plain,
% 0.61/0.79 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e3)),
% 0.61/0.79 inference(transitivity,[status(thm)],[2924, 2463])).
% 0.61/0.79 tff(2926,plain,
% 0.61/0.79 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e3))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2925])).
% 0.61/0.79 tff(2927,plain,
% 0.61/0.79 (~(op(e1, e1) = e3)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[100, 2926])).
% 0.61/0.79 tff(2928,plain,
% 0.61/0.79 ((op(e0, e2) = op(e3, e2)) <=> (e0 = op(e3, e2))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2918])).
% 0.61/0.79 tff(2929,plain,
% 0.61/0.79 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e0)),
% 0.61/0.79 inference(transitivity,[status(thm)],[2928, 271])).
% 0.61/0.79 tff(2930,plain,
% 0.61/0.79 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e0))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2929])).
% 0.61/0.79 tff(2931,plain,
% 0.61/0.79 (~(op(e3, e2) = e0)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[277, 2930])).
% 0.61/0.79 tff(2932,assumption,(op(e1, e1) = e0), introduced(assumption)).
% 0.61/0.79 tff(2933,plain,
% 0.61/0.79 (e0 = op(e1, e1)),
% 0.61/0.79 inference(symmetry,[status(thm)],[2932])).
% 0.61/0.79 tff(2934,plain,
% 0.61/0.79 (op(e1, e0) = op(e1, op(e1, e1))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2933])).
% 0.61/0.79 tff(2935,plain,
% 0.61/0.79 (op(e1, op(e1, e1)) = op(e1, e0)),
% 0.61/0.79 inference(symmetry,[status(thm)],[2934])).
% 0.61/0.79 tff(2936,plain,
% 0.61/0.79 ((op(e1, e1) = op(e3, e1)) <=> (e0 = op(e3, e1))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2932])).
% 0.61/0.79 tff(2937,plain,
% 0.61/0.79 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e0)),
% 0.61/0.79 inference(transitivity,[status(thm)],[2936, 2834])).
% 0.61/0.79 tff(2938,plain,
% 0.61/0.79 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e0))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2937])).
% 0.61/0.79 tff(2939,plain,
% 0.61/0.79 (~(op(e3, e1) = e0)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[348, 2938])).
% 0.61/0.79 tff(2940,plain,
% 0.61/0.79 (op(e3, e0) = e0),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[295, 2939, 2244, 63])).
% 0.61/0.79 tff(2941,plain,
% 0.61/0.79 ((e0 = op(e1, e3)) <=> (op(e1, e3) = e0)),
% 0.61/0.79 inference(commutativity,[status(thm)],[])).
% 0.61/0.79 tff(2942,plain,
% 0.61/0.79 ((op(e1, e1) = op(e1, e3)) <=> (e0 = op(e1, e3))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2932])).
% 0.61/0.79 tff(2943,plain,
% 0.61/0.79 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e0)),
% 0.61/0.79 inference(transitivity,[status(thm)],[2942, 2941])).
% 0.61/0.79 tff(2944,plain,
% 0.61/0.79 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e0))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2943])).
% 0.61/0.79 tff(2945,plain,
% 0.61/0.79 (~(op(e1, e3) = e0)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[838, 2944])).
% 0.61/0.79 tff(2946,plain,
% 0.61/0.79 (op(e2, e3) = e0),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[247, 2945, 2761, 63])).
% 0.61/0.79 tff(2947,plain,
% 0.61/0.79 (op(e3, op(e2, e3)) = op(e3, e0)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2946])).
% 0.61/0.79 tff(2948,plain,
% 0.61/0.79 (op(e3, op(e2, e3)) = e0),
% 0.61/0.79 inference(transitivity,[status(thm)],[2947, 2940])).
% 0.61/0.79 tff(2949,plain,
% 0.61/0.79 ((op(e3, op(e2, e3)) = e3) <=> (e0 = e3)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2948])).
% 0.61/0.79 tff(2950,plain,
% 0.61/0.79 ((e0 = e3) <=> (op(e3, op(e2, e3)) = e3)),
% 0.61/0.79 inference(symmetry,[status(thm)],[2949])).
% 0.61/0.79 tff(2951,plain,
% 0.61/0.79 ((~(e0 = e3)) <=> (~(op(e3, op(e2, e3)) = e3))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2950])).
% 0.61/0.79 tff(2952,plain,
% 0.61/0.79 (~(op(e3, op(e2, e3)) = e3)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[286, 2951])).
% 0.61/0.79 tff(2953,plain,
% 0.61/0.79 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[471, 2952])).
% 0.61/0.79 tff(2954,assumption,(op(e0, e0) = e2), introduced(assumption)).
% 0.61/0.79 tff(2955,plain,
% 0.61/0.79 (op(e0, op(e3, e0)) = op(e0, e0)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2940])).
% 0.61/0.79 tff(2956,plain,
% 0.61/0.79 (op(e0, op(e3, e0)) = e2),
% 0.61/0.79 inference(transitivity,[status(thm)],[2955, 2954])).
% 0.61/0.79 tff(2957,plain,
% 0.61/0.79 ((op(e0, op(e3, e0)) = e0) <=> (e2 = e0)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2956])).
% 0.61/0.79 tff(2958,plain,
% 0.61/0.79 ((op(e0, op(e3, e0)) = e0) <=> (e0 = e2)),
% 0.61/0.79 inference(transitivity,[status(thm)],[2957, 217])).
% 0.61/0.79 tff(2959,plain,
% 0.61/0.79 ((e0 = e2) <=> (op(e0, op(e3, e0)) = e0)),
% 0.61/0.79 inference(symmetry,[status(thm)],[2958])).
% 0.61/0.79 tff(2960,plain,
% 0.61/0.79 ((~(e0 = e2)) <=> (~(op(e0, op(e3, e0)) = e0))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2959])).
% 0.61/0.79 tff(2961,plain,
% 0.61/0.79 (~(op(e0, op(e3, e0)) = e0)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[238, 2960])).
% 0.61/0.79 tff(2962,plain,
% 0.61/0.79 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1654, 2961])).
% 0.61/0.79 tff(2963,plain,
% 0.61/0.79 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[681, 2962, 1221, 2953])).
% 0.61/0.79 tff(2964,plain,
% 0.61/0.79 (op(e1, op(e1, e1)) = e1),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1315, 2963])).
% 0.61/0.79 tff(2965,plain,
% 0.61/0.79 (e1 = op(e1, op(e1, e1))),
% 0.61/0.79 inference(symmetry,[status(thm)],[2964])).
% 0.61/0.79 tff(2966,plain,
% 0.61/0.79 (e1 = op(e1, e0)),
% 0.61/0.79 inference(transitivity,[status(thm)],[2965, 2935])).
% 0.61/0.79 tff(2967,plain,
% 0.61/0.79 (op(e0, e1) = op(e0, op(e1, e0))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2966])).
% 0.61/0.79 tff(2968,plain,
% 0.61/0.79 (op(e0, op(e1, e0)) = op(e0, e1)),
% 0.61/0.79 inference(symmetry,[status(thm)],[2967])).
% 0.61/0.79 tff(2969,plain,
% 0.61/0.79 (op(e0, op(e1, e0)) = e0),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[83, 2963])).
% 0.61/0.79 tff(2970,plain,
% 0.61/0.79 (e0 = op(e0, op(e1, e0))),
% 0.61/0.79 inference(symmetry,[status(thm)],[2969])).
% 0.61/0.79 tff(2971,plain,
% 0.61/0.79 (e0 = e3),
% 0.61/0.79 inference(transitivity,[status(thm)],[2970, 2968, 840])).
% 0.61/0.79 tff(2972,plain,
% 0.61/0.79 ($false),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[286, 2971])).
% 0.61/0.79 tff(2973,plain,((~(op(e1, e1) = e0)) | (~(op(e0, e1) = e3)) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (~(op(e0, e0) = e2)) | (op(e0, e3) = e0) | (op(e3, e3) = e0) | (op(e3, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.79 tff(2974,plain,
% 0.61/0.79 (~(op(e1, e1) = e0)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[2973, 2923, 1815, 2907, 2667, 63, 2931])).
% 0.61/0.79 tff(2975,plain,
% 0.61/0.79 (op(e1, e1) = e1),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[2603, 2974, 12, 2927])).
% 0.61/0.79 tff(2976,plain,
% 0.61/0.79 ((op(e1, e1) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2975])).
% 0.61/0.79 tff(2977,plain,
% 0.61/0.79 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 0.61/0.79 inference(transitivity,[status(thm)],[2976, 1587])).
% 0.61/0.79 tff(2978,plain,
% 0.61/0.79 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2977])).
% 0.61/0.79 tff(2979,plain,
% 0.61/0.79 (~(op(e1, e2) = e1)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[1616, 2978])).
% 0.61/0.79 tff(2980,plain,
% 0.61/0.79 (~(op(e3, e3) = e2)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1987, 2979, 830, 2457, 1815, 12])).
% 0.61/0.79 tff(2981,plain,
% 0.61/0.79 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[1994, 2979, 2980, 2911, 12, 830])).
% 0.61/0.79 tff(2982,plain,
% 0.61/0.79 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e1) = e0)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2918])).
% 0.61/0.79 tff(2983,plain,
% 0.61/0.79 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e1) = e0))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2982])).
% 0.61/0.79 tff(2984,plain,
% 0.61/0.79 (~(op(e0, e1) = e0)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[70, 2983])).
% 0.61/0.79 tff(2985,plain,
% 0.61/0.79 (op(e3, e1) = e2),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[2011, 2457, 1815, 2979, 2911, 12, 830])).
% 0.61/0.79 tff(2986,plain,
% 0.61/0.79 ((op(e3, e1) = e0) <=> (e2 = e0)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2985])).
% 0.61/0.79 tff(2987,plain,
% 0.61/0.79 ((op(e3, e1) = e0) <=> (e0 = e2)),
% 0.61/0.79 inference(transitivity,[status(thm)],[2986, 217])).
% 0.61/0.79 tff(2988,plain,
% 0.61/0.79 ((e0 = e2) <=> (op(e3, e1) = e0)),
% 0.61/0.79 inference(symmetry,[status(thm)],[2987])).
% 0.61/0.79 tff(2989,plain,
% 0.61/0.79 ((~(e0 = e2)) <=> (~(op(e3, e1) = e0))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2988])).
% 0.61/0.79 tff(2990,plain,
% 0.61/0.79 (~(op(e3, e1) = e0)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[238, 2989])).
% 0.61/0.79 tff(2991,plain,
% 0.61/0.79 (op(e2, e1) = e0),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[619, 2990, 2984, 2974])).
% 0.61/0.79 tff(2992,plain,
% 0.61/0.79 (op(e1, op(e2, e1)) = op(e1, e0)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2991])).
% 0.61/0.79 tff(2993,plain,
% 0.61/0.79 ((op(e1, op(e2, e1)) = e1) <=> (op(e1, e0) = e1)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2992])).
% 0.61/0.79 tff(2994,plain,
% 0.61/0.79 ((op(e1, e0) = e1) <=> (op(e1, op(e2, e1)) = e1)),
% 0.61/0.79 inference(symmetry,[status(thm)],[2993])).
% 0.61/0.79 tff(2995,plain,
% 0.61/0.79 ((~(op(e1, e0) = e1)) <=> (~(op(e1, op(e2, e1)) = e1))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2994])).
% 0.61/0.79 tff(2996,plain,
% 0.61/0.79 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e1)),
% 0.61/0.79 inference(monotonicity,[status(thm)],[2975])).
% 0.61/0.80 tff(2997,plain,
% 0.61/0.80 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e1))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[2996])).
% 0.61/0.80 tff(2998,plain,
% 0.61/0.80 (~(op(e1, e0) = e1)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[440, 2997])).
% 0.61/0.80 tff(2999,plain,
% 0.61/0.80 (~(op(e1, op(e2, e1)) = e1)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[2998, 2995])).
% 0.61/0.80 tff(3000,plain,
% 0.61/0.80 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[546, 2999])).
% 0.61/0.80 tff(3001,plain,
% 0.61/0.80 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[681, 3000, 1815, 2981])).
% 0.61/0.80 tff(3002,plain,
% 0.61/0.80 (op(e3, op(e1, e3)) = e3),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[80, 3001])).
% 0.61/0.80 tff(3003,plain,
% 0.61/0.80 ((op(e2, e1) = op(e2, e3)) <=> (e0 = op(e2, e3))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[2991])).
% 0.61/0.80 tff(3004,plain,
% 0.61/0.80 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 0.61/0.80 inference(transitivity,[status(thm)],[3003, 1248])).
% 0.61/0.80 tff(3005,plain,
% 0.61/0.80 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3004])).
% 0.61/0.80 tff(3006,plain,
% 0.61/0.80 (~(op(e2, e3) = e0)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[1005, 3005])).
% 0.61/0.80 tff(3007,plain,
% 0.61/0.80 (op(e1, e3) = e0),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[247, 3006, 2667, 63])).
% 0.61/0.80 tff(3008,plain,
% 0.61/0.80 (op(e3, op(e1, e3)) = op(e3, e0)),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3007])).
% 0.61/0.80 tff(3009,plain,
% 0.61/0.80 (op(e3, e0) = op(e3, op(e1, e3))),
% 0.61/0.80 inference(symmetry,[status(thm)],[3008])).
% 0.61/0.80 tff(3010,plain,
% 0.61/0.80 (op(e3, e0) = e0),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[295, 2990, 2931, 63])).
% 0.61/0.80 tff(3011,plain,
% 0.61/0.80 (e0 = op(e3, e0)),
% 0.61/0.80 inference(symmetry,[status(thm)],[3010])).
% 0.61/0.80 tff(3012,plain,
% 0.61/0.80 (e0 = e3),
% 0.61/0.80 inference(transitivity,[status(thm)],[3011, 3009, 3002])).
% 0.61/0.80 tff(3013,plain,
% 0.61/0.80 ($false),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[286, 3012])).
% 0.61/0.80 tff(3014,plain,((op(e0, e0) = e1) | (op(e3, e3) = e0) | (op(e1, e1) = e2) | (op(e0, e1) = e2) | (op(e0, e0) = e0) | (op(e0, e2) = e1) | (op(e2, op(e0, e2)) = e2) | (op(e1, op(e0, e1)) = e1) | (op(e0, e1) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.80 tff(3015,plain,
% 0.61/0.80 (op(e0, e0) = e1),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[3014, 991, 12, 830, 989, 63, 2452, 1814, 433])).
% 0.61/0.80 tff(3016,plain,
% 0.61/0.80 ((op(e0, e0) = op(e1, e0)) <=> (e1 = op(e1, e0))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3015])).
% 0.61/0.80 tff(3017,plain,
% 0.61/0.80 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e1)),
% 0.61/0.80 inference(transitivity,[status(thm)],[3016, 1043])).
% 0.61/0.80 tff(3018,plain,
% 0.61/0.80 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e1))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3017])).
% 0.61/0.80 tff(3019,plain,
% 0.61/0.80 (~(op(e1, e0) = e1)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[1056, 3018])).
% 0.61/0.80 tff(3020,plain,
% 0.61/0.80 ((op(e0, e0) = op(e3, e0)) <=> (e1 = op(e3, e0))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3015])).
% 0.61/0.80 tff(3021,plain,
% 0.61/0.80 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 0.61/0.80 inference(transitivity,[status(thm)],[3020, 373])).
% 0.61/0.80 tff(3022,plain,
% 0.61/0.80 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e1))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3021])).
% 0.61/0.80 tff(3023,plain,
% 0.61/0.80 (~(op(e3, e0) = e1)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[1638, 3022])).
% 0.61/0.80 tff(3024,plain,
% 0.61/0.80 ((e1 = e2) <=> (op(e0, e0) = e2)),
% 0.61/0.80 inference(monotonicity,[status(thm)],[685])).
% 0.61/0.80 tff(3025,plain,
% 0.61/0.80 ((~(e1 = e2)) <=> (~(op(e0, e0) = e2))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3024])).
% 0.61/0.80 tff(3026,plain,
% 0.61/0.80 (~(op(e0, e0) = e2)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[324, 3025])).
% 0.61/0.80 tff(3027,plain,
% 0.61/0.80 (op(e0, e2) = e2),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[887, 104, 830, 3026])).
% 0.61/0.80 tff(3028,plain,
% 0.61/0.80 ((op(e0, e0) = op(e2, e0)) <=> (e1 = op(e2, e0))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[684])).
% 0.61/0.80 tff(3029,plain,
% 0.61/0.80 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e1)),
% 0.61/0.80 inference(transitivity,[status(thm)],[3028, 1384])).
% 0.61/0.80 tff(3030,plain,
% 0.61/0.80 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e1))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3029])).
% 0.61/0.80 tff(3031,plain,
% 0.61/0.80 (~(op(e2, e0) = e1)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[1827, 3030])).
% 0.61/0.80 tff(3032,plain,
% 0.61/0.80 ((op(e0, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[806])).
% 0.61/0.80 tff(3033,plain,
% 0.61/0.80 ((op(e0, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.61/0.80 inference(transitivity,[status(thm)],[3032, 469])).
% 0.61/0.80 tff(3034,plain,
% 0.61/0.80 ((~(op(e0, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3033])).
% 0.61/0.80 tff(3035,plain,
% 0.61/0.80 (~(op(e3, e2) = e2)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[277, 3034])).
% 0.61/0.80 tff(3036,plain,
% 0.61/0.80 (op(e3, e0) = e2),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[537, 374, 3035, 75])).
% 0.61/0.80 tff(3037,plain,
% 0.61/0.80 (op(e0, op(e3, e0)) = op(e0, e2)),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3036])).
% 0.61/0.80 tff(3038,plain,
% 0.61/0.80 (op(e0, op(e3, e0)) = e2),
% 0.61/0.80 inference(transitivity,[status(thm)],[3037, 806])).
% 0.61/0.80 tff(3039,plain,
% 0.61/0.80 ((op(e0, op(e3, e0)) = e0) <=> (e2 = e0)),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3038])).
% 0.61/0.80 tff(3040,plain,
% 0.61/0.80 ((op(e0, op(e3, e0)) = e0) <=> (e0 = e2)),
% 0.61/0.80 inference(transitivity,[status(thm)],[3039, 217])).
% 0.61/0.80 tff(3041,plain,
% 0.61/0.80 ((e0 = e2) <=> (op(e0, op(e3, e0)) = e0)),
% 0.61/0.80 inference(symmetry,[status(thm)],[3040])).
% 0.61/0.80 tff(3042,plain,
% 0.61/0.80 ((~(e0 = e2)) <=> (~(op(e0, op(e3, e0)) = e0))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3041])).
% 0.61/0.80 tff(3043,plain,
% 0.61/0.80 (~(op(e0, op(e3, e0)) = e0)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[238, 3042])).
% 0.61/0.80 tff(3044,plain,
% 0.61/0.80 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[1654, 3043])).
% 0.61/0.80 tff(3045,plain,
% 0.61/0.80 ((op(e2, e1) = e1) <=> (e2 = e1)),
% 0.61/0.80 inference(monotonicity,[status(thm)],[1704])).
% 0.61/0.80 tff(3046,plain,
% 0.61/0.80 ((op(e2, e1) = e1) <=> (e1 = e2)),
% 0.61/0.80 inference(transitivity,[status(thm)],[3045, 317])).
% 0.61/0.80 tff(3047,plain,
% 0.61/0.80 ((e1 = e2) <=> (op(e2, e1) = e1)),
% 0.61/0.80 inference(symmetry,[status(thm)],[3046])).
% 0.61/0.80 tff(3048,plain,
% 0.61/0.80 ((~(e1 = e2)) <=> (~(op(e2, e1) = e1))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3047])).
% 0.61/0.80 tff(3049,plain,
% 0.61/0.80 (~(op(e2, e1) = e1)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[324, 3048])).
% 0.61/0.80 tff(3050,plain,
% 0.61/0.80 ((op(e0, e2) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[806])).
% 0.61/0.80 tff(3051,plain,
% 0.61/0.80 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 0.61/0.80 inference(transitivity,[status(thm)],[3050, 2081])).
% 0.61/0.80 tff(3052,plain,
% 0.61/0.80 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3051])).
% 0.61/0.80 tff(3053,plain,
% 0.61/0.80 (~(op(e1, e2) = e2)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[703, 3052])).
% 0.61/0.80 tff(3054,plain,
% 0.61/0.80 (op(e1, e2) = e1),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[2123, 1939, 3053, 1221, 3044, 1704])).
% 0.61/0.80 tff(3055,plain,
% 0.61/0.80 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e1)),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3054])).
% 0.61/0.80 tff(3056,plain,
% 0.61/0.80 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e1))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3055])).
% 0.61/0.80 tff(3057,plain,
% 0.61/0.80 (~(op(e1, e1) = e1)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[1616, 3056])).
% 0.61/0.80 tff(3058,plain,
% 0.61/0.80 (op(e3, e1) = e1),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[450, 3057, 433, 3049])).
% 0.61/0.80 tff(3059,plain,
% 0.61/0.80 ((op(e1, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3054])).
% 0.61/0.80 tff(3060,plain,
% 0.61/0.80 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 0.61/0.80 inference(transitivity,[status(thm)],[3059, 1949])).
% 0.61/0.80 tff(3061,plain,
% 0.61/0.80 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3060])).
% 0.61/0.80 tff(3062,plain,
% 0.61/0.80 (~(op(e2, e2) = e1)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[764, 3061])).
% 0.61/0.80 tff(3063,plain,
% 0.61/0.80 (op(e2, e3) = e1),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[964, 3062, 1413, 3049])).
% 0.61/0.80 tff(3064,plain,
% 0.61/0.80 (op(e3, op(e2, e3)) = op(e3, e1)),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3063])).
% 0.61/0.80 tff(3065,plain,
% 0.61/0.80 (op(e3, op(e2, e3)) = e1),
% 0.61/0.80 inference(transitivity,[status(thm)],[3064, 3058])).
% 0.61/0.80 tff(3066,plain,
% 0.61/0.80 ((op(e3, op(e2, e3)) = e3) <=> (e1 = e3)),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3065])).
% 0.61/0.80 tff(3067,plain,
% 0.61/0.80 ((e1 = e3) <=> (op(e3, op(e2, e3)) = e3)),
% 0.61/0.80 inference(symmetry,[status(thm)],[3066])).
% 0.61/0.80 tff(3068,plain,
% 0.61/0.80 ((~(e1 = e3)) <=> (~(op(e3, op(e2, e3)) = e3))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3067])).
% 0.61/0.80 tff(3069,plain,
% 0.61/0.80 (~(op(e3, op(e2, e3)) = e3)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[591, 3068])).
% 0.61/0.80 tff(3070,plain,
% 0.61/0.80 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[471, 3069])).
% 0.61/0.80 tff(3071,plain,
% 0.61/0.80 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[681, 3070, 1221, 3044])).
% 0.61/0.80 tff(3072,plain,
% 0.61/0.80 (op(e3, op(e1, e3)) = e3),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[80, 3071])).
% 0.61/0.80 tff(3073,plain,
% 0.61/0.80 (op(e3, e2) = op(e3, op(e1, e3))),
% 0.61/0.80 inference(symmetry,[status(thm)],[1940])).
% 0.61/0.80 tff(3074,plain,
% 0.61/0.80 ((op(e3, e0) = e0) <=> (e2 = e0)),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3036])).
% 0.61/0.80 tff(3075,plain,
% 0.61/0.80 ((op(e3, e0) = e0) <=> (e0 = e2)),
% 0.61/0.80 inference(transitivity,[status(thm)],[3074, 217])).
% 0.61/0.80 tff(3076,plain,
% 0.61/0.80 ((e0 = e2) <=> (op(e3, e0) = e0)),
% 0.61/0.80 inference(symmetry,[status(thm)],[3075])).
% 0.61/0.80 tff(3077,plain,
% 0.61/0.80 ((~(e0 = e2)) <=> (~(op(e3, e0) = e0))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3076])).
% 0.61/0.80 tff(3078,plain,
% 0.61/0.80 (~(op(e3, e0) = e0)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[238, 3077])).
% 0.61/0.80 tff(3079,plain,
% 0.61/0.80 ((op(e3, e1) = e0) <=> (e1 = e0)),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3058])).
% 0.61/0.80 tff(3080,plain,
% 0.61/0.80 ((op(e3, e1) = e0) <=> (e0 = e1)),
% 0.61/0.80 inference(transitivity,[status(thm)],[3079, 635])).
% 0.61/0.80 tff(3081,plain,
% 0.61/0.80 ((e0 = e1) <=> (op(e3, e1) = e0)),
% 0.61/0.80 inference(symmetry,[status(thm)],[3080])).
% 0.61/0.80 tff(3082,plain,
% 0.61/0.80 ((~(e0 = e1)) <=> (~(op(e3, e1) = e0))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3081])).
% 0.61/0.80 tff(3083,plain,
% 0.61/0.80 (~(op(e3, e1) = e0)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[625, 3082])).
% 0.61/0.80 tff(3084,plain,
% 0.61/0.80 (op(e3, e2) = e0),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[295, 3083, 3078, 63])).
% 0.61/0.80 tff(3085,plain,
% 0.61/0.80 (e0 = op(e3, e2)),
% 0.61/0.80 inference(symmetry,[status(thm)],[3084])).
% 0.61/0.80 tff(3086,plain,
% 0.61/0.80 (e0 = e3),
% 0.61/0.80 inference(transitivity,[status(thm)],[3085, 3073, 3072])).
% 0.61/0.80 tff(3087,plain,
% 0.61/0.80 ($false),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[286, 3086])).
% 0.61/0.80 tff(3088,plain,((op(e3, e1) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e3, e3) = e0) | (op(e0, e1) = e1) | (op(e2, e0) = e1) | (op(e3, e3) = e2) | (op(e0, e3) = e2) | (~(op(e0, e2) = e2)) | (op(e1, e1) = e2) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.80 tff(3089,plain,
% 0.61/0.80 (op(e3, e1) = e2),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[3088, 75, 63, 433, 3031, 1221, 104, 3027, 12, 830])).
% 0.61/0.80 tff(3090,plain,
% 0.61/0.80 ((e1 = op(e0, e0)) <=> (op(e0, e0) = e1)),
% 0.61/0.80 inference(commutativity,[status(thm)],[])).
% 0.61/0.80 tff(3091,plain,
% 0.61/0.80 ((op(e0, e0) = e1) <=> (e1 = op(e0, e0))),
% 0.61/0.80 inference(symmetry,[status(thm)],[3090])).
% 0.61/0.80 tff(3092,plain,
% 0.61/0.80 (e1 = op(e0, e0)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[684, 3091])).
% 0.61/0.80 tff(3093,plain,
% 0.61/0.80 (op(e0, op(e0, e0)) = op(e0, e1)),
% 0.61/0.80 inference(monotonicity,[status(thm)],[684])).
% 0.61/0.80 tff(3094,plain,
% 0.61/0.80 ((e3 = op(e0, op(e0, e0))) <=> (e3 = op(e0, e1))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3093])).
% 0.61/0.80 tff(3095,plain,
% 0.61/0.80 ((e3 = op(e0, op(e0, e0))) <=> (op(e0, e1) = e3)),
% 0.61/0.80 inference(transitivity,[status(thm)],[3094, 2809])).
% 0.61/0.80 tff(3096,plain,
% 0.61/0.80 ((op(e0, e1) = e3) <=> (e3 = op(e0, op(e0, e0)))),
% 0.61/0.80 inference(symmetry,[status(thm)],[3095])).
% 0.61/0.80 tff(3097,plain,
% 0.61/0.80 (e3 = op(e0, op(e0, e0))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[840, 3096])).
% 0.61/0.80 tff(3098,plain,
% 0.61/0.80 (op(e0, op(e0, e0)) = e3),
% 0.61/0.80 inference(transitivity,[status(thm)],[3093, 840])).
% 0.61/0.80 tff(3099,plain,
% 0.61/0.80 (op(op(e0, op(e0, e0)), op(e0, e0)) = op(e3, e1)),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3098, 684])).
% 0.61/0.80 tff(3100,plain,
% 0.61/0.80 (op(e3, e1) = op(op(e0, op(e0, e0)), op(e0, e0))),
% 0.61/0.80 inference(symmetry,[status(thm)],[3099])).
% 0.61/0.80 tff(3101,plain,
% 0.61/0.80 (e2 = op(op(e0, op(e0, e0)), op(e0, e0))),
% 0.61/0.80 inference(transitivity,[status(thm)],[1147, 3100])).
% 0.61/0.80 tff(3102,plain,
% 0.61/0.80 ((~(~((~(e1 = op(e0, e0))) | (~(e3 = op(e0, op(e0, e0)))) | (~(e2 = op(op(e0, op(e0, e0)), op(e0, e0))))))) <=> ((~(e1 = op(e0, e0))) | (~(e3 = op(e0, op(e0, e0)))) | (~(e2 = op(op(e0, op(e0, e0)), op(e0, e0)))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(3103,plain,
% 0.61/0.80 (((e1 = op(e0, e0)) & (e3 = op(e0, op(e0, e0))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0)))) <=> (~((~(e1 = op(e0, e0))) | (~(e3 = op(e0, op(e0, e0)))) | (~(e2 = op(op(e0, op(e0, e0)), op(e0, e0))))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(3104,plain,
% 0.61/0.80 ((~((e1 = op(e0, e0)) & (e3 = op(e0, op(e0, e0))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0))))) <=> (~(~((~(e1 = op(e0, e0))) | (~(e3 = op(e0, op(e0, e0)))) | (~(e2 = op(op(e0, op(e0, e0)), op(e0, e0)))))))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3103])).
% 0.61/0.80 tff(3105,plain,
% 0.61/0.80 ((~((e1 = op(e0, e0)) & (e3 = op(e0, op(e0, e0))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0))))) <=> ((~(e1 = op(e0, e0))) | (~(e3 = op(e0, op(e0, e0)))) | (~(e2 = op(op(e0, op(e0, e0)), op(e0, e0)))))),
% 0.61/0.80 inference(transitivity,[status(thm)],[3104, 3102])).
% 0.61/0.80 tff(3106,plain,
% 0.61/0.80 ((~((e1 = op(e0, e0)) & (e3 = op(e0, op(e0, e0))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0))))) <=> (~((e1 = op(e0, e0)) & (e3 = op(e0, op(e0, e0))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0)))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(3107,plain,
% 0.61/0.80 ((~(((e1 = op(e0, e0)) & (e3 = op(e0, op(e0, e0)))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0))))) <=> (~((e1 = op(e0, e0)) & (e3 = op(e0, op(e0, e0))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0)))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(3108,axiom,(~(((e1 = op(e0, e0)) & (e3 = op(e0, op(e0, e0)))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax16')).
% 0.61/0.80 tff(3109,plain,
% 0.61/0.80 (~((e1 = op(e0, e0)) & (e3 = op(e0, op(e0, e0))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[3108, 3107])).
% 0.61/0.80 tff(3110,plain,
% 0.61/0.80 (~((e1 = op(e0, e0)) & (e3 = op(e0, op(e0, e0))) & (e2 = op(op(e0, op(e0, e0)), op(e0, e0))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[3109, 3106])).
% 0.61/0.80 tff(3111,plain,
% 0.61/0.80 ((~(e1 = op(e0, e0))) | (~(e3 = op(e0, op(e0, e0)))) | (~(e2 = op(op(e0, op(e0, e0)), op(e0, e0))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[3110, 3105])).
% 0.61/0.80 tff(3112,plain,
% 0.61/0.80 ($false),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[3111, 3101, 3097, 3092])).
% 0.61/0.80 tff(3113,plain,((~(op(e0, e1) = e3)) | (~(op(e3, e1) = e2)) | (~(op(e0, e0) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.80 tff(3114,plain,
% 0.61/0.80 (~(op(e0, e1) = e3)),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[3113, 3089, 684])).
% 0.61/0.80 tff(3115,plain,
% 0.61/0.80 (op(e0, e1) = e0),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[860, 3114, 830, 433])).
% 0.61/0.80 tff(3116,plain,
% 0.61/0.80 ((op(e0, e1) = op(e1, e1)) <=> (e0 = op(e1, e1))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3115])).
% 0.61/0.80 tff(3117,plain,
% 0.61/0.80 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e0)),
% 0.61/0.80 inference(transitivity,[status(thm)],[3116, 1501])).
% 0.61/0.80 tff(3118,plain,
% 0.61/0.80 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e0))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3117])).
% 0.61/0.80 tff(3119,plain,
% 0.61/0.80 (~(op(e1, e1) = e0)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[100, 3118])).
% 0.61/0.80 tff(3120,plain,
% 0.61/0.80 ((op(e0, e0) = op(e3, e0)) <=> (e1 = op(e3, e0))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[684])).
% 0.61/0.80 tff(3121,plain,
% 0.61/0.80 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 0.61/0.80 inference(transitivity,[status(thm)],[3120, 373])).
% 0.61/0.80 tff(3122,plain,
% 0.61/0.80 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e1))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[3121])).
% 0.61/0.80 tff(3123,plain,
% 0.61/0.80 (~(op(e3, e0) = e1)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[1638, 3122])).
% 0.61/0.80 tff(3124,plain,
% 0.61/0.80 ((e1 = e3) <=> (op(e0, e0) = e3)),
% 0.61/0.81 inference(monotonicity,[status(thm)],[685])).
% 0.61/0.81 tff(3125,plain,
% 0.61/0.81 ((~(e1 = e3)) <=> (~(op(e0, e0) = e3))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3124])).
% 0.61/0.81 tff(3126,plain,
% 0.61/0.81 (~(op(e0, e0) = e3)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[591, 3125])).
% 0.61/0.81 tff(3127,plain,
% 0.61/0.81 ((op(e0, e2) = e3) <=> (e2 = e3)),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3027])).
% 0.61/0.81 tff(3128,plain,
% 0.61/0.81 ((e2 = e3) <=> (op(e0, e2) = e3)),
% 0.61/0.81 inference(symmetry,[status(thm)],[3127])).
% 0.61/0.81 tff(3129,plain,
% 0.61/0.81 ((~(e2 = e3)) <=> (~(op(e0, e2) = e3))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3128])).
% 0.61/0.81 tff(3130,plain,
% 0.61/0.81 (~(op(e0, e2) = e3)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[462, 3129])).
% 0.61/0.81 tff(3131,plain,
% 0.61/0.81 (op(e0, e3) = e3),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[1562, 3114, 3130, 3126])).
% 0.61/0.81 tff(3132,plain,
% 0.61/0.81 ((op(e0, e3) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3131])).
% 0.61/0.81 tff(3133,plain,
% 0.61/0.81 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.61/0.81 inference(transitivity,[status(thm)],[3132, 78])).
% 0.61/0.81 tff(3134,plain,
% 0.61/0.81 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3133])).
% 0.61/0.81 tff(3135,plain,
% 0.61/0.81 (~(op(e3, e3) = e3)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[725, 3134])).
% 0.61/0.81 tff(3136,plain,
% 0.61/0.81 (op(e3, e3) = e1),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[266, 3135, 63, 75])).
% 0.61/0.81 tff(3137,plain,
% 0.61/0.81 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e1)),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3136])).
% 0.61/0.81 tff(3138,plain,
% 0.61/0.81 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e1))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3137])).
% 0.61/0.81 tff(3139,plain,
% 0.61/0.81 (~(op(e3, e2) = e1)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[1111, 3138])).
% 0.61/0.81 tff(3140,plain,
% 0.61/0.81 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[1632, 1146, 1414])).
% 0.61/0.81 tff(3141,assumption,(~(op(e0, e0) = e3)), introduced(assumption)).
% 0.61/0.81 tff(3142,plain,
% 0.61/0.81 ((e0 = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 0.61/0.81 inference(commutativity,[status(thm)],[])).
% 0.61/0.81 tff(3143,plain,
% 0.61/0.81 (op(e0, e2) = e2),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[887, 104, 830, 1820])).
% 0.61/0.81 tff(3144,plain,
% 0.61/0.81 ((op(e0, e2) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3143])).
% 0.61/0.81 tff(3145,plain,
% 0.61/0.81 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 0.61/0.81 inference(transitivity,[status(thm)],[3144, 2081])).
% 0.61/0.81 tff(3146,plain,
% 0.61/0.81 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3145])).
% 0.61/0.81 tff(3147,plain,
% 0.61/0.81 (~(op(e1, e2) = e2)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[703, 3146])).
% 0.61/0.81 tff(3148,plain,
% 0.61/0.81 (op(e2, e0) = e2),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[1836, 84, 1820, 1698, 830, 104])).
% 0.61/0.81 tff(3149,plain,
% 0.61/0.81 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e2)),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3148])).
% 0.61/0.81 tff(3150,plain,
% 0.61/0.81 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e2))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3149])).
% 0.61/0.81 tff(3151,plain,
% 0.61/0.81 (~(op(e1, e0) = e2)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[1206, 3150])).
% 0.61/0.81 tff(3152,plain,
% 0.61/0.81 (op(e1, e3) = e2),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[135, 3151, 12, 3147])).
% 0.61/0.81 tff(3153,plain,
% 0.61/0.81 (e2 = op(e1, e3)),
% 0.61/0.81 inference(symmetry,[status(thm)],[3152])).
% 0.61/0.81 tff(3154,plain,
% 0.61/0.81 (op(e3, e2) = op(e3, op(e1, e3))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3153])).
% 0.61/0.81 tff(3155,plain,
% 0.61/0.81 (op(e3, e2) = e3),
% 0.61/0.81 inference(transitivity,[status(thm)],[3154, 81])).
% 0.61/0.81 tff(3156,plain,
% 0.61/0.81 ((op(e3, e2) = e1) <=> (e3 = e1)),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3155])).
% 0.61/0.81 tff(3157,plain,
% 0.61/0.81 ((op(e3, e2) = e1) <=> (e1 = e3)),
% 0.61/0.81 inference(transitivity,[status(thm)],[3156, 951])).
% 0.61/0.81 tff(3158,plain,
% 0.61/0.81 ((e1 = e3) <=> (op(e3, e2) = e1)),
% 0.61/0.81 inference(symmetry,[status(thm)],[3157])).
% 0.61/0.81 tff(3159,plain,
% 0.61/0.81 ((~(e1 = e3)) <=> (~(op(e3, e2) = e1))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3158])).
% 0.61/0.81 tff(3160,plain,
% 0.61/0.81 (~(op(e3, e2) = e1)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[591, 3159])).
% 0.61/0.81 tff(3161,plain,
% 0.61/0.81 (op(e3, e3) = e1),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[429, 3160, 1414, 1628])).
% 0.61/0.81 tff(3162,plain,
% 0.61/0.81 (op(e3, op(e3, e3)) = op(e3, e1)),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3161])).
% 0.61/0.81 tff(3163,plain,
% 0.61/0.81 (op(e3, op(e3, e3)) = e2),
% 0.61/0.81 inference(transitivity,[status(thm)],[3162, 1146])).
% 0.61/0.81 tff(3164,plain,
% 0.61/0.81 (op(op(e3, op(e3, e3)), op(e3, e3)) = op(e2, e1)),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3163, 3161])).
% 0.61/0.81 tff(3165,plain,
% 0.61/0.81 ((e0 = op(op(e3, op(e3, e3)), op(e3, e3))) <=> (e0 = op(e2, e1))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3164])).
% 0.61/0.81 tff(3166,plain,
% 0.61/0.81 ((e0 = op(op(e3, op(e3, e3)), op(e3, e3))) <=> (op(e2, e1) = e0)),
% 0.61/0.81 inference(transitivity,[status(thm)],[3165, 3142])).
% 0.61/0.81 tff(3167,plain,
% 0.61/0.81 ((op(e2, e1) = e0) <=> (e0 = op(op(e3, op(e3, e3)), op(e3, e3)))),
% 0.61/0.81 inference(symmetry,[status(thm)],[3166])).
% 0.61/0.81 tff(3168,plain,
% 0.61/0.81 ((op(e2, e0) = e3) <=> (e2 = e3)),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3148])).
% 0.61/0.81 tff(3169,plain,
% 0.61/0.81 ((e2 = e3) <=> (op(e2, e0) = e3)),
% 0.61/0.81 inference(symmetry,[status(thm)],[3168])).
% 0.61/0.81 tff(3170,plain,
% 0.61/0.81 ((~(e2 = e3)) <=> (~(op(e2, e0) = e3))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3169])).
% 0.61/0.81 tff(3171,plain,
% 0.61/0.81 (~(op(e2, e0) = e3)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[462, 3170])).
% 0.61/0.81 tff(3172,plain,
% 0.61/0.81 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e0) = e3)),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3155])).
% 0.61/0.81 tff(3173,plain,
% 0.61/0.81 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = e3))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3172])).
% 0.61/0.81 tff(3174,plain,
% 0.61/0.81 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e0) = op(e3, e2)))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(3175,plain,
% 0.61/0.81 (~(op(e3, e0) = op(e3, e2))),
% 0.61/0.81 inference(and_elim,[status(thm)],[23])).
% 0.61/0.81 tff(3176,plain,
% 0.61/0.81 (~(op(e3, e0) = op(e3, e2))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[3175, 3174])).
% 0.61/0.81 tff(3177,plain,
% 0.61/0.81 (~(op(e3, e0) = e3)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[3176, 3173])).
% 0.61/0.81 tff(3178,plain,
% 0.61/0.81 (((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))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(3179,plain,
% 0.61/0.81 ((((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))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(3180,plain,
% 0.61/0.81 ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) <=> ((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e2, e0) = e3))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(3181,plain,
% 0.61/0.81 (((((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))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3180])).
% 0.61/0.81 tff(3182,plain,
% 0.61/0.81 (((((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))),
% 0.61/0.81 inference(transitivity,[status(thm)],[3181, 3179])).
% 0.61/0.81 tff(3183,plain,
% 0.61/0.81 ((((op(e0, e0) = e3) | (op(e1, e0) = e3)) | (op(e2, e0) = e3)) | (op(e3, e0) = e3)),
% 0.61/0.81 inference(and_elim,[status(thm)],[710])).
% 0.61/0.81 tff(3184,plain,
% 0.61/0.81 ((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e2, e0) = e3) | (op(e3, e0) = e3)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[3183, 3182])).
% 0.61/0.81 tff(3185,plain,
% 0.61/0.81 ((op(e0, e0) = e3) | (op(e1, e0) = e3) | (op(e2, e0) = e3) | (op(e3, e0) = e3)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[3184, 3178])).
% 0.61/0.81 tff(3186,plain,
% 0.61/0.81 (op(e1, e0) = e3),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[3185, 3177, 3141, 3171])).
% 0.61/0.81 tff(3187,plain,
% 0.61/0.81 (e3 = op(e1, e0)),
% 0.61/0.81 inference(symmetry,[status(thm)],[3186])).
% 0.61/0.81 tff(3188,plain,
% 0.61/0.81 (op(e0, e3) = op(e0, op(e1, e0))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3187])).
% 0.61/0.81 tff(3189,plain,
% 0.61/0.81 (op(e0, e3) = e0),
% 0.61/0.81 inference(transitivity,[status(thm)],[3188, 84])).
% 0.61/0.81 tff(3190,plain,
% 0.61/0.81 ((op(e0, e3) = op(e2, e3)) <=> (e0 = op(e2, e3))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3189])).
% 0.61/0.81 tff(3191,plain,
% 0.61/0.81 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e0)),
% 0.61/0.81 inference(transitivity,[status(thm)],[3190, 1248])).
% 0.61/0.81 tff(3192,plain,
% 0.61/0.81 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e0))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3191])).
% 0.61/0.81 tff(3193,plain,
% 0.61/0.81 (~(op(e2, e3) = e0)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[2232, 3192])).
% 0.61/0.81 tff(3194,plain,
% 0.61/0.81 ((op(e2, e0) = e0) <=> (e2 = e0)),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3148])).
% 0.61/0.81 tff(3195,plain,
% 0.61/0.81 ((op(e2, e0) = e0) <=> (e0 = e2)),
% 0.61/0.81 inference(transitivity,[status(thm)],[3194, 217])).
% 0.61/0.81 tff(3196,plain,
% 0.61/0.81 ((e0 = e2) <=> (op(e2, e0) = e0)),
% 0.61/0.81 inference(symmetry,[status(thm)],[3195])).
% 0.61/0.81 tff(3197,plain,
% 0.61/0.81 ((~(e0 = e2)) <=> (~(op(e2, e0) = e0))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3196])).
% 0.61/0.81 tff(3198,plain,
% 0.61/0.81 (~(op(e2, e0) = e0)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[238, 3197])).
% 0.61/0.81 tff(3199,plain,
% 0.61/0.81 (op(e2, e2) = e1),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[1603, 3160, 991, 168])).
% 0.61/0.81 tff(3200,plain,
% 0.61/0.81 ((op(e2, e2) = e0) <=> (e1 = e0)),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3199])).
% 0.61/0.81 tff(3201,plain,
% 0.61/0.81 ((op(e2, e2) = e0) <=> (e0 = e1)),
% 0.61/0.81 inference(transitivity,[status(thm)],[3200, 635])).
% 0.61/0.81 tff(3202,plain,
% 0.61/0.81 ((e0 = e1) <=> (op(e2, e2) = e0)),
% 0.61/0.81 inference(symmetry,[status(thm)],[3201])).
% 0.61/0.81 tff(3203,plain,
% 0.61/0.81 ((~(e0 = e1)) <=> (~(op(e2, e2) = e0))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3202])).
% 0.61/0.81 tff(3204,plain,
% 0.61/0.81 (~(op(e2, e2) = e0)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[625, 3203])).
% 0.61/0.81 tff(3205,plain,
% 0.61/0.81 (((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))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(3206,plain,
% 0.61/0.81 ((((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))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(3207,plain,
% 0.61/0.81 ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) <=> ((op(e2, e0) = e0) | (op(e2, e1) = e0) | (op(e2, e2) = e0))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(3208,plain,
% 0.61/0.81 (((((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))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3207])).
% 0.61/0.81 tff(3209,plain,
% 0.61/0.81 (((((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))),
% 0.61/0.81 inference(transitivity,[status(thm)],[3208, 3206])).
% 0.61/0.81 tff(3210,plain,
% 0.61/0.81 ((((op(e2, e0) = e0) | (op(e2, e1) = e0)) | (op(e2, e2) = e0)) | (op(e2, e3) = e0)),
% 0.61/0.81 inference(and_elim,[status(thm)],[128])).
% 0.61/0.81 tff(3211,plain,
% 0.61/0.81 ((op(e2, e0) = e0) | (op(e2, e1) = e0) | (op(e2, e2) = e0) | (op(e2, e3) = e0)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[3210, 3209])).
% 0.61/0.81 tff(3212,plain,
% 0.61/0.81 ((op(e2, e0) = e0) | (op(e2, e1) = e0) | (op(e2, e2) = e0) | (op(e2, e3) = e0)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[3211, 3205])).
% 0.61/0.81 tff(3213,plain,
% 0.61/0.81 (op(e2, e1) = e0),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[3212, 3204, 3198, 3193])).
% 0.61/0.81 tff(3214,plain,
% 0.61/0.81 (e0 = op(op(e3, op(e3, e3)), op(e3, e3))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[3213, 3167])).
% 0.61/0.81 tff(3215,plain,
% 0.61/0.81 (e1 = op(e3, e3)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[3161, 77])).
% 0.61/0.81 tff(3216,plain,
% 0.61/0.81 (op(e3, e1) = op(e3, op(e3, e3))),
% 0.61/0.81 inference(symmetry,[status(thm)],[3162])).
% 0.61/0.81 tff(3217,plain,
% 0.61/0.81 (e2 = op(e3, op(e3, e3))),
% 0.61/0.81 inference(transitivity,[status(thm)],[1147, 3216])).
% 0.61/0.81 tff(3218,plain,
% 0.61/0.81 ((~(~((~(e1 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3)))) | (~(e0 = op(op(e3, op(e3, e3)), op(e3, e3))))))) <=> ((~(e1 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3)))) | (~(e0 = op(op(e3, op(e3, e3)), op(e3, e3)))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(3219,plain,
% 0.61/0.81 (((e1 = op(e3, e3)) & (e2 = op(e3, op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3)))) <=> (~((~(e1 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3)))) | (~(e0 = op(op(e3, op(e3, e3)), op(e3, e3))))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(3220,plain,
% 0.61/0.81 ((~((e1 = op(e3, e3)) & (e2 = op(e3, op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3))))) <=> (~(~((~(e1 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3)))) | (~(e0 = op(op(e3, op(e3, e3)), op(e3, e3)))))))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3219])).
% 0.61/0.81 tff(3221,plain,
% 0.61/0.81 ((~((e1 = op(e3, e3)) & (e2 = op(e3, op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3))))) <=> ((~(e1 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3)))) | (~(e0 = op(op(e3, op(e3, e3)), op(e3, e3)))))),
% 0.61/0.81 inference(transitivity,[status(thm)],[3220, 3218])).
% 0.61/0.81 tff(3222,plain,
% 0.61/0.81 ((~((e1 = op(e3, e3)) & (e2 = op(e3, op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3))))) <=> (~((e1 = op(e3, e3)) & (e2 = op(e3, op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3)))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(3223,plain,
% 0.61/0.81 ((~(((e1 = op(e3, e3)) & (e2 = op(e3, op(e3, e3)))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3))))) <=> (~((e1 = op(e3, e3)) & (e2 = op(e3, op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3)))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(3224,axiom,(~(((e1 = op(e3, e3)) & (e2 = op(e3, op(e3, e3)))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax15')).
% 0.61/0.81 tff(3225,plain,
% 0.61/0.81 (~((e1 = op(e3, e3)) & (e2 = op(e3, op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[3224, 3223])).
% 0.61/0.81 tff(3226,plain,
% 0.61/0.81 (~((e1 = op(e3, e3)) & (e2 = op(e3, op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[3225, 3222])).
% 0.61/0.81 tff(3227,plain,
% 0.61/0.81 ((~(e1 = op(e3, e3))) | (~(e2 = op(e3, op(e3, e3)))) | (~(e0 = op(op(e3, op(e3, e3)), op(e3, e3))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[3226, 3221])).
% 0.61/0.81 tff(3228,plain,
% 0.61/0.81 (~(e0 = op(op(e3, op(e3, e3)), op(e3, e3)))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[3227, 3217, 3215])).
% 0.61/0.81 tff(3229,plain,
% 0.61/0.81 ($false),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[3228, 3214])).
% 0.61/0.81 tff(3230,plain,(((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))) | (~(op(e3, e1) = e2)) | (op(e0, e0) = e3) | (op(e3, e0) = e1) | (op(e0, e2) = e1) | (op(e1, e2) = e1) | (op(e1, e1) = e2) | (op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.81 tff(3231,plain,
% 0.61/0.81 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[3230, 168, 3141, 1414, 991, 1146, 12, 1820, 830, 104])).
% 0.61/0.81 tff(3232,plain,
% 0.61/0.81 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[681, 3231, 1221, 3140])).
% 0.61/0.81 tff(3233,plain,
% 0.61/0.81 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e2)),
% 0.61/0.81 inference(monotonicity,[status(thm)],[1146])).
% 0.61/0.81 tff(3234,plain,
% 0.61/0.81 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e2))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[3233])).
% 0.61/0.81 tff(3235,plain,
% 0.61/0.81 (~(op(e2, e1) = e2)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[576, 3234])).
% 0.61/0.81 tff(3236,assumption,(~(op(e3, e2) = e1)), introduced(assumption)).
% 0.61/0.81 tff(3237,plain,
% 0.61/0.81 (op(e2, e2) = e1),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[1603, 168, 991, 3236])).
% 0.61/0.81 tff(3238,plain,
% 0.61/0.81 (~(op(e2, op(e2, e2)) = e2)),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[488, 3237, 3235])).
% 0.61/0.81 tff(3239,plain,
% 0.61/0.81 ($false),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[473, 3238, 3232])).
% 0.61/0.81 tff(3240,plain,((op(e1, e2) = e1) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e0, e2) = e1) | (op(e3, e2) = e1) | (op(e0, e0) = e3) | (op(e3, e0) = e1) | (~(op(e3, e1) = e2)) | (op(e1, e1) = e2) | (op(e0, e0) = e2) | (op(e0, e1) = e2) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.81 tff(3241,plain,
% 0.61/0.81 (op(e1, e2) = e1),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[3240, 3139, 991, 1221, 3126, 3123, 3089, 12, 3026, 830, 104])).
% 0.61/0.82 tff(3242,plain,
% 0.61/0.82 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e1)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3241])).
% 0.61/0.82 tff(3243,plain,
% 0.61/0.82 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e1))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3242])).
% 0.61/0.82 tff(3244,plain,
% 0.61/0.82 (~(op(e1, e1) = e1)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[1616, 3243])).
% 0.61/0.82 tff(3245,plain,
% 0.61/0.82 (op(e1, e1) = e3),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[2603, 3244, 12, 3119])).
% 0.61/0.82 tff(3246,plain,
% 0.61/0.82 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e1)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3136])).
% 0.61/0.82 tff(3247,plain,
% 0.61/0.82 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e1))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3246])).
% 0.61/0.82 tff(3248,plain,
% 0.61/0.82 (~(op(e2, e3) = e1)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[387, 3247])).
% 0.61/0.82 tff(3249,plain,
% 0.61/0.82 ((op(e1, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3241])).
% 0.61/0.82 tff(3250,plain,
% 0.61/0.82 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 0.61/0.82 inference(transitivity,[status(thm)],[3249, 1949])).
% 0.61/0.82 tff(3251,plain,
% 0.61/0.82 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3250])).
% 0.61/0.82 tff(3252,plain,
% 0.61/0.82 (~(op(e2, e2) = e1)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[764, 3251])).
% 0.61/0.82 tff(3253,plain,
% 0.61/0.82 (op(e2, e1) = e1),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[964, 3252, 3031, 3248])).
% 0.61/0.82 tff(3254,plain,
% 0.61/0.82 (e1 = op(e2, e1)),
% 0.61/0.82 inference(symmetry,[status(thm)],[3253])).
% 0.61/0.82 tff(3255,plain,
% 0.61/0.82 (op(e1, e1) = op(e1, op(e2, e1))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3254])).
% 0.61/0.82 tff(3256,plain,
% 0.61/0.82 (op(e1, op(e2, e1)) = op(e1, e1)),
% 0.61/0.82 inference(symmetry,[status(thm)],[3255])).
% 0.61/0.82 tff(3257,plain,
% 0.61/0.82 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[1632, 3089, 3123])).
% 0.61/0.82 tff(3258,plain,
% 0.61/0.82 (op(e2, op(e1, e2)) = op(e2, e1)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3241])).
% 0.61/0.82 tff(3259,plain,
% 0.61/0.82 ((op(e2, op(e1, e2)) = e2) <=> (op(e2, e1) = e2)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3258])).
% 0.61/0.82 tff(3260,plain,
% 0.61/0.82 ((op(e2, e1) = e2) <=> (op(e2, op(e1, e2)) = e2)),
% 0.61/0.82 inference(symmetry,[status(thm)],[3259])).
% 0.61/0.82 tff(3261,plain,
% 0.61/0.82 ((~(op(e2, e1) = e2)) <=> (~(op(e2, op(e1, e2)) = e2))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3260])).
% 0.61/0.82 tff(3262,plain,
% 0.61/0.82 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e2)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3089])).
% 0.61/0.82 tff(3263,plain,
% 0.61/0.82 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e2))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3262])).
% 0.61/0.82 tff(3264,plain,
% 0.61/0.82 (~(op(e2, e1) = e2)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[576, 3263])).
% 0.61/0.82 tff(3265,plain,
% 0.61/0.82 (~(op(e2, op(e1, e2)) = e2)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[3264, 3261])).
% 0.61/0.82 tff(3266,plain,
% 0.61/0.82 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[102, 3265])).
% 0.61/0.82 tff(3267,plain,
% 0.61/0.82 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[681, 3266, 1221, 3257])).
% 0.61/0.82 tff(3268,plain,
% 0.61/0.82 (op(e1, op(e2, e1)) = e1),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[546, 3267])).
% 0.61/0.82 tff(3269,plain,
% 0.61/0.82 (e1 = op(e1, op(e2, e1))),
% 0.61/0.82 inference(symmetry,[status(thm)],[3268])).
% 0.61/0.82 tff(3270,plain,
% 0.61/0.82 (e1 = e3),
% 0.61/0.82 inference(transitivity,[status(thm)],[3269, 3256, 3245])).
% 0.61/0.82 tff(3271,plain,
% 0.61/0.82 ($false),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[591, 3270])).
% 0.61/0.82 tff(3272,plain,((op(e3, e3) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e1, e1) = e2) | (op(e0, e2) = e1) | (op(e0, e1) = e2) | (op(e0, e3) = e2) | (op(e3, e3) = e0) | (op(e0, e1) = e1) | (~(op(e0, e0) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.82 tff(3273,plain,
% 0.61/0.82 (op(e3, e3) = e2),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[3272, 104, 12, 991, 830, 1221, 63, 433, 684])).
% 0.61/0.82 tff(3274,plain,
% 0.61/0.82 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[392, 3273])).
% 0.61/0.82 tff(3275,plain,
% 0.61/0.82 ((op(e3, e3) = e1) <=> (e2 = e1)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3273])).
% 0.61/0.82 tff(3276,plain,
% 0.61/0.82 ((op(e3, e3) = e1) <=> (e1 = e2)),
% 0.61/0.82 inference(transitivity,[status(thm)],[3275, 317])).
% 0.61/0.82 tff(3277,plain,
% 0.61/0.82 ((e1 = e2) <=> (op(e3, e3) = e1)),
% 0.61/0.82 inference(symmetry,[status(thm)],[3276])).
% 0.61/0.82 tff(3278,plain,
% 0.61/0.82 ((~(e1 = e2)) <=> (~(op(e3, e3) = e1))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3277])).
% 0.61/0.82 tff(3279,plain,
% 0.61/0.82 (~(op(e3, e3) = e1)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[324, 3278])).
% 0.61/0.82 tff(3280,plain,
% 0.61/0.82 (op(e1, e2) = e1),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[1987, 3273, 830, 104, 1221, 12])).
% 0.61/0.82 tff(3281,plain,
% 0.61/0.82 ((op(e1, e2) = op(e3, e2)) <=> (e1 = op(e3, e2))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3280])).
% 0.61/0.82 tff(3282,plain,
% 0.61/0.82 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e1)),
% 0.61/0.82 inference(transitivity,[status(thm)],[3281, 1618])).
% 0.61/0.82 tff(3283,plain,
% 0.61/0.82 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e1))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3282])).
% 0.61/0.82 tff(3284,plain,
% 0.61/0.82 (~(op(e3, e2) = e1)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[165, 3283])).
% 0.61/0.82 tff(3285,plain,
% 0.61/0.82 (op(e3, e1) = e1),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[429, 3284, 3123, 3279])).
% 0.61/0.82 tff(3286,plain,
% 0.61/0.82 ((op(e1, e2) = op(e1, e3)) <=> (e1 = op(e1, e3))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3280])).
% 0.61/0.82 tff(3287,plain,
% 0.61/0.82 ((op(e1, e2) = op(e1, e3)) <=> (op(e1, e3) = e1)),
% 0.61/0.82 inference(transitivity,[status(thm)],[3286, 831])).
% 0.61/0.82 tff(3288,plain,
% 0.61/0.82 ((~(op(e1, e2) = op(e1, e3))) <=> (~(op(e1, e3) = e1))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3287])).
% 0.61/0.82 tff(3289,plain,
% 0.61/0.82 (~(op(e1, e3) = e1)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[174, 3288])).
% 0.61/0.82 tff(3290,plain,
% 0.61/0.82 ((op(e0, e0) = op(e0, e3)) <=> (e1 = op(e0, e3))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[684])).
% 0.61/0.82 tff(3291,plain,
% 0.61/0.82 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e3) = e1)),
% 0.61/0.82 inference(transitivity,[status(thm)],[3290, 1847])).
% 0.61/0.82 tff(3292,plain,
% 0.61/0.82 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e3) = e1))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3291])).
% 0.61/0.82 tff(3293,plain,
% 0.61/0.82 (~(op(e0, e3) = e1)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[2178, 3292])).
% 0.61/0.82 tff(3294,plain,
% 0.61/0.82 (op(e2, e3) = e1),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[1872, 3279, 3293, 3289])).
% 0.61/0.82 tff(3295,plain,
% 0.61/0.82 (op(e3, op(e2, e3)) = op(e3, e1)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3294])).
% 0.61/0.82 tff(3296,plain,
% 0.61/0.82 (op(e3, op(e2, e3)) = e1),
% 0.61/0.82 inference(transitivity,[status(thm)],[3295, 3285])).
% 0.61/0.82 tff(3297,plain,
% 0.61/0.82 ((op(e3, op(e2, e3)) = e3) <=> (e1 = e3)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3296])).
% 0.61/0.82 tff(3298,plain,
% 0.61/0.82 ((e1 = e3) <=> (op(e3, op(e2, e3)) = e3)),
% 0.61/0.82 inference(symmetry,[status(thm)],[3297])).
% 0.61/0.82 tff(3299,plain,
% 0.61/0.82 ((~(e1 = e3)) <=> (~(op(e3, op(e2, e3)) = e3))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3298])).
% 0.61/0.82 tff(3300,plain,
% 0.61/0.82 (~(op(e3, op(e2, e3)) = e3)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[591, 3299])).
% 0.61/0.82 tff(3301,plain,
% 0.61/0.82 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[471, 3300])).
% 0.61/0.82 tff(3302,plain,
% 0.61/0.82 ((op(e0, e2) = op(e1, e2)) <=> (e2 = op(e1, e2))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3027])).
% 0.61/0.82 tff(3303,plain,
% 0.61/0.82 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e2)),
% 0.61/0.82 inference(transitivity,[status(thm)],[3302, 2081])).
% 0.61/0.82 tff(3304,plain,
% 0.61/0.82 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e2))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3303])).
% 0.61/0.82 tff(3305,plain,
% 0.61/0.82 (~(op(e1, e2) = e2)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[703, 3304])).
% 0.61/0.82 tff(3306,plain,
% 0.61/0.82 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e2)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3273])).
% 0.61/0.82 tff(3307,plain,
% 0.61/0.82 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e2))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3306])).
% 0.61/0.82 tff(3308,plain,
% 0.61/0.82 (~(op(e1, e3) = e2)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[368, 3307])).
% 0.61/0.82 tff(3309,plain,
% 0.61/0.82 (op(e1, e0) = e2),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[135, 3308, 12, 3305])).
% 0.61/0.82 tff(3310,plain,
% 0.61/0.82 (op(e0, op(e1, e0)) = op(e0, e2)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3309])).
% 0.61/0.82 tff(3311,plain,
% 0.61/0.82 (op(e0, op(e1, e0)) = e2),
% 0.61/0.82 inference(transitivity,[status(thm)],[3310, 3027])).
% 0.61/0.82 tff(3312,plain,
% 0.61/0.82 ((op(e0, op(e1, e0)) = e0) <=> (e2 = e0)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3311])).
% 0.61/0.82 tff(3313,plain,
% 0.61/0.82 ((op(e0, op(e1, e0)) = e0) <=> (e0 = e2)),
% 0.61/0.82 inference(transitivity,[status(thm)],[3312, 217])).
% 0.61/0.82 tff(3314,plain,
% 0.61/0.82 ((e0 = e2) <=> (op(e0, op(e1, e0)) = e0)),
% 0.61/0.82 inference(symmetry,[status(thm)],[3313])).
% 0.61/0.82 tff(3315,plain,
% 0.61/0.82 ((~(e0 = e2)) <=> (~(op(e0, op(e1, e0)) = e0))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3314])).
% 0.61/0.82 tff(3316,plain,
% 0.61/0.82 (~(op(e0, op(e1, e0)) = e0)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[238, 3315])).
% 0.61/0.82 tff(3317,plain,
% 0.61/0.82 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[83, 3316])).
% 0.61/0.82 tff(3318,plain,
% 0.61/0.82 ($false),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[681, 3317, 3301, 1221, 3274])).
% 0.61/0.82 tff(3319,plain,((op(e0, e3) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e1, e1) = e2) | (op(e0, e1) = e2) | (op(e0, e2) = e1) | (op(e3, e3) = e0) | (op(e0, e1) = e1) | (~(op(e0, e0) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.82 tff(3320,plain,
% 0.61/0.82 (op(e0, e3) = e2),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[3319, 991, 12, 830, 1815, 63, 433, 3015])).
% 0.61/0.82 tff(3321,plain,
% 0.61/0.82 ((op(e0, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3320])).
% 0.61/0.82 tff(3322,plain,
% 0.61/0.82 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.61/0.82 inference(transitivity,[status(thm)],[3321, 72])).
% 0.61/0.82 tff(3323,plain,
% 0.61/0.82 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3322])).
% 0.61/0.82 tff(3324,plain,
% 0.61/0.82 (~(op(e2, e3) = e2)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[2232, 3323])).
% 0.61/0.82 tff(3325,plain,
% 0.61/0.82 ((op(e0, e3) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3320])).
% 0.61/0.82 tff(3326,plain,
% 0.61/0.82 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.61/0.82 inference(transitivity,[status(thm)],[3325, 1024])).
% 0.61/0.82 tff(3327,plain,
% 0.61/0.82 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3326])).
% 0.61/0.82 tff(3328,plain,
% 0.61/0.82 (~(op(e3, e3) = e2)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[725, 3327])).
% 0.61/0.82 tff(3329,plain,
% 0.61/0.82 (e1 = op(e0, e0)),
% 0.61/0.82 inference(symmetry,[status(thm)],[3015])).
% 0.61/0.82 tff(3330,plain,
% 0.61/0.82 ((e1 = e2) <=> (op(e0, e0) = e2)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3329])).
% 0.61/0.82 tff(3331,plain,
% 0.61/0.82 ((~(e1 = e2)) <=> (~(op(e0, e0) = e2))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3330])).
% 0.61/0.82 tff(3332,plain,
% 0.61/0.82 (~(op(e0, e0) = e2)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[324, 3331])).
% 0.61/0.82 tff(3333,plain,
% 0.61/0.82 ((op(e0, e3) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3320])).
% 0.61/0.82 tff(3334,plain,
% 0.61/0.82 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.61/0.82 inference(transitivity,[status(thm)],[3333, 218])).
% 0.61/0.82 tff(3335,plain,
% 0.61/0.82 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3334])).
% 0.61/0.82 tff(3336,plain,
% 0.61/0.82 (~(op(e1, e3) = e2)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[1755, 3335])).
% 0.61/0.82 tff(3337,plain,
% 0.61/0.82 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e2)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3320])).
% 0.61/0.82 tff(3338,plain,
% 0.61/0.82 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e2))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3337])).
% 0.61/0.82 tff(3339,plain,
% 0.61/0.82 (~(op(e0, e2) = e2)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[215, 3338])).
% 0.61/0.82 tff(3340,plain,
% 0.61/0.82 ((op(e0, e0) = op(e2, e0)) <=> (e1 = op(e2, e0))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3015])).
% 0.61/0.82 tff(3341,plain,
% 0.61/0.82 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e1)),
% 0.61/0.82 inference(transitivity,[status(thm)],[3340, 1384])).
% 0.61/0.82 tff(3342,plain,
% 0.61/0.82 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e1))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3341])).
% 0.61/0.82 tff(3343,plain,
% 0.61/0.82 (~(op(e2, e0) = e1)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[1827, 3342])).
% 0.61/0.82 tff(3344,plain,
% 0.61/0.82 ((op(e0, e3) = e0) <=> (e2 = e0)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3320])).
% 0.61/0.82 tff(3345,plain,
% 0.61/0.82 ((op(e0, e3) = e0) <=> (e0 = e2)),
% 0.61/0.82 inference(transitivity,[status(thm)],[3344, 217])).
% 0.61/0.82 tff(3346,plain,
% 0.61/0.82 ((e0 = e2) <=> (op(e0, e3) = e0)),
% 0.61/0.82 inference(symmetry,[status(thm)],[3345])).
% 0.61/0.82 tff(3347,plain,
% 0.61/0.82 ((~(e0 = e2)) <=> (~(op(e0, e3) = e0))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3346])).
% 0.61/0.82 tff(3348,plain,
% 0.61/0.82 (~(op(e0, e3) = e0)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[238, 3347])).
% 0.61/0.82 tff(3349,plain,
% 0.61/0.82 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[2384, 374, 63, 1414, 75, 640, 12, 830])).
% 0.61/0.82 tff(3350,plain,
% 0.61/0.82 (op(e1, e2) = e1),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[2275, 374, 107, 1820, 75, 12, 767, 1221, 3349, 1704])).
% 0.61/0.82 tff(3351,plain,
% 0.61/0.82 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e1)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3350])).
% 0.61/0.82 tff(3352,plain,
% 0.61/0.82 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e1))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3351])).
% 0.61/0.82 tff(3353,plain,
% 0.61/0.82 (~(op(e1, e1) = e1)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[1616, 3352])).
% 0.61/0.82 tff(3354,plain,
% 0.61/0.82 (op(e3, e1) = e1),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[450, 3353, 433, 3049])).
% 0.61/0.82 tff(3355,plain,
% 0.61/0.82 ((op(e1, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3350])).
% 0.61/0.82 tff(3356,plain,
% 0.61/0.82 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 0.61/0.82 inference(transitivity,[status(thm)],[3355, 1949])).
% 0.61/0.82 tff(3357,plain,
% 0.61/0.82 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3356])).
% 0.61/0.82 tff(3358,plain,
% 0.61/0.82 (~(op(e2, e2) = e1)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[764, 3357])).
% 0.61/0.82 tff(3359,plain,
% 0.61/0.82 (op(e2, e3) = e1),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[964, 3358, 1413, 3049])).
% 0.61/0.82 tff(3360,plain,
% 0.61/0.82 (op(e3, op(e2, e3)) = op(e3, e1)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3359])).
% 0.61/0.82 tff(3361,plain,
% 0.61/0.82 (op(e3, op(e2, e3)) = e1),
% 0.61/0.82 inference(transitivity,[status(thm)],[3360, 3354])).
% 0.61/0.82 tff(3362,plain,
% 0.61/0.82 ((op(e3, op(e2, e3)) = e3) <=> (e1 = e3)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3361])).
% 0.61/0.82 tff(3363,plain,
% 0.61/0.82 ((e1 = e3) <=> (op(e3, op(e2, e3)) = e3)),
% 0.61/0.82 inference(symmetry,[status(thm)],[3362])).
% 0.61/0.82 tff(3364,plain,
% 0.61/0.82 ((~(e1 = e3)) <=> (~(op(e3, op(e2, e3)) = e3))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3363])).
% 0.61/0.82 tff(3365,plain,
% 0.61/0.82 (~(op(e3, op(e2, e3)) = e3)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[591, 3364])).
% 0.61/0.82 tff(3366,plain,
% 0.61/0.82 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[471, 3365])).
% 0.61/0.82 tff(3367,plain,
% 0.61/0.82 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[681, 3366, 1221, 3349])).
% 0.61/0.82 tff(3368,plain,
% 0.61/0.82 (op(e3, op(e1, e3)) = e3),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[80, 3367])).
% 0.61/0.82 tff(3369,plain,
% 0.61/0.82 ((op(e2, e3) = e0) <=> (e1 = e0)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3359])).
% 0.61/0.82 tff(3370,plain,
% 0.61/0.82 ((op(e2, e3) = e0) <=> (e0 = e1)),
% 0.61/0.82 inference(transitivity,[status(thm)],[3369, 635])).
% 0.61/0.82 tff(3371,plain,
% 0.61/0.82 ((e0 = e1) <=> (op(e2, e3) = e0)),
% 0.61/0.82 inference(symmetry,[status(thm)],[3370])).
% 0.61/0.82 tff(3372,plain,
% 0.61/0.82 ((~(e0 = e1)) <=> (~(op(e2, e3) = e0))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3371])).
% 0.61/0.82 tff(3373,plain,
% 0.61/0.82 (~(op(e2, e3) = e0)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[625, 3372])).
% 0.61/0.82 tff(3374,plain,
% 0.61/0.82 (op(e1, e3) = e0),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[247, 3373, 2761, 63])).
% 0.61/0.82 tff(3375,plain,
% 0.61/0.82 (op(e3, op(e1, e3)) = op(e3, e0)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3374])).
% 0.61/0.82 tff(3376,plain,
% 0.61/0.82 (op(e3, e0) = op(e3, op(e1, e3))),
% 0.61/0.82 inference(symmetry,[status(thm)],[3375])).
% 0.61/0.82 tff(3377,plain,
% 0.61/0.82 ((op(e1, e2) = e2) <=> (e1 = e2)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3350])).
% 0.61/0.82 tff(3378,plain,
% 0.61/0.82 ((e1 = e2) <=> (op(e1, e2) = e2)),
% 0.61/0.82 inference(symmetry,[status(thm)],[3377])).
% 0.61/0.82 tff(3379,plain,
% 0.61/0.82 ((~(e1 = e2)) <=> (~(op(e1, e2) = e2))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3378])).
% 0.61/0.82 tff(3380,plain,
% 0.61/0.82 (~(op(e1, e2) = e2)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[324, 3379])).
% 0.61/0.82 tff(3381,plain,
% 0.61/0.82 (((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))),
% 0.61/0.82 inference(rewrite,[status(thm)],[])).
% 0.61/0.82 tff(3382,plain,
% 0.61/0.82 ((((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))),
% 0.61/0.82 inference(rewrite,[status(thm)],[])).
% 0.61/0.82 tff(3383,plain,
% 0.61/0.82 ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) <=> ((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e2, e2) = e2))),
% 0.61/0.82 inference(rewrite,[status(thm)],[])).
% 0.61/0.82 tff(3384,plain,
% 0.61/0.82 (((((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))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3383])).
% 0.61/0.82 tff(3385,plain,
% 0.61/0.82 (((((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))),
% 0.61/0.82 inference(transitivity,[status(thm)],[3384, 3382])).
% 0.61/0.82 tff(3386,plain,
% 0.61/0.82 ((((op(e0, e2) = e2) | (op(e1, e2) = e2)) | (op(e2, e2) = e2)) | (op(e3, e2) = e2)),
% 0.61/0.82 inference(and_elim,[status(thm)],[123])).
% 0.61/0.82 tff(3387,plain,
% 0.61/0.82 ((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e2, e2) = e2) | (op(e3, e2) = e2)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[3386, 3385])).
% 0.61/0.82 tff(3388,plain,
% 0.61/0.82 ((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e2, e2) = e2) | (op(e3, e2) = e2)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[3387, 3381])).
% 0.61/0.82 tff(3389,plain,
% 0.61/0.82 (op(e3, e2) = e2),
% 0.61/0.82 inference(unit_resolution,[status(thm)],[3388, 3380, 796, 1711])).
% 0.61/0.82 tff(3390,plain,
% 0.61/0.82 ((op(e3, e2) = e0) <=> (e2 = e0)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3389])).
% 0.61/0.82 tff(3391,plain,
% 0.61/0.82 ((op(e3, e2) = e0) <=> (e0 = e2)),
% 0.61/0.82 inference(transitivity,[status(thm)],[3390, 217])).
% 0.61/0.82 tff(3392,plain,
% 0.61/0.82 ((e0 = e2) <=> (op(e3, e2) = e0)),
% 0.61/0.82 inference(symmetry,[status(thm)],[3391])).
% 0.61/0.82 tff(3393,plain,
% 0.61/0.82 ((~(e0 = e2)) <=> (~(op(e3, e2) = e0))),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3392])).
% 0.61/0.82 tff(3394,plain,
% 0.61/0.82 (~(op(e3, e2) = e0)),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[238, 3393])).
% 0.61/0.82 tff(3395,plain,
% 0.61/0.82 ((op(e3, e1) = e0) <=> (e1 = e0)),
% 0.61/0.82 inference(monotonicity,[status(thm)],[3354])).
% 0.61/0.83 tff(3396,plain,
% 0.61/0.83 ((op(e3, e1) = e0) <=> (e0 = e1)),
% 0.61/0.83 inference(transitivity,[status(thm)],[3395, 635])).
% 0.61/0.83 tff(3397,plain,
% 0.61/0.83 ((e0 = e1) <=> (op(e3, e1) = e0)),
% 0.61/0.83 inference(symmetry,[status(thm)],[3396])).
% 0.61/0.83 tff(3398,plain,
% 0.61/0.83 ((~(e0 = e1)) <=> (~(op(e3, e1) = e0))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3397])).
% 0.61/0.83 tff(3399,plain,
% 0.61/0.83 (~(op(e3, e1) = e0)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[625, 3398])).
% 0.61/0.83 tff(3400,plain,
% 0.61/0.83 (op(e3, e0) = e0),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[295, 3399, 3394, 63])).
% 0.61/0.83 tff(3401,plain,
% 0.61/0.83 (e0 = op(e3, e0)),
% 0.61/0.83 inference(symmetry,[status(thm)],[3400])).
% 0.61/0.83 tff(3402,plain,
% 0.61/0.83 (e0 = e3),
% 0.61/0.83 inference(transitivity,[status(thm)],[3401, 3376, 3368])).
% 0.61/0.83 tff(3403,plain,
% 0.61/0.83 ($false),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[286, 3402])).
% 0.61/0.83 tff(3404,plain,((op(e3, e1) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e3, e3) = e0) | (op(e0, e3) = e0) | (op(e0, e1) = e1) | (op(e2, e0) = e1) | (op(e0, e2) = e2) | (op(e1, e3) = e2) | (op(e0, e0) = e2) | (op(e3, e3) = e2) | (op(e1, e1) = e2) | (op(e2, e3) = e2) | (op(e3, e0) = e1) | (op(e1, e0) = e1) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.83 tff(3405,plain,
% 0.61/0.83 (op(e3, e1) = e2),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[3404, 3348, 63, 1815, 433, 3343, 3339, 3336, 3332, 3328, 12, 3324, 3023, 3019, 830])).
% 0.61/0.83 tff(3406,plain,
% 0.61/0.83 (~(op(e0, e1) = e3)),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[3113, 3405, 3015])).
% 0.61/0.83 tff(3407,plain,
% 0.61/0.83 (op(e0, e1) = e0),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[860, 3406, 830, 433])).
% 0.61/0.83 tff(3408,plain,
% 0.61/0.83 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[1632, 3405, 3023])).
% 0.61/0.83 tff(3409,plain,
% 0.61/0.83 ((e1 = e3) <=> (op(e0, e0) = e3)),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3329])).
% 0.61/0.83 tff(3410,plain,
% 0.61/0.83 ((~(e1 = e3)) <=> (~(op(e0, e0) = e3))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3409])).
% 0.61/0.83 tff(3411,plain,
% 0.61/0.83 (~(op(e0, e0) = e3)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[591, 3410])).
% 0.61/0.83 tff(3412,plain,
% 0.61/0.83 ((op(e0, e3) = e3) <=> (e2 = e3)),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3320])).
% 0.61/0.83 tff(3413,plain,
% 0.61/0.83 ((e2 = e3) <=> (op(e0, e3) = e3)),
% 0.61/0.83 inference(symmetry,[status(thm)],[3412])).
% 0.61/0.83 tff(3414,plain,
% 0.61/0.83 ((~(e2 = e3)) <=> (~(op(e0, e3) = e3))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3413])).
% 0.61/0.83 tff(3415,plain,
% 0.61/0.83 (~(op(e0, e3) = e3)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[462, 3414])).
% 0.61/0.83 tff(3416,plain,
% 0.61/0.83 (op(e0, e2) = e3),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[1562, 3406, 3415, 3411])).
% 0.61/0.83 tff(3417,plain,
% 0.61/0.83 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3405])).
% 0.61/0.83 tff(3418,plain,
% 0.61/0.83 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3417])).
% 0.61/0.83 tff(3419,plain,
% 0.61/0.83 (~(op(e3, e0) = e2)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[1333, 3418])).
% 0.61/0.83 tff(3420,assumption,(op(e0, e1) = e0), introduced(assumption)).
% 0.61/0.83 tff(3421,plain,
% 0.61/0.83 (e2 = op(e1, e0)),
% 0.61/0.83 inference(symmetry,[status(thm)],[776])).
% 0.61/0.83 tff(3422,plain,
% 0.61/0.83 (op(e0, e2) = op(e0, op(e1, e0))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3421])).
% 0.61/0.83 tff(3423,plain,
% 0.61/0.83 (op(e0, op(e1, e0)) = op(e0, e2)),
% 0.61/0.83 inference(symmetry,[status(thm)],[3422])).
% 0.61/0.83 tff(3424,plain,
% 0.61/0.83 (op(e0, e1) = e3),
% 0.61/0.83 inference(transitivity,[status(thm)],[3420, 1833, 3423, 903])).
% 0.61/0.83 tff(3425,plain,
% 0.61/0.83 ($false),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[544, 3424])).
% 0.61/0.83 tff(3426,plain,((~(op(e1, e0) = e2)) | (op(e0, e1) = e3) | (~(op(e0, e2) = e3)) | (~(op(e0, op(e1, e0)) = e0)) | (~(op(e0, e1) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.83 tff(3427,plain,
% 0.61/0.83 (~(op(e1, e0) = e2)),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[3426, 84, 903, 544, 3420])).
% 0.61/0.83 tff(3428,plain,
% 0.61/0.83 (op(e1, e2) = e2),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[135, 3427, 12, 107])).
% 0.61/0.83 tff(3429,plain,
% 0.61/0.83 (e2 = op(e1, e2)),
% 0.61/0.83 inference(symmetry,[status(thm)],[3428])).
% 0.61/0.83 tff(3430,plain,
% 0.61/0.83 (op(e2, e2) = op(e2, op(e1, e2))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3429])).
% 0.61/0.83 tff(3431,plain,
% 0.61/0.83 (op(e2, e2) = e2),
% 0.61/0.83 inference(transitivity,[status(thm)],[3430, 103])).
% 0.61/0.83 tff(3432,plain,
% 0.61/0.83 (op(e2, e0) = e2),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[757, 3427, 1820, 1699])).
% 0.61/0.83 tff(3433,plain,
% 0.61/0.83 ((op(e2, e0) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3432])).
% 0.61/0.83 tff(3434,plain,
% 0.61/0.83 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.61/0.83 inference(transitivity,[status(thm)],[3433, 810])).
% 0.61/0.83 tff(3435,plain,
% 0.61/0.83 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3434])).
% 0.61/0.83 tff(3436,plain,
% 0.61/0.83 (~(op(e2, e2) = e2)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[1200, 3435])).
% 0.61/0.83 tff(3437,plain,
% 0.61/0.83 ($false),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[3436, 3431])).
% 0.61/0.83 tff(3438,plain,(((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))) | (op(e1, e1) = e2) | (op(e1, e3) = e2) | (op(e0, e0) = e2) | (op(e3, e0) = e2) | (~(op(e0, e2) = e3)) | (op(e0, e1) = e3) | (~(op(e0, e1) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.83 tff(3439,plain,
% 0.61/0.83 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[3438, 3336, 12, 3332, 3419, 3416, 3406, 3407])).
% 0.61/0.83 tff(3440,plain,
% 0.61/0.83 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[681, 3439, 1815, 3408])).
% 0.61/0.83 tff(3441,plain,
% 0.61/0.83 (op(e0, op(e2, e0)) = e0),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[967, 3440])).
% 0.61/0.83 tff(3442,assumption,(op(e2, e0) = e3), introduced(assumption)).
% 0.61/0.83 tff(3443,plain,
% 0.61/0.83 (e3 = op(e2, e0)),
% 0.61/0.83 inference(symmetry,[status(thm)],[3442])).
% 0.61/0.83 tff(3444,plain,
% 0.61/0.83 (op(e0, e3) = op(e0, op(e2, e0))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3443])).
% 0.61/0.83 tff(3445,plain,
% 0.61/0.83 (op(e0, op(e2, e0)) = op(e0, e3)),
% 0.61/0.83 inference(symmetry,[status(thm)],[3444])).
% 0.61/0.83 tff(3446,plain,
% 0.61/0.83 (op(e0, e1) = e2),
% 0.61/0.83 inference(transitivity,[status(thm)],[3420, 1897, 3445, 1114])).
% 0.61/0.83 tff(3447,plain,
% 0.61/0.83 ($false),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[830, 3446])).
% 0.61/0.83 tff(3448,plain,((~(op(e2, e0) = e3)) | (op(e0, e1) = e2) | (~(op(e0, e3) = e2)) | (~(op(e0, op(e2, e0)) = e0)) | (~(op(e0, e1) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.83 tff(3449,plain,
% 0.61/0.83 (~(op(e2, e0) = e3)),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[3448, 3320, 830, 3441, 3407])).
% 0.61/0.83 tff(3450,plain,
% 0.61/0.83 (op(e0, e1) = e3),
% 0.61/0.83 inference(transitivity,[status(thm)],[3420, 1897, 1220, 903])).
% 0.61/0.83 tff(3451,plain,
% 0.61/0.83 ($false),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[544, 3450])).
% 0.61/0.83 tff(3452,plain,((~(op(e2, e0) = e2)) | (op(e0, e1) = e3) | (~(op(e0, e1) = e0)) | (~(op(e0, op(e2, e0)) = e0)) | (~(op(e0, e2) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.83 tff(3453,plain,
% 0.61/0.83 (~(op(e2, e0) = e2)),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[3452, 3406, 3407, 3441, 3416])).
% 0.61/0.83 tff(3454,plain,
% 0.61/0.83 (op(e2, e0) = e0),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[1909, 3453, 3343, 3449])).
% 0.61/0.83 tff(3455,plain,
% 0.61/0.83 (e0 = op(e2, e0)),
% 0.61/0.83 inference(symmetry,[status(thm)],[3454])).
% 0.61/0.83 tff(3456,plain,
% 0.61/0.83 (op(e0, e0) = op(e0, op(e2, e0))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3455])).
% 0.61/0.83 tff(3457,plain,
% 0.61/0.83 (op(e0, op(e2, e0)) = op(e0, e0)),
% 0.61/0.83 inference(symmetry,[status(thm)],[3456])).
% 0.61/0.83 tff(3458,plain,
% 0.61/0.83 (e0 = op(e0, op(e2, e0))),
% 0.61/0.83 inference(symmetry,[status(thm)],[3441])).
% 0.61/0.83 tff(3459,plain,
% 0.61/0.83 (op(e0, e1) = e1),
% 0.61/0.83 inference(transitivity,[status(thm)],[3407, 3458, 3457, 3015])).
% 0.61/0.83 tff(3460,plain,
% 0.61/0.83 ($false),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[433, 3459])).
% 0.61/0.83 tff(3461,plain,((op(e0, e2) = e1) | (op(e0, e1) = e1) | (op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e3, e3) = e0) | (op(e0, e0) = e0) | (op(e2, op(e0, e2)) = e2) | (op(e1, op(e0, e1)) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.83 tff(3462,plain,
% 0.61/0.83 (op(e2, op(e0, e2)) = e2),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[3461, 991, 830, 12, 63, 989, 2451, 1814])).
% 0.61/0.83 tff(3463,plain,
% 0.61/0.83 ($false),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[1009, 3462, 991, 992])).
% 0.61/0.83 tff(3464,plain,((op(e0, e2) = e1) | (~(op(e2, e1) = e2)) | (op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e3, e3) = e0) | (op(e0, e0) = e0) | (op(e1, op(e0, e1)) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.83 tff(3465,plain,
% 0.61/0.83 (op(e0, e2) = e1),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[3464, 1704, 830, 12, 63, 989, 1814])).
% 0.61/0.83 tff(3466,plain,
% 0.61/0.83 ((op(e0, e2) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3465])).
% 0.61/0.83 tff(3467,plain,
% 0.61/0.83 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 0.61/0.83 inference(transitivity,[status(thm)],[3466, 1587])).
% 0.61/0.83 tff(3468,plain,
% 0.61/0.83 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3467])).
% 0.61/0.83 tff(3469,plain,
% 0.61/0.83 (~(op(e1, e2) = e1)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[703, 3468])).
% 0.61/0.83 tff(3470,plain,
% 0.61/0.83 (op(e3, e0) = e2),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[1713, 336, 374, 393, 12, 830])).
% 0.61/0.83 tff(3471,plain,
% 0.61/0.83 ((op(e3, e0) = e1) <=> (e2 = e1)),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3470])).
% 0.61/0.83 tff(3472,plain,
% 0.61/0.83 ((op(e3, e0) = e1) <=> (e1 = e2)),
% 0.61/0.83 inference(transitivity,[status(thm)],[3471, 317])).
% 0.61/0.83 tff(3473,plain,
% 0.61/0.83 ((e1 = e2) <=> (op(e3, e0) = e1)),
% 0.61/0.83 inference(symmetry,[status(thm)],[3472])).
% 0.61/0.83 tff(3474,plain,
% 0.61/0.83 ((~(e1 = e2)) <=> (~(op(e3, e0) = e1))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3473])).
% 0.61/0.83 tff(3475,plain,
% 0.61/0.83 (~(op(e3, e0) = e1)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[324, 3474])).
% 0.61/0.83 tff(3476,plain,
% 0.61/0.83 (op(e1, e1) = e1),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[450, 352, 433, 3049])).
% 0.61/0.83 tff(3477,plain,
% 0.61/0.83 ((op(e1, e0) = op(e1, e1)) <=> (op(e1, e0) = e1)),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3476])).
% 0.61/0.83 tff(3478,plain,
% 0.61/0.83 ((~(op(e1, e0) = op(e1, e1))) <=> (~(op(e1, e0) = e1))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3477])).
% 0.61/0.83 tff(3479,plain,
% 0.61/0.83 (~(op(e1, e0) = e1)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[440, 3478])).
% 0.61/0.83 tff(3480,plain,
% 0.61/0.83 ($false),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[2384, 3479, 3475, 63, 374, 393, 334, 12, 830])).
% 0.61/0.83 tff(3481,plain,(((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (op(e3, e3) = e0) | (op(e3, e1) = e2) | (op(e1, e1) = e2) | (op(e0, e1) = e2) | (op(e0, e1) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.83 tff(3482,plain,
% 0.61/0.83 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[3481, 374, 63, 12, 830, 2451])).
% 0.61/0.83 tff(3483,plain,
% 0.61/0.83 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, op(e2, e1)) = e1)),
% 0.61/0.83 inference(transitivity,[status(thm)],[3467, 1998])).
% 0.61/0.83 tff(3484,plain,
% 0.61/0.83 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, op(e2, e1)) = e1))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3483])).
% 0.61/0.83 tff(3485,plain,
% 0.61/0.83 (~(op(e1, op(e2, e1)) = e1)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[703, 3484])).
% 0.61/0.83 tff(3486,plain,
% 0.61/0.83 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[546, 3485])).
% 0.61/0.83 tff(3487,plain,
% 0.61/0.83 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[681, 3486, 1815, 3482])).
% 0.61/0.83 tff(3488,plain,
% 0.61/0.83 (op(e2, op(e1, e2)) = e2),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[102, 3487])).
% 0.61/0.83 tff(3489,plain,
% 0.61/0.83 (~(op(e1, e2) = e2)),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[1269, 3488, 1711])).
% 0.61/0.83 tff(3490,plain,
% 0.61/0.83 (op(e0, op(e1, e0)) = e0),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[83, 3487])).
% 0.61/0.83 tff(3491,plain,
% 0.61/0.83 (e0 = e1),
% 0.61/0.83 inference(transitivity,[status(thm)],[1833, 777, 798])).
% 0.61/0.83 tff(3492,plain,
% 0.61/0.83 ($false),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[625, 3491])).
% 0.61/0.83 tff(3493,plain,((~(op(e1, e0) = e2)) | (~(op(e0, op(e1, e0)) = e0)) | (~(op(e0, e2) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.83 tff(3494,plain,
% 0.61/0.83 (~(op(e1, e0) = e2)),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[3493, 3490, 3465])).
% 0.61/0.83 tff(3495,plain,
% 0.61/0.83 (op(e1, e3) = e2),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[135, 3494, 12, 3489])).
% 0.61/0.83 tff(3496,plain,
% 0.61/0.83 ($false),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[2123, 3495, 3489, 1704, 1815, 3482, 3469])).
% 0.61/0.83 tff(3497,plain,((op(e3, e1) = e2) | (op(e1, e1) = e2) | (op(e0, e1) = e2) | (op(e3, e3) = e0) | (op(e0, e0) = e0) | (op(e1, op(e0, e1)) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.83 tff(3498,plain,
% 0.61/0.83 (op(e3, e1) = e2),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[3497, 830, 12, 63, 989, 1814])).
% 0.61/0.83 tff(3499,plain,
% 0.61/0.83 ((e2 = op(e2, e0)) <=> (op(e2, e0) = e2)),
% 0.61/0.83 inference(commutativity,[status(thm)],[])).
% 0.61/0.83 tff(3500,plain,
% 0.61/0.83 ((op(e1, e1) = e1) <=> (op(e1, e1) = op(e1, e2))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[1724])).
% 0.61/0.83 tff(3501,plain,
% 0.61/0.83 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e1)),
% 0.61/0.83 inference(symmetry,[status(thm)],[3500])).
% 0.61/0.83 tff(3502,plain,
% 0.61/0.83 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e1))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3501])).
% 0.61/0.83 tff(3503,plain,
% 0.61/0.83 (~(op(e1, e1) = e1)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[1616, 3502])).
% 0.61/0.83 tff(3504,plain,
% 0.61/0.83 ((op(e3, e1) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[1146])).
% 0.61/0.83 tff(3505,plain,
% 0.61/0.83 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.61/0.83 inference(transitivity,[status(thm)],[3504, 1024])).
% 0.61/0.83 tff(3506,plain,
% 0.61/0.83 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3505])).
% 0.61/0.83 tff(3507,plain,
% 0.61/0.83 (~(op(e3, e3) = e2)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[399, 3506])).
% 0.61/0.83 tff(3508,plain,
% 0.61/0.83 (op(e3, e3) = e3),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[266, 372, 63, 3507])).
% 0.61/0.83 tff(3509,plain,
% 0.61/0.83 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e3)),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3508])).
% 0.61/0.83 tff(3510,plain,
% 0.61/0.83 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e3))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3509])).
% 0.61/0.83 tff(3511,plain,
% 0.61/0.83 (~(op(e1, e3) = e3)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[368, 3510])).
% 0.61/0.83 tff(3512,plain,
% 0.61/0.83 (op(e3, e0) = op(e1, e2)),
% 0.61/0.83 inference(transitivity,[status(thm)],[1729, 1609, 1723])).
% 0.61/0.83 tff(3513,plain,
% 0.61/0.83 ((op(e3, e0) = e3) <=> (op(e1, e2) = e3)),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3512])).
% 0.61/0.83 tff(3514,plain,
% 0.61/0.83 ((op(e1, e2) = e3) <=> (op(e3, e0) = e3)),
% 0.61/0.83 inference(symmetry,[status(thm)],[3513])).
% 0.61/0.83 tff(3515,plain,
% 0.61/0.83 ((~(op(e1, e2) = e3)) <=> (~(op(e3, e0) = e3))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3514])).
% 0.61/0.83 tff(3516,plain,
% 0.61/0.83 ((e1 = e3) <=> (op(e1, e2) = e3)),
% 0.61/0.83 inference(monotonicity,[status(thm)],[1724])).
% 0.61/0.83 tff(3517,plain,
% 0.61/0.83 ((~(e1 = e3)) <=> (~(op(e1, e2) = e3))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3516])).
% 0.61/0.83 tff(3518,plain,
% 0.61/0.83 (~(op(e1, e2) = e3)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[591, 3517])).
% 0.61/0.83 tff(3519,plain,
% 0.61/0.83 (~(op(e3, e0) = e3)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[3518, 3515])).
% 0.61/0.83 tff(3520,plain,
% 0.61/0.83 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3508])).
% 0.61/0.83 tff(3521,plain,
% 0.61/0.83 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e2) = e3))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3520])).
% 0.61/0.83 tff(3522,plain,
% 0.61/0.83 (~(op(e3, e2) = e3)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[1111, 3521])).
% 0.61/0.83 tff(3523,plain,
% 0.61/0.83 (op(e0, e3) = e1),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[718, 1732, 433, 1728])).
% 0.61/0.83 tff(3524,plain,
% 0.61/0.83 (op(e0, e0) = e2),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[2585, 3523, 1221, 3522, 3519, 3511, 3507, 1814, 3503, 989, 1732, 830])).
% 0.61/0.83 tff(3525,plain,
% 0.61/0.83 ((op(e0, e0) = op(e2, e0)) <=> (e2 = op(e2, e0))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3524])).
% 0.61/0.83 tff(3526,plain,
% 0.61/0.83 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e2)),
% 0.61/0.83 inference(transitivity,[status(thm)],[3525, 3499])).
% 0.61/0.83 tff(3527,plain,
% 0.61/0.83 ((op(e2, e0) = e2) <=> (op(e0, e0) = op(e2, e0))),
% 0.61/0.83 inference(symmetry,[status(thm)],[3526])).
% 0.61/0.83 tff(3528,plain,
% 0.61/0.83 ((op(e3, e1) = e0) <=> (e2 = e0)),
% 0.61/0.83 inference(monotonicity,[status(thm)],[1146])).
% 0.61/0.83 tff(3529,plain,
% 0.61/0.83 ((op(e3, e1) = e0) <=> (e0 = e2)),
% 0.61/0.83 inference(transitivity,[status(thm)],[3528, 217])).
% 0.61/0.83 tff(3530,plain,
% 0.61/0.83 ((e0 = e2) <=> (op(e3, e1) = e0)),
% 0.61/0.83 inference(symmetry,[status(thm)],[3529])).
% 0.61/0.83 tff(3531,plain,
% 0.61/0.83 ((~(e0 = e2)) <=> (~(op(e3, e1) = e0))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3530])).
% 0.61/0.83 tff(3532,plain,
% 0.61/0.83 (~(op(e3, e1) = e0)),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[238, 3531])).
% 0.61/0.83 tff(3533,plain,
% 0.61/0.83 ((op(e3, e0) = e0) <=> (op(e1, e2) = e0)),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3512])).
% 0.61/0.83 tff(3534,plain,
% 0.61/0.83 ((op(e1, e2) = e0) <=> (op(e3, e0) = e0)),
% 0.61/0.83 inference(symmetry,[status(thm)],[3533])).
% 0.61/0.83 tff(3535,plain,
% 0.61/0.83 ((~(op(e1, e2) = e0)) <=> (~(op(e3, e0) = e0))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[3534])).
% 0.61/0.83 tff(3536,plain,
% 0.61/0.83 ((e0 = e1) <=> (e0 = op(e1, e2))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[1724])).
% 0.61/0.83 tff(3537,plain,
% 0.61/0.83 ((e0 = e1) <=> (op(e1, e2) = e0)),
% 0.61/0.83 inference(transitivity,[status(thm)],[3536, 1299])).
% 0.61/0.84 tff(3538,plain,
% 0.61/0.84 ((~(e0 = e1)) <=> (~(op(e1, e2) = e0))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3537])).
% 0.61/0.84 tff(3539,plain,
% 0.61/0.84 (~(op(e1, e2) = e0)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[625, 3538])).
% 0.61/0.84 tff(3540,plain,
% 0.61/0.84 (~(op(e3, e0) = e0)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[3539, 3535])).
% 0.61/0.84 tff(3541,plain,
% 0.61/0.84 (op(e3, e2) = e0),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[295, 3540, 3532, 63])).
% 0.61/0.84 tff(3542,plain,
% 0.61/0.84 (e0 = op(e3, e2)),
% 0.61/0.84 inference(symmetry,[status(thm)],[3541])).
% 0.61/0.84 tff(3543,plain,
% 0.61/0.84 (op(e2, e0) = op(e2, op(e3, e2))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3542])).
% 0.61/0.84 tff(3544,plain,
% 0.61/0.84 (op(e2, e0) = e2),
% 0.61/0.84 inference(transitivity,[status(thm)],[3543, 336])).
% 0.61/0.84 tff(3545,plain,
% 0.61/0.84 (op(e0, e0) = op(e2, e0)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[3544, 3527])).
% 0.61/0.84 tff(3546,plain,
% 0.61/0.84 ($false),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[1827, 3545])).
% 0.61/0.84 tff(3547,plain,(((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e1, op(e0, e1)) = e1) | (op(e0, e0) = e0) | (op(e0, e1) = e2) | (op(e0, e1) = e1) | (op(e3, e3) = e0) | (~(op(e3, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.84 tff(3548,plain,
% 0.61/0.84 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[3547, 830, 1814, 989, 1815, 2451, 63, 3498])).
% 0.61/0.84 tff(3549,plain,
% 0.61/0.84 ((op(e0, e2) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[798])).
% 0.61/0.84 tff(3550,plain,
% 0.61/0.84 ((op(e0, e2) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 0.61/0.84 inference(transitivity,[status(thm)],[3549, 1587])).
% 0.61/0.84 tff(3551,plain,
% 0.61/0.84 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3550])).
% 0.61/0.84 tff(3552,plain,
% 0.61/0.84 (~(op(e1, e2) = e1)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[703, 3551])).
% 0.61/0.84 tff(3553,plain,
% 0.61/0.84 (op(e2, op(e0, e2)) = op(e2, e1)),
% 0.61/0.84 inference(monotonicity,[status(thm)],[798])).
% 0.61/0.84 tff(3554,plain,
% 0.61/0.84 ((op(e2, op(e0, e2)) = e2) <=> (op(e2, e1) = e2)),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3553])).
% 0.61/0.84 tff(3555,plain,
% 0.61/0.84 ((~(op(e2, op(e0, e2)) = e2)) <=> (~(op(e2, e1) = e2))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3554])).
% 0.61/0.84 tff(3556,plain,
% 0.61/0.84 (~(op(e2, e1) = e2)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[2452, 3555])).
% 0.61/0.84 tff(3557,plain,
% 0.61/0.84 (op(e3, e1) = e2),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[1018, 3556, 12, 830])).
% 0.61/0.84 tff(3558,plain,
% 0.61/0.84 ((op(e3, e1) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3557])).
% 0.61/0.84 tff(3559,plain,
% 0.61/0.84 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.61/0.84 inference(transitivity,[status(thm)],[3558, 1024])).
% 0.61/0.84 tff(3560,plain,
% 0.61/0.84 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3559])).
% 0.61/0.84 tff(3561,plain,
% 0.61/0.84 (~(op(e3, e3) = e2)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[399, 3560])).
% 0.61/0.84 tff(3562,plain,
% 0.61/0.84 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3557])).
% 0.61/0.84 tff(3563,plain,
% 0.61/0.84 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3562])).
% 0.61/0.84 tff(3564,plain,
% 0.61/0.84 (~(op(e3, e0) = e2)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[1333, 3563])).
% 0.61/0.84 tff(3565,plain,
% 0.61/0.84 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[1994, 3564, 3561, 3552, 12, 830])).
% 0.61/0.84 tff(3566,plain,
% 0.61/0.84 ((op(e0, e2) = e2) <=> (e1 = e2)),
% 0.61/0.84 inference(monotonicity,[status(thm)],[798])).
% 0.61/0.84 tff(3567,plain,
% 0.61/0.84 ((e1 = e2) <=> (op(e0, e2) = e2)),
% 0.61/0.84 inference(symmetry,[status(thm)],[3566])).
% 0.61/0.84 tff(3568,plain,
% 0.61/0.84 ((~(e1 = e2)) <=> (~(op(e0, e2) = e2))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3567])).
% 0.61/0.84 tff(3569,plain,
% 0.61/0.84 (~(op(e0, e2) = e2)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[324, 3568])).
% 0.61/0.84 tff(3570,plain,
% 0.61/0.84 (op(e0, e3) = e2),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[887, 1820, 830, 3569])).
% 0.61/0.84 tff(3571,plain,
% 0.61/0.84 ((op(e0, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3570])).
% 0.61/0.84 tff(3572,plain,
% 0.61/0.84 ((op(e0, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.61/0.84 inference(transitivity,[status(thm)],[3571, 72])).
% 0.61/0.84 tff(3573,plain,
% 0.61/0.84 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3572])).
% 0.61/0.84 tff(3574,plain,
% 0.61/0.84 (~(op(e2, e3) = e2)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[2232, 3573])).
% 0.61/0.84 tff(3575,plain,
% 0.61/0.84 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e0) = e1)),
% 0.61/0.84 inference(monotonicity,[status(thm)],[798])).
% 0.61/0.84 tff(3576,plain,
% 0.61/0.84 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e0) = e1))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3575])).
% 0.61/0.84 tff(3577,plain,
% 0.61/0.84 (~(op(e0, e0) = e1)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[1190, 3576])).
% 0.61/0.84 tff(3578,plain,
% 0.61/0.84 (op(e0, e0) = e3),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[1100, 1820, 989, 3577])).
% 0.61/0.84 tff(3579,plain,
% 0.61/0.84 ((op(e0, e0) = op(e2, e0)) <=> (e3 = op(e2, e0))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3578])).
% 0.61/0.84 tff(3580,plain,
% 0.61/0.84 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e3)),
% 0.61/0.84 inference(transitivity,[status(thm)],[3579, 1337])).
% 0.61/0.84 tff(3581,plain,
% 0.61/0.84 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e3))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3580])).
% 0.61/0.84 tff(3582,plain,
% 0.61/0.84 (~(op(e2, e0) = e3)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[1827, 3581])).
% 0.61/0.84 tff(3583,plain,
% 0.61/0.84 (op(e3, e1) = e2),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[1018, 10, 12, 830])).
% 0.61/0.84 tff(3584,plain,
% 0.61/0.84 ((op(e3, e1) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3583])).
% 0.61/0.84 tff(3585,plain,
% 0.61/0.84 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.61/0.84 inference(transitivity,[status(thm)],[3584, 1024])).
% 0.61/0.84 tff(3586,plain,
% 0.61/0.84 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3585])).
% 0.61/0.84 tff(3587,plain,
% 0.61/0.84 (~(op(e3, e3) = e2)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[399, 3586])).
% 0.61/0.84 tff(3588,plain,
% 0.61/0.84 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3583])).
% 0.61/0.84 tff(3589,plain,
% 0.61/0.84 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3588])).
% 0.61/0.84 tff(3590,plain,
% 0.61/0.84 (~(op(e3, e0) = e2)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[1333, 3589])).
% 0.61/0.84 tff(3591,plain,
% 0.61/0.84 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[1994, 3590, 3587, 3552, 12, 830])).
% 0.61/0.84 tff(3592,plain,
% 0.61/0.84 ((op(e0, e3) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3570])).
% 0.61/0.84 tff(3593,plain,
% 0.61/0.84 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.61/0.84 inference(transitivity,[status(thm)],[3592, 218])).
% 0.61/0.84 tff(3594,plain,
% 0.61/0.84 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3593])).
% 0.61/0.84 tff(3595,plain,
% 0.61/0.84 (~(op(e1, e3) = e2)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[1755, 3594])).
% 0.61/0.84 tff(3596,plain,
% 0.61/0.84 (~(op(e1, e0) = e2)),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[3493, 84, 798])).
% 0.61/0.84 tff(3597,plain,
% 0.61/0.84 (op(e1, e2) = e2),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[135, 3596, 12, 107])).
% 0.61/0.84 tff(3598,plain,
% 0.61/0.84 (e2 = op(e1, e2)),
% 0.61/0.84 inference(symmetry,[status(thm)],[3597])).
% 0.61/0.84 tff(3599,plain,
% 0.61/0.84 (op(e2, e2) = op(e2, op(e1, e2))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3598])).
% 0.61/0.84 tff(3600,plain,
% 0.61/0.84 (op(e2, e2) = e2),
% 0.61/0.84 inference(transitivity,[status(thm)],[3599, 103])).
% 0.61/0.84 tff(3601,plain,
% 0.61/0.84 (op(e2, e0) = e2),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[757, 3596, 1820, 1699])).
% 0.61/0.84 tff(3602,plain,
% 0.61/0.84 ((op(e2, e0) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3601])).
% 0.61/0.84 tff(3603,plain,
% 0.61/0.84 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.61/0.84 inference(transitivity,[status(thm)],[3602, 810])).
% 0.61/0.84 tff(3604,plain,
% 0.61/0.84 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3603])).
% 0.61/0.84 tff(3605,plain,
% 0.61/0.84 (~(op(e2, e2) = e2)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[1200, 3604])).
% 0.61/0.84 tff(3606,plain,
% 0.61/0.84 ($false),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[3605, 3600])).
% 0.61/0.84 tff(3607,plain,(((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))) | (op(e1, e1) = e2) | (op(e1, e3) = e2) | (op(e0, e0) = e2) | (op(e3, e0) = e2) | (~(op(e0, e2) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.61/0.84 tff(3608,plain,
% 0.61/0.84 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[3607, 3595, 12, 1820, 3590, 798])).
% 0.61/0.84 tff(3609,plain,
% 0.61/0.84 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[681, 3608, 1221, 3591])).
% 0.61/0.84 tff(3610,plain,
% 0.61/0.84 (op(e0, op(e2, e0)) = e0),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[967, 3609])).
% 0.61/0.84 tff(3611,plain,
% 0.61/0.84 (~(op(e2, e0) = e0)),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[1900, 3578, 3610])).
% 0.61/0.84 tff(3612,plain,
% 0.61/0.84 ((op(e0, e2) = e0) <=> (e1 = e0)),
% 0.61/0.84 inference(monotonicity,[status(thm)],[798])).
% 0.61/0.84 tff(3613,plain,
% 0.61/0.84 ((op(e0, e2) = e0) <=> (e0 = e1)),
% 0.61/0.84 inference(transitivity,[status(thm)],[3612, 635])).
% 0.61/0.84 tff(3614,plain,
% 0.61/0.84 ((e0 = e1) <=> (op(e0, e2) = e0)),
% 0.61/0.84 inference(symmetry,[status(thm)],[3613])).
% 0.61/0.84 tff(3615,plain,
% 0.61/0.84 ((~(e0 = e1)) <=> (~(op(e0, e2) = e0))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3614])).
% 0.61/0.84 tff(3616,plain,
% 0.61/0.84 (~(op(e0, e2) = e0)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[625, 3615])).
% 0.61/0.84 tff(3617,plain,
% 0.61/0.84 ((op(e0, e3) = e0) <=> (e2 = e0)),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3570])).
% 0.61/0.84 tff(3618,plain,
% 0.61/0.84 ((op(e0, e3) = e0) <=> (e0 = e2)),
% 0.61/0.84 inference(transitivity,[status(thm)],[3617, 217])).
% 0.61/0.84 tff(3619,plain,
% 0.61/0.84 ((e0 = e2) <=> (op(e0, e3) = e0)),
% 0.61/0.84 inference(symmetry,[status(thm)],[3618])).
% 0.61/0.84 tff(3620,plain,
% 0.61/0.84 ((~(e0 = e2)) <=> (~(op(e0, e3) = e0))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3619])).
% 0.61/0.84 tff(3621,plain,
% 0.61/0.84 (~(op(e0, e3) = e0)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[238, 3620])).
% 0.61/0.84 tff(3622,plain,
% 0.61/0.84 (op(e0, e1) = e0),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[1357, 3621, 989, 3616])).
% 0.61/0.84 tff(3623,plain,
% 0.61/0.84 (op(e1, op(e0, e1)) = op(e1, e0)),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3622])).
% 0.61/0.84 tff(3624,plain,
% 0.61/0.84 ((op(e1, op(e0, e1)) = e1) <=> (op(e1, e0) = e1)),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3623])).
% 0.61/0.84 tff(3625,plain,
% 0.61/0.84 ((~(op(e1, op(e0, e1)) = e1)) <=> (~(op(e1, e0) = e1))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3624])).
% 0.61/0.84 tff(3626,plain,
% 0.61/0.84 (~(op(e1, e0) = e1)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[1814, 3625])).
% 0.61/0.84 tff(3627,plain,
% 0.61/0.84 ((op(e0, e0) = op(e3, e0)) <=> (e3 = op(e3, e0))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3578])).
% 0.61/0.84 tff(3628,plain,
% 0.61/0.84 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 0.61/0.84 inference(transitivity,[status(thm)],[3627, 2715])).
% 0.61/0.84 tff(3629,plain,
% 0.61/0.84 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e3))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3628])).
% 0.61/0.84 tff(3630,plain,
% 0.61/0.84 (~(op(e3, e0) = e3)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[1638, 3629])).
% 0.61/0.84 tff(3631,plain,
% 0.61/0.84 (op(e3, op(e2, e3)) = e3),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[471, 3609])).
% 0.61/0.84 tff(3632,plain,
% 0.61/0.84 ((op(e0, e1) = op(e2, e1)) <=> (e0 = op(e2, e1))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3622])).
% 0.61/0.84 tff(3633,plain,
% 0.61/0.84 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 0.61/0.84 inference(transitivity,[status(thm)],[3632, 3142])).
% 0.61/0.84 tff(3634,plain,
% 0.61/0.84 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e0))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3633])).
% 0.61/0.84 tff(3635,plain,
% 0.61/0.84 (~(op(e2, e1) = e0)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[61, 3634])).
% 0.61/0.84 tff(3636,plain,
% 0.61/0.84 (op(e2, e2) = e2),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[524, 74, 10, 767])).
% 0.61/0.84 tff(3637,plain,
% 0.61/0.84 ((op(e2, e2) = e0) <=> (e2 = e0)),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3636])).
% 0.61/0.84 tff(3638,plain,
% 0.61/0.84 ((op(e2, e2) = e0) <=> (e0 = e2)),
% 0.61/0.84 inference(transitivity,[status(thm)],[3637, 217])).
% 0.61/0.84 tff(3639,plain,
% 0.61/0.84 ((e0 = e2) <=> (op(e2, e2) = e0)),
% 0.61/0.84 inference(symmetry,[status(thm)],[3638])).
% 0.61/0.84 tff(3640,plain,
% 0.61/0.84 ((~(e0 = e2)) <=> (~(op(e2, e2) = e0))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3639])).
% 0.61/0.84 tff(3641,plain,
% 0.61/0.84 (~(op(e2, e2) = e0)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[238, 3640])).
% 0.61/0.84 tff(3642,assumption,(~(op(e2, e0) = e3)), introduced(assumption)).
% 0.61/0.84 tff(3643,assumption,(~(op(e2, e0) = e0)), introduced(assumption)).
% 0.61/0.84 tff(3644,plain,
% 0.61/0.84 (op(e2, e0) = e1),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[1909, 74, 3643, 3642])).
% 0.61/0.84 tff(3645,plain,
% 0.61/0.84 ((op(e2, e0) = op(e3, e0)) <=> (e1 = op(e3, e0))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3644])).
% 0.61/0.84 tff(3646,plain,
% 0.61/0.84 ((op(e2, e0) = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 0.61/0.84 inference(transitivity,[status(thm)],[3645, 373])).
% 0.61/0.84 tff(3647,plain,
% 0.61/0.84 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e1))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3646])).
% 0.61/0.84 tff(3648,plain,
% 0.61/0.84 (~(op(e3, e0) = e1)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[1229, 3647])).
% 0.61/0.84 tff(3649,plain,
% 0.61/0.84 (op(e2, e0) = e1),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[1423, 1414, 1139, 640])).
% 0.61/0.84 tff(3650,plain,
% 0.61/0.84 ((op(e2, e0) = e0) <=> (e1 = e0)),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3649])).
% 0.61/0.84 tff(3651,plain,
% 0.61/0.84 ((op(e2, e0) = e0) <=> (e0 = e1)),
% 0.61/0.84 inference(transitivity,[status(thm)],[3650, 635])).
% 0.61/0.84 tff(3652,plain,
% 0.61/0.84 ((e0 = e1) <=> (op(e2, e0) = e0)),
% 0.61/0.84 inference(symmetry,[status(thm)],[3651])).
% 0.61/0.84 tff(3653,plain,
% 0.61/0.84 ((~(e0 = e1)) <=> (~(op(e2, e0) = e0))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3652])).
% 0.61/0.84 tff(3654,plain,
% 0.61/0.84 (~(op(e2, e0) = e0)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[625, 3653])).
% 0.61/0.84 tff(3655,plain,
% 0.61/0.84 (op(e2, e3) = e0),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[3212, 3654, 605, 491])).
% 0.61/0.84 tff(3656,plain,
% 0.61/0.84 (e0 = op(e2, e3)),
% 0.61/0.84 inference(symmetry,[status(thm)],[3655])).
% 0.61/0.84 tff(3657,plain,
% 0.61/0.84 (op(e3, e0) = op(e3, op(e2, e3))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3656])).
% 0.61/0.84 tff(3658,plain,
% 0.61/0.84 (((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2) | (op(e3, e0) = e3)) <=> ((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2) | (op(e3, e0) = e3))),
% 0.61/0.84 inference(rewrite,[status(thm)],[])).
% 0.61/0.84 tff(3659,plain,
% 0.61/0.84 ((((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2)) | (op(e3, e0) = e3)) <=> ((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2) | (op(e3, e0) = e3))),
% 0.61/0.84 inference(rewrite,[status(thm)],[])).
% 0.61/0.84 tff(3660,plain,
% 0.61/0.84 ((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) <=> ((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2))),
% 0.61/0.84 inference(rewrite,[status(thm)],[])).
% 0.61/0.84 tff(3661,plain,
% 0.61/0.84 (((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) | (op(e3, e0) = e3)) <=> (((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2)) | (op(e3, e0) = e3))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3660])).
% 0.61/0.84 tff(3662,plain,
% 0.61/0.84 (((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) | (op(e3, e0) = e3)) <=> ((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2) | (op(e3, e0) = e3))),
% 0.61/0.84 inference(transitivity,[status(thm)],[3661, 3659])).
% 0.61/0.84 tff(3663,plain,
% 0.61/0.84 ((((op(e3, e0) = e0) | (op(e3, e0) = e1)) | (op(e3, e0) = e2)) | (op(e3, e0) = e3)),
% 0.61/0.84 inference(and_elim,[status(thm)],[184])).
% 0.61/0.84 tff(3664,plain,
% 0.61/0.84 ((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2) | (op(e3, e0) = e3)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[3663, 3662])).
% 0.61/0.84 tff(3665,plain,
% 0.61/0.84 ((op(e3, e0) = e0) | (op(e3, e0) = e1) | (op(e3, e0) = e2) | (op(e3, e0) = e3)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[3664, 3658])).
% 0.61/0.84 tff(3666,plain,
% 0.61/0.84 (op(e3, e0) = e0),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[3665, 1414, 2536, 1699])).
% 0.61/0.84 tff(3667,plain,
% 0.61/0.84 (e0 = op(e3, e0)),
% 0.61/0.84 inference(symmetry,[status(thm)],[3666])).
% 0.61/0.84 tff(3668,plain,
% 0.61/0.84 (e0 = e3),
% 0.61/0.84 inference(transitivity,[status(thm)],[3667, 3657, 496])).
% 0.61/0.84 tff(3669,plain,
% 0.61/0.84 ($false),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[286, 3668])).
% 0.61/0.84 tff(3670,plain,((op(e3, e0) = e1) | (~(op(e3, op(e2, e3)) = e3)) | (op(e2, e1) = e0) | (op(e2, e2) = e0) | (op(e3, e0) = e3) | (op(e3, e0) = e2) | (op(e0, e0) = e1) | (op(e1, e0) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.84 tff(3671,plain,
% 0.61/0.84 ($false),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[3670, 3648, 3641, 605, 496, 2536, 1699, 1139, 640])).
% 0.61/0.84 tff(3672,plain,((op(e2, e0) = e2) | (op(e2, e1) = e0) | (~(op(e3, op(e2, e3)) = e3)) | (op(e3, e0) = e3) | (op(e3, e0) = e2) | (op(e0, e0) = e1) | (op(e1, e0) = e1) | (op(e2, e0) = e0) | (op(e2, e0) = e3) | (op(e2, e1) = e2) | (op(e2, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.84 tff(3673,plain,
% 0.61/0.84 (op(e2, e0) = e2),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[3672, 3635, 3631, 3630, 3590, 3577, 3626, 3611, 3582, 10, 3574])).
% 0.61/0.84 tff(3674,plain,
% 0.61/0.84 (op(e0, op(e2, e0)) = op(e0, e2)),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3673])).
% 0.61/0.84 tff(3675,plain,
% 0.61/0.84 (e0 = op(e0, op(e2, e0))),
% 0.61/0.84 inference(symmetry,[status(thm)],[3610])).
% 0.61/0.84 tff(3676,plain,
% 0.61/0.84 (e0 = e1),
% 0.61/0.84 inference(transitivity,[status(thm)],[3675, 3674, 798])).
% 0.61/0.84 tff(3677,plain,
% 0.61/0.84 ($false),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[625, 3676])).
% 0.61/0.84 tff(3678,plain,((op(e0, e0) = e2) | (~(op(e0, e2) = e1)) | (op(e2, e1) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e1, e1) = e2) | (op(e1, op(e0, e1)) = e1) | (op(e0, e0) = e0) | (op(e0, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.84 tff(3679,plain,
% 0.61/0.84 (op(e0, e0) = e2),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[3678, 798, 3556, 1815, 12, 1814, 989, 830])).
% 0.61/0.84 tff(3680,plain,
% 0.61/0.84 ((op(e0, e0) = op(e0, e3)) <=> (e2 = op(e0, e3))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3679])).
% 0.61/0.84 tff(3681,plain,
% 0.61/0.84 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e3) = e2)),
% 0.61/0.84 inference(transitivity,[status(thm)],[3680, 85])).
% 0.61/0.84 tff(3682,plain,
% 0.61/0.84 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e3) = e2))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3681])).
% 0.61/0.84 tff(3683,plain,
% 0.61/0.84 (~(op(e0, e3) = e2)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[2178, 3682])).
% 0.61/0.84 tff(3684,plain,
% 0.61/0.84 ((op(e0, e0) = op(e1, e0)) <=> (e2 = op(e1, e0))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3679])).
% 0.61/0.84 tff(3685,plain,
% 0.61/0.84 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e2)),
% 0.61/0.84 inference(transitivity,[status(thm)],[3684, 1816])).
% 0.61/0.84 tff(3686,plain,
% 0.61/0.84 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e2))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3685])).
% 0.61/0.84 tff(3687,plain,
% 0.61/0.84 (~(op(e1, e0) = e2)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[1056, 3686])).
% 0.61/0.84 tff(3688,plain,
% 0.61/0.84 (op(e0, op(e0, e0)) = op(e0, e2)),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3679])).
% 0.61/0.84 tff(3689,plain,
% 0.61/0.84 (op(e0, op(e0, e0)) = e1),
% 0.61/0.84 inference(transitivity,[status(thm)],[3688, 798])).
% 0.61/0.84 tff(3690,plain,
% 0.61/0.84 (op(op(e0, op(e0, e0)), op(e0, e0)) = op(e1, e2)),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3689, 3679])).
% 0.61/0.84 tff(3691,plain,
% 0.61/0.84 ((e3 = op(op(e0, op(e0, e0)), op(e0, e0))) <=> (e3 = op(e1, e2))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3690])).
% 0.61/0.84 tff(3692,plain,
% 0.61/0.84 ((e3 = op(op(e0, op(e0, e0)), op(e0, e0))) <=> (op(e1, e2) = e3)),
% 0.61/0.84 inference(transitivity,[status(thm)],[3691, 2877])).
% 0.61/0.84 tff(3693,plain,
% 0.61/0.84 ((~(e3 = op(op(e0, op(e0, e0)), op(e0, e0)))) <=> (~(op(e1, e2) = e3))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[3692])).
% 0.61/0.84 tff(3694,plain,
% 0.61/0.84 ((e2 = op(e0, e0)) <=> (op(e0, e0) = e2)),
% 0.61/0.84 inference(commutativity,[status(thm)],[])).
% 0.61/0.84 tff(3695,plain,
% 0.61/0.84 ((op(e0, e0) = e2) <=> (e2 = op(e0, e0))),
% 0.61/0.84 inference(symmetry,[status(thm)],[3694])).
% 0.61/0.84 tff(3696,plain,
% 0.61/0.84 (e2 = op(e0, e0)),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[3679, 3695])).
% 0.61/0.84 tff(3697,plain,
% 0.61/0.84 (op(e0, e2) = op(e0, op(e0, e0))),
% 0.61/0.84 inference(symmetry,[status(thm)],[3688])).
% 0.61/0.84 tff(3698,plain,
% 0.61/0.84 (e1 = op(e0, op(e0, e0))),
% 0.61/0.84 inference(transitivity,[status(thm)],[800, 3697])).
% 0.61/0.84 tff(3699,plain,
% 0.61/0.84 ((~(~((~(e2 = op(e0, e0))) | (~(e1 = op(e0, op(e0, e0)))) | (~(e3 = op(op(e0, op(e0, e0)), op(e0, e0))))))) <=> ((~(e2 = op(e0, e0))) | (~(e1 = op(e0, op(e0, e0)))) | (~(e3 = op(op(e0, op(e0, e0)), op(e0, e0)))))),
% 0.61/0.84 inference(rewrite,[status(thm)],[])).
% 0.61/0.85 tff(3700,plain,
% 0.61/0.85 (((e2 = op(e0, e0)) & (e1 = op(e0, op(e0, e0))) & (e3 = op(op(e0, op(e0, e0)), op(e0, e0)))) <=> (~((~(e2 = op(e0, e0))) | (~(e1 = op(e0, op(e0, e0)))) | (~(e3 = op(op(e0, op(e0, e0)), op(e0, e0))))))),
% 0.61/0.85 inference(rewrite,[status(thm)],[])).
% 0.61/0.85 tff(3701,plain,
% 0.61/0.85 ((~((e2 = op(e0, e0)) & (e1 = op(e0, op(e0, e0))) & (e3 = op(op(e0, op(e0, e0)), op(e0, e0))))) <=> (~(~((~(e2 = op(e0, e0))) | (~(e1 = op(e0, op(e0, e0)))) | (~(e3 = op(op(e0, op(e0, e0)), op(e0, e0)))))))),
% 0.61/0.85 inference(monotonicity,[status(thm)],[3700])).
% 0.61/0.85 tff(3702,plain,
% 0.61/0.85 ((~((e2 = op(e0, e0)) & (e1 = op(e0, op(e0, e0))) & (e3 = op(op(e0, op(e0, e0)), op(e0, e0))))) <=> ((~(e2 = op(e0, e0))) | (~(e1 = op(e0, op(e0, e0)))) | (~(e3 = op(op(e0, op(e0, e0)), op(e0, e0)))))),
% 0.61/0.85 inference(transitivity,[status(thm)],[3701, 3699])).
% 0.61/0.85 tff(3703,plain,
% 0.61/0.85 ((~((e2 = op(e0, e0)) & (e1 = op(e0, op(e0, e0))) & (e3 = op(op(e0, op(e0, e0)), op(e0, e0))))) <=> (~((e2 = op(e0, e0)) & (e1 = op(e0, op(e0, e0))) & (e3 = op(op(e0, op(e0, e0)), op(e0, e0)))))),
% 0.61/0.85 inference(rewrite,[status(thm)],[])).
% 0.61/0.85 tff(3704,plain,
% 0.61/0.85 ((~(((e2 = op(e0, e0)) & (e1 = op(e0, op(e0, e0)))) & (e3 = op(op(e0, op(e0, e0)), op(e0, e0))))) <=> (~((e2 = op(e0, e0)) & (e1 = op(e0, op(e0, e0))) & (e3 = op(op(e0, op(e0, e0)), op(e0, e0)))))),
% 0.61/0.85 inference(rewrite,[status(thm)],[])).
% 0.61/0.85 tff(3705,axiom,(~(((e2 = op(e0, e0)) & (e1 = op(e0, op(e0, e0)))) & (e3 = op(op(e0, op(e0, e0)), op(e0, e0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax20')).
% 0.61/0.85 tff(3706,plain,
% 0.61/0.85 (~((e2 = op(e0, e0)) & (e1 = op(e0, op(e0, e0))) & (e3 = op(op(e0, op(e0, e0)), op(e0, e0))))),
% 0.61/0.85 inference(modus_ponens,[status(thm)],[3705, 3704])).
% 0.61/0.85 tff(3707,plain,
% 0.61/0.85 (~((e2 = op(e0, e0)) & (e1 = op(e0, op(e0, e0))) & (e3 = op(op(e0, op(e0, e0)), op(e0, e0))))),
% 0.61/0.85 inference(modus_ponens,[status(thm)],[3706, 3703])).
% 0.61/0.85 tff(3708,plain,
% 0.61/0.85 ((~(e2 = op(e0, e0))) | (~(e1 = op(e0, op(e0, e0)))) | (~(e3 = op(op(e0, op(e0, e0)), op(e0, e0))))),
% 0.61/0.85 inference(modus_ponens,[status(thm)],[3707, 3702])).
% 0.61/0.85 tff(3709,plain,
% 0.61/0.85 (~(e3 = op(op(e0, op(e0, e0)), op(e0, e0)))),
% 0.61/0.85 inference(unit_resolution,[status(thm)],[3708, 3698, 3696])).
% 0.61/0.85 tff(3710,plain,
% 0.61/0.85 (~(op(e1, e2) = e3)),
% 0.61/0.85 inference(modus_ponens,[status(thm)],[3709, 3693])).
% 0.61/0.85 tff(3711,plain,
% 0.61/0.85 ((op(e0, e0) = op(e2, e0)) <=> (e2 = op(e2, e0))),
% 0.61/0.85 inference(monotonicity,[status(thm)],[3679])).
% 0.61/0.85 tff(3712,plain,
% 0.61/0.85 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e2)),
% 0.61/0.85 inference(transitivity,[status(thm)],[3711, 3499])).
% 0.61/0.85 tff(3713,plain,
% 0.61/0.85 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e2))),
% 0.61/0.85 inference(monotonicity,[status(thm)],[3712])).
% 0.61/0.85 tff(3714,plain,
% 0.61/0.85 (~(op(e2, e0) = e2)),
% 0.61/0.85 inference(modus_ponens,[status(thm)],[1827, 3713])).
% 0.61/0.85 tff(3715,plain,
% 0.61/0.85 (~(op(e2, op(e1, e2)) = e2)),
% 0.61/0.85 inference(unit_resolution,[status(thm)],[199, 3714, 3552, 3710, 12, 3687, 3561, 3683])).
% 0.61/0.85 tff(3716,plain,
% 0.61/0.85 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.61/0.85 inference(unit_resolution,[status(thm)],[102, 3715])).
% 0.61/0.85 tff(3717,plain,
% 0.61/0.85 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.61/0.85 inference(unit_resolution,[status(thm)],[681, 3716, 1815, 3565])).
% 0.61/0.85 tff(3718,plain,
% 0.61/0.85 (op(e3, op(e2, e3)) = e3),
% 0.61/0.85 inference(unit_resolution,[status(thm)],[471, 3717])).
% 0.61/0.85 tff(3719,plain,
% 0.61/0.85 ((op(e3, e1) = e0) <=> (e2 = e0)),
% 0.61/0.85 inference(monotonicity,[status(thm)],[3557])).
% 0.61/0.85 tff(3720,plain,
% 0.61/0.85 ((op(e3, e1) = e0) <=> (e0 = e2)),
% 0.61/0.85 inference(transitivity,[status(thm)],[3719, 217])).
% 0.61/0.85 tff(3721,plain,
% 0.61/0.85 ((e0 = e2) <=> (op(e3, e1) = e0)),
% 0.61/0.85 inference(symmetry,[status(thm)],[3720])).
% 0.61/0.85 tff(3722,plain,
% 0.61/0.85 ((~(e0 = e2)) <=> (~(op(e3, e1) = e0))),
% 0.61/0.85 inference(monotonicity,[status(thm)],[3721])).
% 0.61/0.85 tff(3723,plain,
% 0.61/0.85 (~(op(e3, e1) = e0)),
% 0.61/0.85 inference(modus_ponens,[status(thm)],[238, 3722])).
% 0.61/0.85 tff(3724,plain,
% 0.61/0.85 ((op(e0, e2) = e3) <=> (e1 = e3)),
% 0.61/0.85 inference(monotonicity,[status(thm)],[798])).
% 0.61/0.85 tff(3725,plain,
% 0.61/0.85 ((e1 = e3) <=> (op(e0, e2) = e3)),
% 0.70/0.85 inference(symmetry,[status(thm)],[3724])).
% 0.70/0.85 tff(3726,plain,
% 0.70/0.85 ((~(e1 = e3)) <=> (~(op(e0, e2) = e3))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3725])).
% 0.70/0.85 tff(3727,plain,
% 0.70/0.85 (~(op(e0, e2) = e3)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[591, 3726])).
% 0.70/0.85 tff(3728,plain,
% 0.70/0.85 ((op(e0, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[798])).
% 0.70/0.85 tff(3729,plain,
% 0.70/0.85 ((op(e0, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 0.70/0.85 inference(transitivity,[status(thm)],[3728, 1949])).
% 0.70/0.85 tff(3730,plain,
% 0.70/0.85 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3729])).
% 0.70/0.85 tff(3731,plain,
% 0.70/0.85 (~(op(e2, e2) = e1)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[816, 3730])).
% 0.70/0.85 tff(3732,plain,
% 0.70/0.85 (op(e2, op(e2, e2)) = e2),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[473, 3717])).
% 0.70/0.85 tff(3733,plain,
% 0.70/0.85 (~(op(e2, e2) = e0)),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[481, 3714, 3732])).
% 0.70/0.85 tff(3734,plain,
% 0.70/0.85 (~(op(e2, e3) = e2)),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[515, 3733, 3731, 3718])).
% 0.70/0.85 tff(3735,plain,
% 0.70/0.85 (op(e2, e2) = e2),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[524, 3734, 3556, 3714])).
% 0.70/0.85 tff(3736,plain,
% 0.70/0.85 ((op(e2, e2) = e3) <=> (e2 = e3)),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3735])).
% 0.70/0.85 tff(3737,plain,
% 0.70/0.85 ((e2 = e3) <=> (op(e2, e2) = e3)),
% 0.70/0.85 inference(symmetry,[status(thm)],[3736])).
% 0.70/0.85 tff(3738,plain,
% 0.70/0.85 ((~(e2 = e3)) <=> (~(op(e2, e2) = e3))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3737])).
% 0.70/0.85 tff(3739,plain,
% 0.70/0.85 (~(op(e2, e2) = e3)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[462, 3738])).
% 0.70/0.85 tff(3740,plain,
% 0.70/0.85 (((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))),
% 0.70/0.85 inference(rewrite,[status(thm)],[])).
% 0.70/0.85 tff(3741,plain,
% 0.70/0.85 ((((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))),
% 0.70/0.85 inference(rewrite,[status(thm)],[])).
% 0.70/0.85 tff(3742,plain,
% 0.70/0.85 ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) <=> ((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3))),
% 0.70/0.85 inference(rewrite,[status(thm)],[])).
% 0.70/0.85 tff(3743,plain,
% 0.70/0.85 (((((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))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3742])).
% 0.70/0.85 tff(3744,plain,
% 0.70/0.85 (((((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))),
% 0.70/0.85 inference(transitivity,[status(thm)],[3743, 3741])).
% 0.70/0.85 tff(3745,plain,
% 0.70/0.85 ((((op(e0, e2) = e3) | (op(e1, e2) = e3)) | (op(e2, e2) = e3)) | (op(e3, e2) = e3)),
% 0.70/0.85 inference(and_elim,[status(thm)],[121])).
% 0.70/0.85 tff(3746,plain,
% 0.70/0.85 ((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3) | (op(e3, e2) = e3)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[3745, 3744])).
% 0.70/0.85 tff(3747,plain,
% 0.70/0.85 ((op(e0, e2) = e3) | (op(e1, e2) = e3) | (op(e2, e2) = e3) | (op(e3, e2) = e3)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[3746, 3740])).
% 0.70/0.85 tff(3748,plain,
% 0.70/0.85 (op(e3, e2) = e3),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[3747, 3739, 3727, 3710])).
% 0.70/0.85 tff(3749,plain,
% 0.70/0.85 ((op(e3, e2) = e0) <=> (e3 = e0)),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3748])).
% 0.70/0.85 tff(3750,plain,
% 0.70/0.85 ((op(e3, e2) = e0) <=> (e0 = e3)),
% 0.70/0.85 inference(transitivity,[status(thm)],[3749, 279])).
% 0.70/0.85 tff(3751,plain,
% 0.70/0.85 ((e0 = e3) <=> (op(e3, e2) = e0)),
% 0.70/0.85 inference(symmetry,[status(thm)],[3750])).
% 0.70/0.85 tff(3752,plain,
% 0.70/0.85 ((~(e0 = e3)) <=> (~(op(e3, e2) = e0))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3751])).
% 0.70/0.85 tff(3753,plain,
% 0.70/0.85 (~(op(e3, e2) = e0)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[286, 3752])).
% 0.70/0.85 tff(3754,plain,
% 0.70/0.85 (op(e3, e0) = e0),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[295, 3753, 3723, 63])).
% 0.70/0.85 tff(3755,plain,
% 0.70/0.85 ((op(e2, e0) = op(e3, e0)) <=> (op(e2, e0) = e0)),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3754])).
% 0.70/0.85 tff(3756,plain,
% 0.70/0.85 ((~(op(e2, e0) = op(e3, e0))) <=> (~(op(e2, e0) = e0))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3755])).
% 0.70/0.85 tff(3757,plain,
% 0.70/0.85 (~(op(e2, e0) = e0)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[1229, 3756])).
% 0.70/0.85 tff(3758,plain,
% 0.70/0.85 ((op(e3, e2) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3748])).
% 0.70/0.85 tff(3759,plain,
% 0.70/0.85 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.70/0.85 inference(transitivity,[status(thm)],[3758, 78])).
% 0.70/0.85 tff(3760,plain,
% 0.70/0.85 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3759])).
% 0.70/0.85 tff(3761,plain,
% 0.70/0.85 (~(op(e3, e3) = e3)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[1111, 3760])).
% 0.70/0.85 tff(3762,plain,
% 0.70/0.85 (op(e3, e3) = e1),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[266, 3761, 63, 3561])).
% 0.70/0.85 tff(3763,plain,
% 0.70/0.85 (op(e3, op(e3, e3)) = op(e3, e1)),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3762])).
% 0.70/0.85 tff(3764,plain,
% 0.70/0.85 (op(e3, op(e3, e3)) = e2),
% 0.70/0.85 inference(transitivity,[status(thm)],[3763, 3557])).
% 0.70/0.85 tff(3765,plain,
% 0.70/0.85 (op(op(e3, op(e3, e3)), op(e3, e3)) = op(e2, e1)),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3764, 3762])).
% 0.70/0.85 tff(3766,plain,
% 0.70/0.85 ((e0 = op(op(e3, op(e3, e3)), op(e3, e3))) <=> (e0 = op(e2, e1))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3765])).
% 0.70/0.85 tff(3767,plain,
% 0.70/0.85 ((e0 = op(op(e3, op(e3, e3)), op(e3, e3))) <=> (op(e2, e1) = e0)),
% 0.70/0.85 inference(transitivity,[status(thm)],[3766, 3142])).
% 0.70/0.85 tff(3768,plain,
% 0.70/0.85 ((~(e0 = op(op(e3, op(e3, e3)), op(e3, e3)))) <=> (~(op(e2, e1) = e0))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3767])).
% 0.70/0.85 tff(3769,plain,
% 0.70/0.85 (e1 = op(e3, e3)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[3762, 77])).
% 0.70/0.85 tff(3770,plain,
% 0.70/0.85 (op(e3, e1) = op(e3, op(e3, e3))),
% 0.70/0.85 inference(symmetry,[status(thm)],[3763])).
% 0.70/0.85 tff(3771,plain,
% 0.70/0.85 (e2 = op(e3, e1)),
% 0.70/0.85 inference(symmetry,[status(thm)],[3557])).
% 0.70/0.85 tff(3772,plain,
% 0.70/0.85 (e2 = op(e3, op(e3, e3))),
% 0.70/0.85 inference(transitivity,[status(thm)],[3771, 3770])).
% 0.70/0.85 tff(3773,plain,
% 0.70/0.85 (~(e0 = op(op(e3, op(e3, e3)), op(e3, e3)))),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[3227, 3772, 3769])).
% 0.70/0.85 tff(3774,plain,
% 0.70/0.85 (~(op(e2, e1) = e0)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[3773, 3768])).
% 0.70/0.85 tff(3775,plain,
% 0.70/0.85 (op(e2, e3) = e0),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[3212, 3774, 3733, 3757])).
% 0.70/0.85 tff(3776,plain,
% 0.70/0.85 (op(e3, op(e2, e3)) = op(e3, e0)),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3775])).
% 0.70/0.85 tff(3777,plain,
% 0.70/0.85 (op(e3, e0) = op(e3, op(e2, e3))),
% 0.70/0.85 inference(symmetry,[status(thm)],[3776])).
% 0.70/0.85 tff(3778,plain,
% 0.70/0.85 (e0 = op(e3, e0)),
% 0.70/0.85 inference(symmetry,[status(thm)],[3754])).
% 0.70/0.85 tff(3779,plain,
% 0.70/0.85 ((op(e1, e2) = op(e2, e2)) <=> (op(e1, e2) = e2)),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3735])).
% 0.70/0.85 tff(3780,plain,
% 0.70/0.85 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e1, e2) = e2))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3779])).
% 0.70/0.85 tff(3781,plain,
% 0.70/0.85 (~(op(e1, e2) = e2)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[764, 3780])).
% 0.70/0.85 tff(3782,plain,
% 0.70/0.85 (op(e1, e2) = e0),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[193, 3781, 3552, 3710])).
% 0.70/0.85 tff(3783,plain,
% 0.70/0.85 (op(e1, e2) = e3),
% 0.70/0.85 inference(transitivity,[status(thm)],[3782, 3778, 3777, 3718])).
% 0.70/0.85 tff(3784,plain,
% 0.70/0.85 ($false),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[3710, 3783])).
% 0.70/0.85 tff(3785,plain,((~(op(e0, e2) = e1)) | (op(e3, e3) = e0) | (op(e1, e1) = e2) | (op(e1, op(e0, e1)) = e1) | (op(e0, e0) = e0) | (op(e0, e1) = e2) | (op(e2, op(e0, e2)) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.85 tff(3786,plain,
% 0.70/0.85 (op(e2, op(e0, e2)) = e2),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[3785, 798, 12, 1814, 989, 830, 63])).
% 0.70/0.85 tff(3787,plain,
% 0.70/0.85 (op(e2, e1) = e2),
% 0.70/0.85 inference(transitivity,[status(thm)],[801, 3786])).
% 0.70/0.85 tff(3788,plain,
% 0.70/0.85 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e2)),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3498])).
% 0.70/0.85 tff(3789,plain,
% 0.70/0.85 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e2))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3788])).
% 0.70/0.85 tff(3790,plain,
% 0.70/0.85 (~(op(e2, e1) = e2)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[576, 3789])).
% 0.70/0.85 tff(3791,plain,
% 0.70/0.85 ($false),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[3790, 3787])).
% 0.70/0.85 tff(3792,plain,((~(op(e0, e2) = e1)) | (op(e1, e1) = e2) | (op(e1, op(e0, e1)) = e1) | (op(e0, e0) = e0) | (op(e0, e1) = e2) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.85 tff(3793,plain,
% 0.70/0.85 (~(op(e0, e2) = e1)),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[3792, 830, 1814, 989, 12, 63])).
% 0.70/0.85 tff(3794,plain,
% 0.70/0.85 ((op(e3, e1) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3498])).
% 0.70/0.85 tff(3795,plain,
% 0.70/0.85 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.70/0.85 inference(transitivity,[status(thm)],[3794, 1024])).
% 0.70/0.85 tff(3796,plain,
% 0.70/0.85 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3795])).
% 0.70/0.85 tff(3797,plain,
% 0.70/0.85 (~(op(e3, e3) = e2)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[399, 3796])).
% 0.70/0.85 tff(3798,plain,
% 0.70/0.85 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3498])).
% 0.70/0.85 tff(3799,plain,
% 0.70/0.85 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3798])).
% 0.70/0.85 tff(3800,plain,
% 0.70/0.85 (~(op(e3, e0) = e2)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[1333, 3799])).
% 0.70/0.85 tff(3801,plain,
% 0.70/0.85 (op(e0, e3) = e2),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[147, 767, 107, 3797])).
% 0.70/0.85 tff(3802,plain,
% 0.70/0.85 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3801])).
% 0.70/0.85 tff(3803,plain,
% 0.70/0.85 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3802])).
% 0.70/0.85 tff(3804,plain,
% 0.70/0.85 (~(op(e0, e0) = e2)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[2178, 3803])).
% 0.70/0.85 tff(3805,plain,
% 0.70/0.85 (~(op(e0, e2) = e1)),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[3607, 3804, 12, 107, 79, 3800])).
% 0.70/0.85 tff(3806,plain,
% 0.70/0.85 (op(e2, e2) = e2),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[524, 767, 3790, 74])).
% 0.70/0.85 tff(3807,plain,
% 0.70/0.85 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e2)),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3806])).
% 0.70/0.85 tff(3808,plain,
% 0.70/0.85 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e2))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3807])).
% 0.70/0.85 tff(3809,plain,
% 0.70/0.85 (~(op(e0, e2) = e2)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[816, 3808])).
% 0.70/0.85 tff(3810,plain,
% 0.70/0.85 (op(e2, op(e0, e2)) = e2),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[3461, 3805, 830, 12, 63, 989, 2451, 1814])).
% 0.70/0.85 tff(3811,plain,
% 0.70/0.85 (~(op(e0, e2) = e0)),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[901, 3810, 74])).
% 0.70/0.85 tff(3812,plain,
% 0.70/0.85 (~(op(e0, e2) = e3)),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[908, 3810, 767])).
% 0.70/0.85 tff(3813,plain,
% 0.70/0.85 ($false),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[917, 3812, 3811, 3809, 3805])).
% 0.70/0.85 tff(3814,plain,((op(e2, e3) = e2) | (op(e2, e0) = e2) | (op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e3, e3) = e0) | (op(e0, e0) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e1, e3) = e2) | ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.85 tff(3815,plain,
% 0.70/0.85 (op(e2, e3) = e2),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[3814, 79, 830, 12, 63, 989, 1814, 107, 74])).
% 0.70/0.85 tff(3816,plain,
% 0.70/0.85 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e2)),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3815])).
% 0.70/0.85 tff(3817,plain,
% 0.70/0.85 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e2))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3816])).
% 0.70/0.85 tff(3818,plain,
% 0.70/0.85 (~(op(e2, e2) = e2)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[153, 3817])).
% 0.70/0.85 tff(3819,plain,
% 0.70/0.85 ((op(e3, e1) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3498])).
% 0.70/0.85 tff(3820,plain,
% 0.70/0.85 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.70/0.85 inference(transitivity,[status(thm)],[3819, 469])).
% 0.70/0.85 tff(3821,plain,
% 0.70/0.85 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3820])).
% 0.70/0.85 tff(3822,plain,
% 0.70/0.85 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e1) = op(e3, e2)))),
% 0.70/0.85 inference(rewrite,[status(thm)],[])).
% 0.70/0.85 tff(3823,plain,
% 0.70/0.85 (~(op(e3, e1) = op(e3, e2))),
% 0.70/0.85 inference(and_elim,[status(thm)],[21])).
% 0.70/0.85 tff(3824,plain,
% 0.70/0.85 (~(op(e3, e1) = op(e3, e2))),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[3823, 3822])).
% 0.70/0.85 tff(3825,plain,
% 0.70/0.85 (~(op(e3, e2) = e2)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[3824, 3821])).
% 0.70/0.85 tff(3826,plain,
% 0.70/0.85 (~(op(e1, e2) = e2)),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[1269, 3818, 103])).
% 0.70/0.85 tff(3827,plain,
% 0.70/0.85 (op(e0, e2) = e2),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[3388, 3826, 3825, 3818])).
% 0.70/0.85 tff(3828,plain,
% 0.70/0.85 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e2)),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3815])).
% 0.70/0.85 tff(3829,plain,
% 0.70/0.85 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e2))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3828])).
% 0.70/0.85 tff(3830,plain,
% 0.70/0.85 (~(op(e0, e3) = e2)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[2232, 3829])).
% 0.70/0.85 tff(3831,plain,
% 0.70/0.85 (op(e1, e0) = e2),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[156, 3830, 12, 107, 3797, 103])).
% 0.70/0.85 tff(3832,plain,
% 0.70/0.85 (~(op(e0, e2) = e1)),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[3493, 3831, 84])).
% 0.70/0.85 tff(3833,plain,
% 0.70/0.85 (op(e2, op(e0, e2)) = e2),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[3461, 3832, 830, 12, 63, 989, 2451, 1814])).
% 0.70/0.85 tff(3834,plain,
% 0.70/0.85 ($false),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[819, 3833, 3827])).
% 0.70/0.85 tff(3835,plain,(((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))) | (op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e3, e3) = e0) | (op(e0, e0) = e0) | (op(e1, op(e0, e1)) = e1) | (op(e1, e3) = e2) | (op(e2, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.85 tff(3836,plain,
% 0.70/0.85 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[3835, 107, 12, 63, 989, 1814, 830, 74])).
% 0.70/0.85 tff(3837,plain,
% 0.70/0.85 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[681, 3836, 1815, 3548])).
% 0.70/0.85 tff(3838,plain,
% 0.70/0.85 (op(e3, op(e2, e3)) = e3),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[471, 3837])).
% 0.70/0.85 tff(3839,plain,
% 0.70/0.85 (op(e2, op(e2, e2)) = e2),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[473, 3837])).
% 0.70/0.85 tff(3840,plain,
% 0.70/0.85 (~(op(e2, e2) = e1)),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[488, 3839, 3790])).
% 0.70/0.85 tff(3841,plain,
% 0.70/0.85 (~(op(e2, e2) = e0)),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[481, 3839, 74])).
% 0.70/0.85 tff(3842,plain,
% 0.70/0.85 (~(op(e2, e3) = e2)),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[515, 3841, 3840, 3838])).
% 0.70/0.85 tff(3843,plain,
% 0.70/0.85 (op(e0, e3) = e2),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[147, 3842, 107, 3797])).
% 0.70/0.85 tff(3844,plain,
% 0.70/0.85 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3843])).
% 0.70/0.85 tff(3845,plain,
% 0.70/0.85 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3844])).
% 0.70/0.85 tff(3846,plain,
% 0.70/0.85 (~(op(e0, e0) = e2)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[2178, 3845])).
% 0.70/0.85 tff(3847,plain,
% 0.70/0.85 (~(op(e0, e2) = e1)),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[3678, 3846, 3790, 1815, 12, 1814, 989, 830])).
% 0.70/0.85 tff(3848,plain,
% 0.70/0.85 (op(e2, e2) = e2),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[524, 3842, 3790, 74])).
% 0.70/0.85 tff(3849,plain,
% 0.70/0.85 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e2)),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3848])).
% 0.70/0.85 tff(3850,plain,
% 0.70/0.85 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e2))),
% 0.70/0.85 inference(monotonicity,[status(thm)],[3849])).
% 0.70/0.85 tff(3851,plain,
% 0.70/0.85 (~(op(e0, e2) = e2)),
% 0.70/0.85 inference(modus_ponens,[status(thm)],[816, 3850])).
% 0.70/0.85 tff(3852,plain,
% 0.70/0.85 (op(e2, op(e0, e2)) = e2),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[3461, 3847, 830, 12, 63, 989, 2451, 1814])).
% 0.70/0.85 tff(3853,plain,
% 0.70/0.85 (~(op(e0, e2) = e0)),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[901, 3852, 74])).
% 0.70/0.85 tff(3854,plain,
% 0.70/0.85 (~(op(e0, e2) = e3)),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[908, 3852, 3842])).
% 0.70/0.85 tff(3855,plain,
% 0.70/0.85 ($false),
% 0.70/0.85 inference(unit_resolution,[status(thm)],[917, 3854, 3853, 3851, 3847])).
% 0.70/0.85 tff(3856,plain,((op(e1, e3) = e2) | (op(e2, e0) = e2) | (op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e3, e3) = e0) | (op(e0, e0) = e0) | (op(e1, op(e0, e1)) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.86 tff(3857,plain,
% 0.70/0.86 (op(e1, e3) = e2),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[3856, 74, 830, 12, 63, 989, 1814])).
% 0.70/0.86 tff(3858,plain,
% 0.70/0.86 ((op(e1, e3) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3857])).
% 0.70/0.86 tff(3859,plain,
% 0.70/0.86 ((op(e1, e3) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.70/0.86 inference(transitivity,[status(thm)],[3858, 72])).
% 0.70/0.86 tff(3860,plain,
% 0.70/0.86 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3859])).
% 0.70/0.86 tff(3861,plain,
% 0.70/0.86 (~(op(e2, e3) = e2)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[944, 3860])).
% 0.70/0.86 tff(3862,plain,
% 0.70/0.86 (op(e2, e2) = e2),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[524, 3861, 3790, 74])).
% 0.70/0.86 tff(3863,plain,
% 0.70/0.86 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e2)),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3862])).
% 0.70/0.86 tff(3864,plain,
% 0.70/0.86 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e2))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3863])).
% 0.70/0.86 tff(3865,plain,
% 0.70/0.86 (~(op(e0, e2) = e2)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[816, 3864])).
% 0.70/0.86 tff(3866,plain,
% 0.70/0.86 (~(op(e0, e2) = e0)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[901, 3462, 74])).
% 0.70/0.86 tff(3867,plain,
% 0.70/0.86 (~(op(e0, e2) = e3)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[908, 3462, 3861])).
% 0.70/0.86 tff(3868,plain,
% 0.70/0.86 ($false),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[917, 3867, 3866, 3865, 991])).
% 0.70/0.86 tff(3869,plain,((op(e0, e2) = e1) | (op(e2, e0) = e2) | (op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e3, e3) = e0) | (op(e0, e0) = e0) | (op(e1, op(e0, e1)) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.86 tff(3870,plain,
% 0.70/0.86 (op(e2, e0) = e2),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[3869, 3793, 830, 12, 63, 989, 1814])).
% 0.70/0.86 tff(3871,plain,
% 0.70/0.86 ((op(e2, e0) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3870])).
% 0.70/0.86 tff(3872,plain,
% 0.70/0.86 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.70/0.86 inference(transitivity,[status(thm)],[3871, 810])).
% 0.70/0.86 tff(3873,plain,
% 0.70/0.86 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3872])).
% 0.70/0.86 tff(3874,plain,
% 0.70/0.86 (~(op(e2, e2) = e2)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1200, 3873])).
% 0.70/0.86 tff(3875,plain,
% 0.70/0.86 (op(e2, op(e0, e2)) = e2),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[3461, 3793, 830, 12, 63, 989, 2451, 1814])).
% 0.70/0.86 tff(3876,plain,
% 0.70/0.86 (~(op(e0, e2) = e2)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[819, 3875])).
% 0.70/0.86 tff(3877,plain,
% 0.70/0.86 (op(e1, e2) = e2),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[3388, 3874, 3825, 3876])).
% 0.70/0.86 tff(3878,plain,
% 0.70/0.86 (~(op(e2, op(e1, e2)) = e2)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1269, 3877, 3874])).
% 0.70/0.86 tff(3879,plain,
% 0.70/0.86 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[102, 3878])).
% 0.70/0.86 tff(3880,plain,
% 0.70/0.86 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[681, 3879, 1815, 3548])).
% 0.70/0.86 tff(3881,plain,
% 0.70/0.86 (op(e1, op(e2, e1)) = e1),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[546, 3880])).
% 0.70/0.86 tff(3882,plain,
% 0.70/0.86 ((op(e2, e0) = e1) <=> (e2 = e1)),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3870])).
% 0.70/0.86 tff(3883,plain,
% 0.70/0.86 ((op(e2, e0) = e1) <=> (e1 = e2)),
% 0.70/0.86 inference(transitivity,[status(thm)],[3882, 317])).
% 0.70/0.86 tff(3884,plain,
% 0.70/0.86 ((e1 = e2) <=> (op(e2, e0) = e1)),
% 0.70/0.86 inference(symmetry,[status(thm)],[3883])).
% 0.70/0.86 tff(3885,plain,
% 0.70/0.86 ((~(e1 = e2)) <=> (~(op(e2, e0) = e1))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3884])).
% 0.70/0.86 tff(3886,plain,
% 0.70/0.86 (~(op(e2, e0) = e1)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[324, 3885])).
% 0.70/0.86 tff(3887,plain,
% 0.70/0.86 (op(e2, e1) = e1),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[2417, 3880, 3886, 3498, 3790])).
% 0.70/0.86 tff(3888,plain,
% 0.70/0.86 (e1 = op(e2, e1)),
% 0.70/0.86 inference(symmetry,[status(thm)],[3887])).
% 0.70/0.86 tff(3889,plain,
% 0.70/0.86 (op(e1, e1) = op(e1, op(e2, e1))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3888])).
% 0.70/0.86 tff(3890,plain,
% 0.70/0.86 (op(e1, e1) = e1),
% 0.70/0.86 inference(transitivity,[status(thm)],[3889, 3881])).
% 0.70/0.86 tff(3891,plain,
% 0.70/0.86 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e1)),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3887])).
% 0.70/0.86 tff(3892,plain,
% 0.70/0.86 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e1))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3891])).
% 0.70/0.86 tff(3893,plain,
% 0.70/0.86 (~(op(e1, e1) = e1)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[633, 3892])).
% 0.70/0.86 tff(3894,plain,
% 0.70/0.86 ($false),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[3893, 3890])).
% 0.70/0.86 tff(3895,plain,((op(e0, e1) = e2) | (op(e1, e1) = e2) | (op(e3, e3) = e0) | (op(e0, e0) = e0) | (op(e1, op(e0, e1)) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.86 tff(3896,plain,
% 0.70/0.86 ((op(e1, e1) = e2) | (op(e3, e3) = e0) | (op(e0, e0) = e0) | (op(e1, op(e0, e1)) = e1)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[3895, 1605])).
% 0.70/0.86 tff(3897,plain,
% 0.70/0.86 (op(e1, op(e0, e1)) = e1),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[3896, 1813, 63, 1807])).
% 0.70/0.86 tff(3898,plain,
% 0.70/0.86 (~(op(e1, e1) = e1)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1768, 3897])).
% 0.70/0.86 tff(3899,plain,
% 0.70/0.86 ((~(op(e0, e1) = e1)) | (op(e1, e1) = e2) | (op(e0, e0) = e0) | (op(e3, e3) = e0)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[2450, 1605])).
% 0.70/0.86 tff(3900,plain,
% 0.70/0.86 (~(op(e0, e1) = e1)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[3899, 1807, 1813, 63])).
% 0.70/0.86 tff(3901,plain,
% 0.70/0.86 ((op(e1, e3) = e1) <=> (e2 = e1)),
% 0.70/0.86 inference(monotonicity,[status(thm)],[1742])).
% 0.70/0.86 tff(3902,plain,
% 0.70/0.86 ((op(e1, e3) = e1) <=> (e1 = e2)),
% 0.70/0.86 inference(transitivity,[status(thm)],[3901, 317])).
% 0.70/0.86 tff(3903,plain,
% 0.70/0.86 ((e1 = e2) <=> (op(e1, e3) = e1)),
% 0.70/0.86 inference(symmetry,[status(thm)],[3902])).
% 0.70/0.86 tff(3904,plain,
% 0.70/0.86 ((~(e1 = e2)) <=> (~(op(e1, e3) = e1))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3903])).
% 0.70/0.86 tff(3905,plain,
% 0.70/0.86 (~(op(e1, e3) = e1)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[324, 3904])).
% 0.70/0.86 tff(3906,plain,
% 0.70/0.86 (~(op(e0, e1) = e3)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[846, 3905, 3897])).
% 0.70/0.86 tff(3907,plain,
% 0.70/0.86 (op(e0, e1) = e0),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1678, 3906, 3900])).
% 0.70/0.86 tff(3908,plain,
% 0.70/0.86 ((op(e0, e1) = op(e1, e1)) <=> (e0 = op(e1, e1))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3907])).
% 0.70/0.86 tff(3909,plain,
% 0.70/0.86 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e0)),
% 0.70/0.86 inference(transitivity,[status(thm)],[3908, 1501])).
% 0.70/0.86 tff(3910,plain,
% 0.70/0.86 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e0))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3909])).
% 0.70/0.86 tff(3911,plain,
% 0.70/0.86 (~(op(e1, e1) = e0)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[100, 3910])).
% 0.70/0.86 tff(3912,plain,
% 0.70/0.86 (op(e1, e1) = e3),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[2603, 3911, 1807, 3898])).
% 0.70/0.86 tff(3913,plain,
% 0.70/0.86 ((op(e0, e0) = op(e3, e0)) <=> (e2 = op(e3, e0))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[1808])).
% 0.70/0.86 tff(3914,plain,
% 0.70/0.86 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e2)),
% 0.70/0.86 inference(transitivity,[status(thm)],[3913, 1223])).
% 0.70/0.86 tff(3915,plain,
% 0.70/0.86 ((~(op(e0, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e2))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3914])).
% 0.70/0.86 tff(3916,plain,
% 0.70/0.86 (~(op(e3, e0) = e2)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1638, 3915])).
% 0.70/0.86 tff(3917,plain,
% 0.70/0.86 (op(e3, e1) = e2),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[537, 3916, 1859, 75])).
% 0.70/0.86 tff(3918,plain,
% 0.70/0.86 ((op(e3, e1) = e1) <=> (e2 = e1)),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3917])).
% 0.70/0.86 tff(3919,plain,
% 0.70/0.86 ((op(e3, e1) = e1) <=> (e1 = e2)),
% 0.70/0.86 inference(transitivity,[status(thm)],[3918, 317])).
% 0.70/0.86 tff(3920,plain,
% 0.70/0.86 ((e1 = e2) <=> (op(e3, e1) = e1)),
% 0.70/0.86 inference(symmetry,[status(thm)],[3919])).
% 0.70/0.86 tff(3921,plain,
% 0.70/0.86 ((~(e1 = e2)) <=> (~(op(e3, e1) = e1))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3920])).
% 0.70/0.86 tff(3922,plain,
% 0.70/0.86 (~(op(e3, e1) = e1)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[324, 3921])).
% 0.70/0.86 tff(3923,plain,
% 0.70/0.86 (op(e2, e1) = e1),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1076, 3922, 3897, 3898])).
% 0.70/0.86 tff(3924,plain,
% 0.70/0.86 (e1 = op(e2, e1)),
% 0.70/0.86 inference(symmetry,[status(thm)],[3923])).
% 0.70/0.86 tff(3925,plain,
% 0.70/0.86 (op(e1, e1) = op(e1, op(e2, e1))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3924])).
% 0.70/0.86 tff(3926,plain,
% 0.70/0.86 (op(e1, op(e2, e1)) = op(e1, e1)),
% 0.70/0.86 inference(symmetry,[status(thm)],[3925])).
% 0.70/0.86 tff(3927,plain,
% 0.70/0.86 (e0 = op(e0, e1)),
% 0.70/0.86 inference(symmetry,[status(thm)],[3907])).
% 0.70/0.86 tff(3928,plain,
% 0.70/0.86 (op(e1, e0) = op(e1, op(e0, e1))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3927])).
% 0.70/0.86 tff(3929,plain,
% 0.70/0.86 (op(e1, e0) = e1),
% 0.70/0.86 inference(transitivity,[status(thm)],[3928, 3897])).
% 0.70/0.86 tff(3930,plain,
% 0.70/0.86 ((op(e1, e0) = op(e3, e0)) <=> (e1 = op(e3, e0))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3929])).
% 0.70/0.86 tff(3931,plain,
% 0.70/0.86 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 0.70/0.86 inference(transitivity,[status(thm)],[3930, 373])).
% 0.70/0.86 tff(3932,plain,
% 0.70/0.86 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e1))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3931])).
% 0.70/0.86 tff(3933,plain,
% 0.70/0.86 (~(op(e3, e0) = e1)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[420, 3932])).
% 0.70/0.86 tff(3934,plain,
% 0.70/0.86 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1632, 3933, 3917])).
% 0.70/0.86 tff(3935,plain,
% 0.70/0.86 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[681, 3934, 1221, 1852])).
% 0.70/0.86 tff(3936,plain,
% 0.70/0.86 (op(e1, op(e2, e1)) = e1),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[546, 3935])).
% 0.70/0.86 tff(3937,plain,
% 0.70/0.86 (e1 = op(e1, op(e2, e1))),
% 0.70/0.86 inference(symmetry,[status(thm)],[3936])).
% 0.70/0.86 tff(3938,plain,
% 0.70/0.86 (e1 = e3),
% 0.70/0.86 inference(transitivity,[status(thm)],[3937, 3926, 3912])).
% 0.70/0.86 tff(3939,plain,
% 0.70/0.86 ($false),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[591, 3938])).
% 0.70/0.86 tff(3940,plain,((op(e0, e3) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))) | (op(e3, e3) = e0) | (op(e3, e2) = e2) | (op(e3, e3) = e2) | (op(e2, e3) = e2) | (op(e0, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.86 tff(3941,plain,
% 0.70/0.86 (op(e0, e3) = e2),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[3940, 1766, 1798, 63, 1805, 75, 767, 1801])).
% 0.70/0.86 tff(3942,plain,
% 0.70/0.86 ((op(e0, e3) = e1) <=> (e2 = e1)),
% 0.70/0.86 inference(monotonicity,[status(thm)],[1114])).
% 0.70/0.86 tff(3943,plain,
% 0.70/0.86 ((op(e0, e3) = e1) <=> (e1 = e2)),
% 0.70/0.86 inference(transitivity,[status(thm)],[3942, 317])).
% 0.70/0.86 tff(3944,plain,
% 0.70/0.86 ((e1 = e2) <=> (op(e0, e3) = e1)),
% 0.70/0.86 inference(symmetry,[status(thm)],[3943])).
% 0.70/0.86 tff(3945,plain,
% 0.70/0.86 ((~(e1 = e2)) <=> (~(op(e0, e3) = e1))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3944])).
% 0.70/0.86 tff(3946,plain,
% 0.70/0.86 (~(op(e0, e3) = e1)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[324, 3945])).
% 0.70/0.86 tff(3947,plain,
% 0.70/0.86 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1734, 1607, 3946, 12])).
% 0.70/0.86 tff(3948,plain,
% 0.70/0.86 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[681, 3947, 1798, 1852])).
% 0.70/0.86 tff(3949,plain,
% 0.70/0.86 (op(e1, op(e2, e1)) = e1),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[546, 3948])).
% 0.70/0.86 tff(3950,plain,
% 0.70/0.86 ((op(e0, e3) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[1114])).
% 0.70/0.86 tff(3951,plain,
% 0.70/0.86 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.70/0.86 inference(transitivity,[status(thm)],[3950, 218])).
% 0.70/0.86 tff(3952,plain,
% 0.70/0.86 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3951])).
% 0.70/0.86 tff(3953,plain,
% 0.70/0.86 (~(op(e1, e3) = e2)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1755, 3952])).
% 0.70/0.86 tff(3954,plain,
% 0.70/0.86 (op(e1, e0) = e2),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[135, 12, 1740, 3953])).
% 0.70/0.86 tff(3955,plain,
% 0.70/0.86 ((op(e1, e0) = e1) <=> (e2 = e1)),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3954])).
% 0.70/0.86 tff(3956,plain,
% 0.70/0.86 ((op(e1, e0) = e1) <=> (e1 = e2)),
% 0.70/0.86 inference(transitivity,[status(thm)],[3955, 317])).
% 0.70/0.86 tff(3957,plain,
% 0.70/0.86 ((e1 = e2) <=> (op(e1, e0) = e1)),
% 0.70/0.86 inference(symmetry,[status(thm)],[3956])).
% 0.70/0.86 tff(3958,plain,
% 0.70/0.86 ((~(e1 = e2)) <=> (~(op(e1, e0) = e1))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3957])).
% 0.70/0.86 tff(3959,plain,
% 0.70/0.86 (~(op(e1, e0) = e1)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[324, 3958])).
% 0.70/0.86 tff(3960,plain,
% 0.70/0.86 (~(op(e2, e1) = e0)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[642, 3949, 3959])).
% 0.70/0.86 tff(3961,plain,
% 0.70/0.86 ((op(e3, e1) = e0) <=> (e2 = e0)),
% 0.70/0.86 inference(monotonicity,[status(thm)],[1607])).
% 0.70/0.86 tff(3962,plain,
% 0.70/0.86 ((op(e3, e1) = e0) <=> (e0 = e2)),
% 0.70/0.86 inference(transitivity,[status(thm)],[3961, 217])).
% 0.70/0.86 tff(3963,plain,
% 0.70/0.86 ((e0 = e2) <=> (op(e3, e1) = e0)),
% 0.70/0.86 inference(symmetry,[status(thm)],[3962])).
% 0.70/0.86 tff(3964,plain,
% 0.70/0.86 ((~(e0 = e2)) <=> (~(op(e3, e1) = e0))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3963])).
% 0.70/0.86 tff(3965,plain,
% 0.70/0.86 (~(op(e3, e1) = e0)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[238, 3964])).
% 0.70/0.86 tff(3966,plain,
% 0.70/0.86 ((op(e0, e1) = e0) <=> (e3 = e0)),
% 0.70/0.86 inference(monotonicity,[status(thm)],[840])).
% 0.70/0.86 tff(3967,plain,
% 0.70/0.86 ((op(e0, e1) = e0) <=> (e0 = e3)),
% 0.70/0.86 inference(transitivity,[status(thm)],[3966, 279])).
% 0.70/0.86 tff(3968,plain,
% 0.70/0.86 ((e0 = e3) <=> (op(e0, e1) = e0)),
% 0.70/0.86 inference(symmetry,[status(thm)],[3967])).
% 0.70/0.86 tff(3969,plain,
% 0.70/0.86 ((~(e0 = e3)) <=> (~(op(e0, e1) = e0))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3968])).
% 0.70/0.86 tff(3970,plain,
% 0.70/0.86 (~(op(e0, e1) = e0)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[286, 3969])).
% 0.70/0.86 tff(3971,plain,
% 0.70/0.86 ((e3 = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 0.70/0.86 inference(commutativity,[status(thm)],[])).
% 0.70/0.86 tff(3972,plain,
% 0.70/0.86 ((op(e0, e1) = op(e2, e1)) <=> (e3 = op(e2, e1))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[840])).
% 0.70/0.86 tff(3973,plain,
% 0.70/0.86 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e3)),
% 0.70/0.86 inference(transitivity,[status(thm)],[3972, 3971])).
% 0.70/0.86 tff(3974,plain,
% 0.70/0.86 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e3))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3973])).
% 0.70/0.86 tff(3975,plain,
% 0.70/0.86 (~(op(e2, e1) = e3)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[61, 3974])).
% 0.70/0.86 tff(3976,plain,
% 0.70/0.86 ($false),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[627, 3975, 3970, 10, 609, 605, 551])).
% 0.70/0.86 tff(3977,plain,((~(op(e0, e1) = e3)) | (op(e2, e1) = e2) | (op(e3, e1) = e0) | (op(e2, e1) = e0) | (~(op(e1, op(e2, e1)) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.86 tff(3978,plain,
% 0.70/0.86 (~(op(e0, e1) = e3)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[3977, 3965, 10, 3960, 3949])).
% 0.70/0.86 tff(3979,plain,
% 0.70/0.86 (op(e0, op(e2, e0)) = e0),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[967, 3948])).
% 0.70/0.86 tff(3980,plain,
% 0.70/0.86 (op(e3, op(e2, e3)) = e3),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[471, 3948])).
% 0.70/0.86 tff(3981,plain,
% 0.70/0.86 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e2)),
% 0.70/0.86 inference(monotonicity,[status(thm)],[1607])).
% 0.70/0.86 tff(3982,plain,
% 0.70/0.86 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e2))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3981])).
% 0.70/0.86 tff(3983,plain,
% 0.70/0.86 (~(op(e3, e0) = e2)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[1333, 3982])).
% 0.70/0.86 tff(3984,plain,
% 0.70/0.86 ((op(e0, e0) = e0) <=> (e1 = e0)),
% 0.70/0.86 inference(monotonicity,[status(thm)],[684])).
% 0.70/0.86 tff(3985,plain,
% 0.70/0.86 ((op(e0, e0) = e0) <=> (e0 = e1)),
% 0.70/0.86 inference(transitivity,[status(thm)],[3984, 635])).
% 0.70/0.86 tff(3986,plain,
% 0.70/0.86 ((e0 = e1) <=> (op(e0, e0) = e0)),
% 0.70/0.86 inference(symmetry,[status(thm)],[3985])).
% 0.70/0.86 tff(3987,plain,
% 0.70/0.86 ((~(e0 = e1)) <=> (~(op(e0, e0) = e0))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3986])).
% 0.70/0.86 tff(3988,plain,
% 0.70/0.86 (~(op(e0, e0) = e0)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[625, 3987])).
% 0.70/0.86 tff(3989,plain,
% 0.70/0.86 (~(op(e0, e1) = e3)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[3113, 684, 1146])).
% 0.70/0.86 tff(3990,plain,
% 0.70/0.86 (op(e0, e1) = e0),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1678, 3989, 433])).
% 0.70/0.86 tff(3991,plain,
% 0.70/0.86 (op(e1, op(e0, e1)) = op(e1, e0)),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3990])).
% 0.70/0.86 tff(3992,plain,
% 0.70/0.86 (op(e1, op(e0, e1)) = e2),
% 0.70/0.86 inference(transitivity,[status(thm)],[3991, 776])).
% 0.70/0.86 tff(3993,plain,
% 0.70/0.86 ((op(e1, op(e0, e1)) = e1) <=> (e2 = e1)),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3992])).
% 0.70/0.86 tff(3994,plain,
% 0.70/0.86 ((op(e1, op(e0, e1)) = e1) <=> (e1 = e2)),
% 0.70/0.86 inference(transitivity,[status(thm)],[3993, 317])).
% 0.70/0.86 tff(3995,plain,
% 0.70/0.86 ((e1 = e2) <=> (op(e1, op(e0, e1)) = e1)),
% 0.70/0.86 inference(symmetry,[status(thm)],[3994])).
% 0.70/0.86 tff(3996,plain,
% 0.70/0.86 ((~(e1 = e2)) <=> (~(op(e1, op(e0, e1)) = e1))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3995])).
% 0.70/0.86 tff(3997,plain,
% 0.70/0.86 (~(op(e1, op(e0, e1)) = e1)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[324, 3996])).
% 0.70/0.86 tff(3998,plain,
% 0.70/0.86 ($false),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[3896, 3997, 3988, 63, 12])).
% 0.70/0.86 tff(3999,plain,((~(op(e0, e0) = e1)) | (op(e3, e3) = e0) | (op(e1, e1) = e2) | (~(op(e1, e0) = e2)) | (op(e0, e1) = e1) | (~(op(e3, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.86 tff(4000,plain,
% 0.70/0.86 (~(op(e0, e0) = e1)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[3999, 433, 12, 3954, 63, 1607])).
% 0.70/0.86 tff(4001,plain,
% 0.70/0.86 (op(e0, e2) = e1),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[718, 1139, 3946, 433])).
% 0.70/0.86 tff(4002,plain,
% 0.70/0.86 ((op(e0, e2) = e3) <=> (e1 = e3)),
% 0.70/0.86 inference(monotonicity,[status(thm)],[4001])).
% 0.70/0.86 tff(4003,plain,
% 0.70/0.86 ((e1 = e3) <=> (op(e0, e2) = e3)),
% 0.70/0.86 inference(symmetry,[status(thm)],[4002])).
% 0.70/0.86 tff(4004,plain,
% 0.70/0.86 ((~(e1 = e3)) <=> (~(op(e0, e2) = e3))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[4003])).
% 0.70/0.86 tff(4005,plain,
% 0.70/0.86 (~(op(e0, e2) = e3)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[591, 4004])).
% 0.70/0.86 tff(4006,plain,
% 0.70/0.86 ((op(e0, e3) = e3) <=> (e2 = e3)),
% 0.70/0.86 inference(monotonicity,[status(thm)],[1114])).
% 0.70/0.86 tff(4007,plain,
% 0.70/0.86 ((e2 = e3) <=> (op(e0, e3) = e3)),
% 0.70/0.86 inference(symmetry,[status(thm)],[4006])).
% 0.70/0.86 tff(4008,plain,
% 0.70/0.86 ((~(e2 = e3)) <=> (~(op(e0, e3) = e3))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[4007])).
% 0.70/0.86 tff(4009,plain,
% 0.70/0.86 (~(op(e0, e3) = e3)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[462, 4008])).
% 0.70/0.86 tff(4010,plain,
% 0.70/0.86 (op(e0, e0) = e3),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1562, 544, 4009, 4005])).
% 0.70/0.86 tff(4011,plain,
% 0.70/0.86 ((op(e0, e0) = op(e3, e0)) <=> (e3 = op(e3, e0))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[4010])).
% 0.70/0.86 tff(4012,plain,
% 0.70/0.86 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e3)),
% 0.70/0.86 inference(transitivity,[status(thm)],[4011, 2715])).
% 0.70/0.86 tff(4013,plain,
% 0.70/0.86 ((op(e3, e0) = e3) <=> (op(e0, e0) = op(e3, e0))),
% 0.70/0.86 inference(symmetry,[status(thm)],[4012])).
% 0.70/0.86 tff(4014,plain,
% 0.70/0.86 (~(op(e2, e0) = e0)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1900, 4010, 1896])).
% 0.70/0.86 tff(4015,plain,
% 0.70/0.86 (op(e0, e1) = e0),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1678, 544, 433])).
% 0.70/0.86 tff(4016,plain,
% 0.70/0.86 ((~(op(e2, e0) = e3)) | (~(op(e0, e3) = e2)) | (~(op(e0, op(e2, e0)) = e0)) | (~(op(e0, e1) = e0))),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[3448, 1605])).
% 0.70/0.86 tff(4017,plain,
% 0.70/0.86 (~(op(e2, e0) = e3)),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[4016, 4015, 1114, 1896])).
% 0.70/0.86 tff(4018,plain,
% 0.70/0.86 (op(e3, e0) = e3),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[3672, 4017, 74, 1139, 496, 605, 767, 1699, 640, 10, 4014])).
% 0.70/0.86 tff(4019,plain,
% 0.70/0.86 (op(e0, e0) = op(e3, e0)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[4018, 4013])).
% 0.70/0.86 tff(4020,plain,
% 0.70/0.86 ($false),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[1638, 4019])).
% 0.70/0.86 tff(4021,plain,((op(e0, e1) = e3) | (op(e2, e0) = e2) | (op(e0, e0) = e1) | (~(op(e3, op(e2, e3)) = e3)) | (op(e2, e1) = e0) | (op(e2, e3) = e2) | (op(e3, e0) = e2) | (op(e1, e0) = e1) | (op(e2, e1) = e2) | (~(op(e0, op(e2, e0)) = e0)) | (~(op(e0, e3) = e2)) | (op(e0, e1) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.86 tff(4022,plain,
% 0.70/0.86 ($false),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[4021, 4000, 433, 74, 496, 605, 767, 3983, 3959, 10, 1896, 1114, 544])).
% 0.70/0.86 tff(4023,plain,((op(e0, e1) = e1) | (op(e2, e0) = e2) | (~(op(e3, op(e2, e3)) = e3)) | (op(e2, e1) = e0) | (op(e2, e3) = e2) | (op(e2, e1) = e2) | (~(op(e0, op(e2, e0)) = e0)) | (~(op(e0, e3) = e2)) | (op(e0, e1) = e3) | (op(e1, e1) = e2) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.86 tff(4024,plain,
% 0.70/0.86 (op(e0, e1) = e1),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[4023, 3980, 74, 3960, 767, 10, 3979, 1114, 3978, 12, 63])).
% 0.70/0.86 tff(4025,plain,
% 0.70/0.86 ((op(e0, e1) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[4024])).
% 0.70/0.86 tff(4026,plain,
% 0.70/0.86 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 0.70/0.86 inference(transitivity,[status(thm)],[4025, 2032])).
% 0.70/0.86 tff(4027,plain,
% 0.70/0.86 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[4026])).
% 0.70/0.86 tff(4028,plain,
% 0.70/0.86 (~(op(e2, e1) = e1)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[61, 4027])).
% 0.70/0.86 tff(4029,plain,
% 0.70/0.86 (op(e2, e0) = e1),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[2417, 4028, 1607, 3948, 10])).
% 0.70/0.86 tff(4030,plain,
% 0.70/0.86 (e1 = op(e2, e0)),
% 0.70/0.86 inference(symmetry,[status(thm)],[4029])).
% 0.70/0.86 tff(4031,plain,
% 0.70/0.86 (op(e0, e1) = op(e0, op(e2, e0))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[4030])).
% 0.70/0.86 tff(4032,plain,
% 0.70/0.86 (op(e0, op(e2, e0)) = op(e0, e1)),
% 0.70/0.86 inference(symmetry,[status(thm)],[4031])).
% 0.70/0.86 tff(4033,plain,
% 0.70/0.86 (e0 = op(e0, op(e2, e0))),
% 0.70/0.86 inference(symmetry,[status(thm)],[3979])).
% 0.70/0.86 tff(4034,plain,
% 0.70/0.86 (e0 = e1),
% 0.70/0.86 inference(transitivity,[status(thm)],[4033, 4032, 4024])).
% 0.70/0.86 tff(4035,plain,
% 0.70/0.86 ($false),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[625, 4034])).
% 0.70/0.86 tff(4036,plain,((op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e2, e0) = e2) | (op(e2, e3) = e2) | (~(op(e0, e3) = e2)) | (op(e3, e3) = e0) | (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.86 tff(4037,plain,
% 0.70/0.86 (op(e1, e1) = e2),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[4036, 767, 74, 10, 3941, 63, 1766])).
% 0.70/0.86 tff(4038,plain,
% 0.70/0.86 ((op(e1, e1) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[4037])).
% 0.70/0.86 tff(4039,plain,
% 0.70/0.86 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 0.70/0.86 inference(transitivity,[status(thm)],[4038, 326])).
% 0.70/0.86 tff(4040,plain,
% 0.70/0.86 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[4039])).
% 0.70/0.86 tff(4041,plain,
% 0.70/0.86 (~(op(e3, e1) = e2)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[348, 4040])).
% 0.70/0.86 tff(4042,plain,
% 0.70/0.86 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3941])).
% 0.70/0.86 tff(4043,plain,
% 0.70/0.86 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[4042])).
% 0.70/0.86 tff(4044,plain,
% 0.70/0.86 (~(op(e0, e0) = e2)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[2178, 4043])).
% 0.70/0.86 tff(4045,plain,
% 0.70/0.86 (e2 = op(e2, e2)),
% 0.70/0.86 inference(symmetry,[status(thm)],[1737])).
% 0.70/0.86 tff(4046,plain,
% 0.70/0.86 ((e0 = e2) <=> (e0 = op(e2, e2))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[4045])).
% 0.70/0.86 tff(4047,plain,
% 0.70/0.86 ((e0 = e2) <=> (op(e2, e2) = e0)),
% 0.70/0.86 inference(transitivity,[status(thm)],[4046, 1275])).
% 0.70/0.86 tff(4048,plain,
% 0.70/0.86 ((~(e0 = e2)) <=> (~(op(e2, e2) = e0))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[4047])).
% 0.70/0.86 tff(4049,plain,
% 0.70/0.86 (~(op(e2, e2) = e0)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[238, 4048])).
% 0.70/0.86 tff(4050,plain,
% 0.70/0.86 (op(e3, e0) = e2),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[537, 4041, 1805, 75])).
% 0.70/0.86 tff(4051,plain,
% 0.70/0.86 ((op(e0, e3) = e0) <=> (e2 = e0)),
% 0.70/0.86 inference(monotonicity,[status(thm)],[3941])).
% 0.70/0.86 tff(4052,plain,
% 0.70/0.86 ((op(e0, e3) = e0) <=> (e0 = e2)),
% 0.70/0.86 inference(transitivity,[status(thm)],[4051, 217])).
% 0.70/0.86 tff(4053,plain,
% 0.70/0.86 ((e0 = e2) <=> (op(e0, e3) = e0)),
% 0.70/0.86 inference(symmetry,[status(thm)],[4052])).
% 0.70/0.86 tff(4054,plain,
% 0.70/0.86 ((~(e0 = e2)) <=> (~(op(e0, e3) = e0))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[4053])).
% 0.70/0.86 tff(4055,plain,
% 0.70/0.86 (~(op(e0, e3) = e0)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[238, 4054])).
% 0.70/0.86 tff(4056,plain,
% 0.70/0.86 ((e1 = e2) <=> (e1 = op(e2, e2))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[4045])).
% 0.70/0.86 tff(4057,plain,
% 0.70/0.86 ((e1 = e2) <=> (op(e2, e2) = e1)),
% 0.70/0.86 inference(transitivity,[status(thm)],[4056, 1949])).
% 0.70/0.86 tff(4058,plain,
% 0.70/0.86 ((~(e1 = e2)) <=> (~(op(e2, e2) = e1))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[4057])).
% 0.70/0.86 tff(4059,plain,
% 0.70/0.86 (~(op(e2, e2) = e1)),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[324, 4058])).
% 0.70/0.86 tff(4060,plain,
% 0.70/0.86 ((e1 = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 0.70/0.86 inference(commutativity,[status(thm)],[])).
% 0.70/0.87 tff(4061,assumption,(op(e3, e0) = e2), introduced(assumption)).
% 0.70/0.87 tff(4062,plain,
% 0.70/0.87 (op(e0, e1) = e0),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1678, 433, 544])).
% 0.70/0.87 tff(4063,plain,
% 0.70/0.87 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e0)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4062])).
% 0.70/0.87 tff(4064,plain,
% 0.70/0.87 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e0))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4063])).
% 0.70/0.87 tff(4065,plain,
% 0.70/0.87 (~(op(e0, e0) = e0)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[745, 4064])).
% 0.70/0.87 tff(4066,plain,
% 0.70/0.87 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[455, 433, 63, 374])).
% 0.70/0.87 tff(4067,plain,
% 0.70/0.87 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[681, 4066, 1221, 1852])).
% 0.70/0.87 tff(4068,plain,
% 0.70/0.87 (op(e0, op(e2, e0)) = e0),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[967, 4067])).
% 0.70/0.87 tff(4069,plain,
% 0.70/0.87 ((op(e0, e1) = op(e2, e1)) <=> (e0 = op(e2, e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4062])).
% 0.70/0.87 tff(4070,plain,
% 0.70/0.87 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4069, 3142])).
% 0.70/0.87 tff(4071,plain,
% 0.70/0.87 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e0))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4070])).
% 0.70/0.87 tff(4072,plain,
% 0.70/0.87 (~(op(e2, e1) = e0)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[61, 4071])).
% 0.70/0.87 tff(4073,plain,
% 0.70/0.87 (op(e3, op(e2, e3)) = e3),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[471, 4067])).
% 0.70/0.87 tff(4074,assumption,(op(e2, e3) = e0), introduced(assumption)).
% 0.70/0.87 tff(4075,plain,
% 0.70/0.87 (op(e3, op(e2, e3)) = op(e3, e0)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4074])).
% 0.70/0.87 tff(4076,plain,
% 0.70/0.87 (op(e3, e0) = op(e3, op(e2, e3))),
% 0.70/0.87 inference(symmetry,[status(thm)],[4075])).
% 0.70/0.87 tff(4077,plain,
% 0.70/0.87 (e2 = op(e3, e0)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4061])).
% 0.70/0.87 tff(4078,plain,
% 0.70/0.87 (e2 = e3),
% 0.70/0.87 inference(transitivity,[status(thm)],[4077, 4076, 496])).
% 0.70/0.87 tff(4079,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[462, 4078])).
% 0.70/0.87 tff(4080,plain,((~(op(e2, e3) = e0)) | (~(op(e3, op(e2, e3)) = e3)) | (~(op(e3, e0) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(4081,plain,
% 0.70/0.87 (~(op(e2, e3) = e0)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[4080, 4073, 4061])).
% 0.70/0.87 tff(4082,plain,
% 0.70/0.87 (op(e2, e0) = e0),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[3212, 4081, 491, 4072])).
% 0.70/0.87 tff(4083,plain,
% 0.70/0.87 (~(op(e0, e0) = e3)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1900, 4082, 4068])).
% 0.70/0.87 tff(4084,plain,
% 0.70/0.87 (op(e0, e0) = e1),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1100, 4083, 1820, 4065])).
% 0.70/0.87 tff(4085,plain,
% 0.70/0.87 (e0 = op(e2, e0)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4082])).
% 0.70/0.87 tff(4086,plain,
% 0.70/0.87 (op(e0, e0) = op(e0, op(e2, e0))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4085])).
% 0.70/0.87 tff(4087,plain,
% 0.70/0.87 (op(e0, op(e2, e0)) = op(e0, e0)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4086])).
% 0.70/0.87 tff(4088,plain,
% 0.70/0.87 (e0 = op(e0, op(e2, e0))),
% 0.70/0.87 inference(symmetry,[status(thm)],[4068])).
% 0.70/0.87 tff(4089,plain,
% 0.70/0.87 (e0 = e1),
% 0.70/0.87 inference(transitivity,[status(thm)],[4088, 4087, 4084])).
% 0.70/0.87 tff(4090,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[625, 4089])).
% 0.70/0.87 tff(4091,plain,((op(e0, e1) = e1) | (op(e0, e0) = e2) | (op(e2, e2) = e0) | (~(op(e3, e0) = e2)) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))) | (op(e3, e3) = e0) | (op(e3, e1) = e2) | (op(e0, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(4092,plain,
% 0.70/0.87 (op(e0, e1) = e1),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[4091, 544, 491, 4061, 1798, 1852, 63, 374, 1820])).
% 0.70/0.87 tff(4093,plain,
% 0.70/0.87 ((op(e0, e1) = op(e0, e2)) <=> (e1 = op(e0, e2))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4092])).
% 0.70/0.87 tff(4094,plain,
% 0.70/0.87 ((op(e0, e1) = op(e0, e2)) <=> (op(e0, e2) = e1)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4093, 4060])).
% 0.70/0.87 tff(4095,plain,
% 0.70/0.87 ((~(op(e0, e1) = op(e0, e2))) <=> (~(op(e0, e2) = e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4094])).
% 0.70/0.87 tff(4096,plain,
% 0.70/0.87 (~(op(e0, e2) = e1)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[70, 4095])).
% 0.70/0.87 tff(4097,plain,
% 0.70/0.87 ((op(e3, e0) = e0) <=> (e2 = e0)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4061])).
% 0.70/0.87 tff(4098,plain,
% 0.70/0.87 ((op(e3, e0) = e0) <=> (e0 = e2)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4097, 217])).
% 0.70/0.87 tff(4099,plain,
% 0.70/0.87 ((e0 = e2) <=> (op(e3, e0) = e0)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4098])).
% 0.70/0.87 tff(4100,plain,
% 0.70/0.87 ((~(e0 = e2)) <=> (~(op(e3, e0) = e0))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4099])).
% 0.70/0.87 tff(4101,plain,
% 0.70/0.87 (~(op(e3, e0) = e0)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[238, 4100])).
% 0.70/0.87 tff(4102,plain,
% 0.70/0.87 ((op(e3, e0) = e1) <=> (e2 = e1)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4061])).
% 0.70/0.87 tff(4103,plain,
% 0.70/0.87 ((op(e3, e0) = e1) <=> (e1 = e2)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4102, 317])).
% 0.70/0.87 tff(4104,plain,
% 0.70/0.87 ((e1 = e2) <=> (op(e3, e0) = e1)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4103])).
% 0.70/0.87 tff(4105,plain,
% 0.70/0.87 ((~(e1 = e2)) <=> (~(op(e3, e0) = e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4104])).
% 0.70/0.87 tff(4106,plain,
% 0.70/0.87 (~(op(e3, e0) = e1)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[324, 4105])).
% 0.70/0.87 tff(4107,plain,
% 0.70/0.87 ((op(e0, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4092])).
% 0.70/0.87 tff(4108,plain,
% 0.70/0.87 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4107, 1640])).
% 0.70/0.87 tff(4109,plain,
% 0.70/0.87 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4108])).
% 0.70/0.87 tff(4110,plain,
% 0.70/0.87 (~(op(e3, e1) = e1)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[332, 4109])).
% 0.70/0.87 tff(4111,plain,
% 0.70/0.87 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1651, 4110, 4106, 10])).
% 0.70/0.87 tff(4112,plain,
% 0.70/0.87 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[681, 4111, 1798, 1852])).
% 0.70/0.87 tff(4113,plain,
% 0.70/0.87 (op(e1, op(e2, e1)) = e1),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[546, 4112])).
% 0.70/0.87 tff(4114,plain,
% 0.70/0.87 (op(e3, op(e2, e3)) = e3),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[471, 4112])).
% 0.70/0.87 tff(4115,plain,
% 0.70/0.87 (~(op(e2, e3) = e0)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[4080, 4114, 4061])).
% 0.70/0.87 tff(4116,plain,
% 0.70/0.87 (op(e1, e3) = e0),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[247, 4115, 63, 2761])).
% 0.70/0.87 tff(4117,plain,
% 0.70/0.87 ((op(e1, e3) = e1) <=> (e0 = e1)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4116])).
% 0.70/0.87 tff(4118,plain,
% 0.70/0.87 ((e0 = e1) <=> (op(e1, e3) = e1)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4117])).
% 0.70/0.87 tff(4119,plain,
% 0.70/0.87 ((~(e0 = e1)) <=> (~(op(e1, e3) = e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4118])).
% 0.70/0.87 tff(4120,plain,
% 0.70/0.87 (~(op(e1, e3) = e1)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[625, 4119])).
% 0.70/0.87 tff(4121,plain,
% 0.70/0.87 (~(op(e2, e1) = e3)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[937, 4120, 4113])).
% 0.70/0.87 tff(4122,plain,
% 0.70/0.87 (~(op(e3, e1) = e0)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[593, 4121, 10, 4113, 544])).
% 0.70/0.87 tff(4123,plain,
% 0.70/0.87 (op(e3, e2) = e0),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[295, 4122, 63, 4101])).
% 0.70/0.87 tff(4124,plain,
% 0.70/0.87 ((op(e3, e2) = e1) <=> (e0 = e1)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4123])).
% 0.70/0.87 tff(4125,plain,
% 0.70/0.87 ((e0 = e1) <=> (op(e3, e2) = e1)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4124])).
% 0.70/0.87 tff(4126,plain,
% 0.70/0.87 ((~(e0 = e1)) <=> (~(op(e3, e2) = e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4125])).
% 0.70/0.87 tff(4127,plain,
% 0.70/0.87 (~(op(e3, e2) = e1)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[625, 4126])).
% 0.70/0.87 tff(4128,plain,
% 0.70/0.87 ((op(e0, e1) = op(e2, e1)) <=> (e1 = op(e2, e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4092])).
% 0.70/0.87 tff(4129,plain,
% 0.70/0.87 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e1)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4128, 2032])).
% 0.70/0.87 tff(4130,plain,
% 0.70/0.87 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4129])).
% 0.70/0.87 tff(4131,plain,
% 0.70/0.87 (~(op(e2, e1) = e1)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[61, 4130])).
% 0.70/0.87 tff(4132,plain,
% 0.70/0.87 (op(e2, e1) = e0),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[585, 4121, 10, 4131])).
% 0.70/0.87 tff(4133,plain,
% 0.70/0.87 (op(e1, e0) = e1),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[642, 4132, 4113])).
% 0.70/0.87 tff(4134,plain,
% 0.70/0.87 ((op(e1, e0) = op(e1, e2)) <=> (e1 = op(e1, e2))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4133])).
% 0.70/0.87 tff(4135,plain,
% 0.70/0.87 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e2) = e1)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4134, 1587])).
% 0.70/0.87 tff(4136,plain,
% 0.70/0.87 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e2) = e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4135])).
% 0.70/0.87 tff(4137,plain,
% 0.70/0.87 (~(op(e1, e2) = e1)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[1428, 4136])).
% 0.70/0.87 tff(4138,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1603, 4137, 4127, 4096, 490])).
% 0.70/0.87 tff(4139,plain,((op(e0, e1) = e3) | (op(e2, e2) = e1) | (op(e3, e3) = e0) | (op(e2, e1) = e2) | (op(e0, e3) = e0) | (~(op(e3, e0) = e2)) | (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))) | (op(e2, e2) = e0) | (op(e3, e1) = e2) | (op(e0, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(4140,plain,
% 0.70/0.87 (op(e0, e1) = e3),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[4139, 4059, 63, 10, 4055, 4050, 1766, 4049, 4041, 4044])).
% 0.70/0.87 tff(4141,plain,
% 0.70/0.87 ((op(e0, e1) = e1) <=> (e3 = e1)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4140])).
% 0.70/0.87 tff(4142,plain,
% 0.70/0.87 ((op(e0, e1) = e1) <=> (e1 = e3)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4141, 951])).
% 0.70/0.87 tff(4143,plain,
% 0.70/0.87 ((e1 = e3) <=> (op(e0, e1) = e1)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4142])).
% 0.70/0.87 tff(4144,plain,
% 0.70/0.87 ((~(e1 = e3)) <=> (~(op(e0, e1) = e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4143])).
% 0.70/0.87 tff(4145,plain,
% 0.70/0.87 (~(op(e0, e1) = e1)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[591, 4144])).
% 0.70/0.87 tff(4146,plain,
% 0.70/0.87 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[455, 4145, 63, 4041])).
% 0.70/0.87 tff(4147,plain,
% 0.70/0.87 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[681, 4146, 1798, 1766])).
% 0.70/0.87 tff(4148,plain,
% 0.70/0.87 (op(e3, op(e2, e3)) = e3),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[471, 4147])).
% 0.70/0.87 tff(4149,plain,
% 0.70/0.87 (~(op(e2, e3) = e0)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[4080, 4148, 4050])).
% 0.70/0.87 tff(4150,plain,
% 0.70/0.87 (op(e1, e3) = e0),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[247, 4149, 63, 4055])).
% 0.70/0.87 tff(4151,plain,
% 0.70/0.87 (e0 = op(e1, e3)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4150])).
% 0.70/0.87 tff(4152,plain,
% 0.70/0.87 ((e0 = e1) <=> (op(e1, e3) = e1)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4151])).
% 0.70/0.87 tff(4153,plain,
% 0.70/0.87 ((~(e0 = e1)) <=> (~(op(e1, e3) = e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4152])).
% 0.70/0.87 tff(4154,plain,
% 0.70/0.87 (~(op(e1, e3) = e1)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[625, 4153])).
% 0.70/0.87 tff(4155,plain,
% 0.70/0.87 ((op(e0, e3) = e1) <=> (e2 = e1)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[3941])).
% 0.70/0.87 tff(4156,plain,
% 0.70/0.87 ((op(e0, e3) = e1) <=> (e1 = e2)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4155, 317])).
% 0.70/0.87 tff(4157,plain,
% 0.70/0.87 ((e1 = e2) <=> (op(e0, e3) = e1)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4156])).
% 0.70/0.87 tff(4158,plain,
% 0.70/0.87 ((~(e1 = e2)) <=> (~(op(e0, e3) = e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4157])).
% 0.70/0.87 tff(4159,plain,
% 0.70/0.87 (~(op(e0, e3) = e1)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[324, 4158])).
% 0.70/0.87 tff(4160,plain,
% 0.70/0.87 ((op(e1, e1) = e1) <=> (e2 = e1)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4037])).
% 0.70/0.87 tff(4161,plain,
% 0.70/0.87 ((op(e1, e1) = e1) <=> (e1 = e2)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4160, 317])).
% 0.70/0.87 tff(4162,plain,
% 0.70/0.87 ((e1 = e2) <=> (op(e1, e1) = e1)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4161])).
% 0.70/0.87 tff(4163,plain,
% 0.70/0.87 ((~(e1 = e2)) <=> (~(op(e1, e1) = e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4162])).
% 0.70/0.87 tff(4164,plain,
% 0.70/0.87 (~(op(e1, e1) = e1)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[324, 4163])).
% 0.70/0.87 tff(4165,plain,
% 0.70/0.87 (op(e1, op(e2, e1)) = e1),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[546, 4147])).
% 0.70/0.87 tff(4166,assumption,(op(e1, e1) = e2), introduced(assumption)).
% 0.70/0.87 tff(4167,plain,
% 0.70/0.87 (op(e1, op(e2, e1)) = op(e1, e1)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[1020])).
% 0.70/0.87 tff(4168,plain,
% 0.70/0.87 (e1 = e2),
% 0.70/0.87 inference(transitivity,[status(thm)],[552, 4167, 4166])).
% 0.70/0.87 tff(4169,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[324, 4168])).
% 0.70/0.87 tff(4170,plain,((~(op(e2, e1) = e1)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e1, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(4171,plain,
% 0.70/0.87 (~(op(e2, e1) = e1)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[4170, 4165, 4037])).
% 0.70/0.87 tff(4172,plain,
% 0.70/0.87 (op(e3, e1) = e1),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[450, 4171, 4145, 4164])).
% 0.70/0.87 tff(4173,plain,
% 0.70/0.87 ((op(e3, e1) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4172])).
% 0.70/0.87 tff(4174,plain,
% 0.70/0.87 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4173, 76])).
% 0.70/0.87 tff(4175,plain,
% 0.70/0.87 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4174])).
% 0.70/0.87 tff(4176,plain,
% 0.70/0.87 (~(op(e3, e3) = e1)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[399, 4175])).
% 0.70/0.87 tff(4177,plain,
% 0.70/0.87 (op(e2, e3) = e1),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1872, 4176, 4159, 4154])).
% 0.70/0.87 tff(4178,plain,
% 0.70/0.87 (e1 = op(e2, e3)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4177])).
% 0.70/0.87 tff(4179,plain,
% 0.70/0.87 (op(e3, e1) = op(e3, op(e2, e3))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4178])).
% 0.70/0.87 tff(4180,plain,
% 0.70/0.87 (e1 = op(e3, e1)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4172])).
% 0.70/0.87 tff(4181,plain,
% 0.70/0.87 (e1 = e3),
% 0.70/0.87 inference(transitivity,[status(thm)],[4180, 4179, 4148])).
% 0.70/0.87 tff(4182,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[591, 4181])).
% 0.70/0.87 tff(4183,plain,((op(e2, e3) = e2) | (op(e3, e3) = e0) | (op(e2, e1) = e2) | (op(e3, e3) = e2) | (op(e2, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(4184,plain,
% 0.70/0.87 (op(e2, e3) = e2),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[4183, 63, 10, 75, 74])).
% 0.70/0.87 tff(4185,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[515, 482, 472, 492, 489])).
% 0.70/0.87 tff(4186,plain,(((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))) | (~(op(e2, e3) = e2)) | (op(e2, e0) = e2) | (op(e2, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(4187,plain,
% 0.70/0.87 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[4186, 4184, 74, 10])).
% 0.70/0.87 tff(4188,plain,
% 0.70/0.87 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1659, 1132, 10])).
% 0.70/0.87 tff(4189,plain,
% 0.70/0.87 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[681, 4188, 1798, 4187])).
% 0.70/0.87 tff(4190,plain,
% 0.70/0.87 (op(e2, op(e1, e2)) = e2),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[102, 4189])).
% 0.70/0.87 tff(4191,plain,
% 0.70/0.87 (op(e1, op(e0, e1)) = op(e1, e1)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[1132])).
% 0.70/0.87 tff(4192,plain,
% 0.70/0.87 ((op(e1, op(e0, e1)) = e1) <=> (op(e1, e1) = e1)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4191])).
% 0.70/0.87 tff(4193,plain,
% 0.70/0.87 ((op(e1, e1) = e1) <=> (op(e1, op(e0, e1)) = e1)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4192])).
% 0.70/0.87 tff(4194,plain,
% 0.70/0.87 ((~(op(e1, e1) = e1)) <=> (~(op(e1, op(e0, e1)) = e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4193])).
% 0.70/0.87 tff(4195,plain,
% 0.70/0.87 ((op(e0, e1) = op(e1, e1)) <=> (e1 = op(e1, e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[1132])).
% 0.70/0.87 tff(4196,plain,
% 0.70/0.87 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e1)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4195, 434])).
% 0.70/0.87 tff(4197,plain,
% 0.70/0.87 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4196])).
% 0.70/0.87 tff(4198,plain,
% 0.70/0.87 (~(op(e1, e1) = e1)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[100, 4197])).
% 0.70/0.87 tff(4199,plain,
% 0.70/0.87 (~(op(e1, op(e0, e1)) = e1)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[4198, 4194])).
% 0.70/0.87 tff(4200,plain,
% 0.70/0.87 ((op(e2, e3) = e1) <=> (e2 = e1)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4184])).
% 0.70/0.87 tff(4201,plain,
% 0.70/0.87 ((op(e2, e3) = e1) <=> (e1 = e2)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4200, 317])).
% 0.70/0.87 tff(4202,plain,
% 0.70/0.87 ((e1 = e2) <=> (op(e2, e3) = e1)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4201])).
% 0.70/0.87 tff(4203,plain,
% 0.70/0.87 ((~(e1 = e2)) <=> (~(op(e2, e3) = e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4202])).
% 0.70/0.87 tff(4204,plain,
% 0.70/0.87 (~(op(e2, e3) = e1)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[324, 4203])).
% 0.70/0.87 tff(4205,plain,
% 0.70/0.87 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1876, 1607, 4204, 1722])).
% 0.70/0.87 tff(4206,plain,
% 0.70/0.87 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[681, 4205, 1798, 4187])).
% 0.70/0.87 tff(4207,plain,
% 0.70/0.87 (op(e0, op(e1, e0)) = e0),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[83, 4206])).
% 0.70/0.87 tff(4208,plain,
% 0.70/0.87 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e2)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4184])).
% 0.70/0.87 tff(4209,plain,
% 0.70/0.87 ((~(op(e0, e3) = op(e2, e3))) <=> (~(op(e0, e3) = e2))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4208])).
% 0.70/0.87 tff(4210,plain,
% 0.70/0.87 (~(op(e0, e3) = e2)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[2232, 4209])).
% 0.70/0.87 tff(4211,plain,
% 0.70/0.87 (op(e1, e0) = e2),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[205, 4206, 10, 74, 4210, 75, 12])).
% 0.70/0.87 tff(4212,plain,
% 0.70/0.87 (e2 = op(e1, e0)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4211])).
% 0.70/0.87 tff(4213,plain,
% 0.70/0.87 (op(e0, e2) = op(e0, op(e1, e0))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4212])).
% 0.70/0.87 tff(4214,plain,
% 0.70/0.87 (op(e0, e2) = e0),
% 0.70/0.87 inference(transitivity,[status(thm)],[4213, 4207])).
% 0.70/0.87 tff(4215,plain,
% 0.70/0.87 (op(e0, e0) = e0),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[3896, 12, 63, 1814])).
% 0.70/0.87 tff(4216,plain,
% 0.70/0.87 ((op(e0, e0) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4215])).
% 0.70/0.87 tff(4217,plain,
% 0.70/0.87 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4216, 988])).
% 0.70/0.87 tff(4218,plain,
% 0.70/0.87 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4217])).
% 0.70/0.87 tff(4219,plain,
% 0.70/0.87 (~(op(e0, e2) = e0)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[1190, 4218])).
% 0.70/0.87 tff(4220,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[4219, 4214])).
% 0.70/0.87 tff(4221,plain,((op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e2, e0) = e2) | (op(e3, e3) = e2) | (op(e0, e3) = e1) | (op(e3, e3) = e0) | (op(e1, op(e0, e1)) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(4222,plain,
% 0.70/0.87 (op(e1, e1) = e2),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[4221, 1851, 74, 75, 10, 63, 4199])).
% 0.70/0.87 tff(4223,plain,
% 0.70/0.87 (e2 = op(e1, e1)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4222])).
% 0.70/0.87 tff(4224,plain,
% 0.70/0.87 (op(e1, e2) = op(e1, op(e1, e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4223])).
% 0.70/0.87 tff(4225,plain,
% 0.70/0.87 (op(e1, op(e1, e1)) = op(e1, e2)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4224])).
% 0.70/0.87 tff(4226,plain,
% 0.70/0.87 (op(e1, op(e1, e1)) = e1),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1315, 4189])).
% 0.70/0.87 tff(4227,plain,
% 0.70/0.87 (e1 = op(e1, op(e1, e1))),
% 0.70/0.87 inference(symmetry,[status(thm)],[4226])).
% 0.70/0.87 tff(4228,plain,
% 0.70/0.87 (e1 = op(e1, e2)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4227, 4225])).
% 0.70/0.87 tff(4229,plain,
% 0.70/0.87 (op(e2, e1) = op(e2, op(e1, e2))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4228])).
% 0.70/0.87 tff(4230,plain,
% 0.70/0.87 (op(e2, e1) = e2),
% 0.70/0.87 inference(transitivity,[status(thm)],[4229, 4190])).
% 0.70/0.87 tff(4231,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[10, 4230])).
% 0.70/0.87 tff(4232,plain,((~(op(e0, e1) = e1)) | (op(e2, e1) = e2) | (op(e2, e0) = e2) | (op(e3, e3) = e2) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(4233,plain,
% 0.70/0.87 (~(op(e0, e1) = e1)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[4232, 63, 74, 75, 10])).
% 0.70/0.87 tff(4234,plain,
% 0.70/0.87 ((op(e3, e0) = op(e1, e0)) <=> (op(e1, e0) = op(e3, e0))),
% 0.70/0.87 inference(commutativity,[status(thm)],[])).
% 0.70/0.87 tff(4235,plain,
% 0.70/0.87 (op(e1, op(e0, e1)) = op(e1, e0)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[3420])).
% 0.70/0.87 tff(4236,plain,
% 0.70/0.87 ((op(e0, e0) = op(e0, e1)) <=> (op(e0, e0) = e0)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[3420])).
% 0.70/0.87 tff(4237,plain,
% 0.70/0.87 ((~(op(e0, e0) = op(e0, e1))) <=> (~(op(e0, e0) = e0))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4236])).
% 0.70/0.87 tff(4238,plain,
% 0.70/0.87 (~(op(e0, e0) = e0)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[745, 4237])).
% 0.70/0.87 tff(4239,plain,
% 0.70/0.87 (op(e1, op(e0, e1)) = e1),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[3896, 12, 63, 4238])).
% 0.70/0.87 tff(4240,plain,
% 0.70/0.87 (e1 = op(e1, op(e0, e1))),
% 0.70/0.87 inference(symmetry,[status(thm)],[4239])).
% 0.70/0.87 tff(4241,plain,
% 0.70/0.87 (e1 = op(e1, e0)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4240, 4235])).
% 0.70/0.87 tff(4242,plain,
% 0.70/0.87 ((op(e3, e0) = e1) <=> (op(e3, e0) = op(e1, e0))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4241])).
% 0.70/0.87 tff(4243,plain,
% 0.70/0.87 ((op(e3, e0) = e1) <=> (op(e1, e0) = op(e3, e0))),
% 0.70/0.87 inference(transitivity,[status(thm)],[4242, 4234])).
% 0.70/0.87 tff(4244,plain,
% 0.70/0.87 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4243])).
% 0.70/0.87 tff(4245,plain,
% 0.70/0.87 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4244])).
% 0.70/0.87 tff(4246,plain,
% 0.70/0.87 (~(op(e3, e0) = e1)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[420, 4245])).
% 0.70/0.87 tff(4247,plain,
% 0.70/0.87 ((op(e3, e1) = e1) <=> (e2 = e1)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[1607])).
% 0.70/0.87 tff(4248,plain,
% 0.70/0.87 ((op(e3, e1) = e1) <=> (e1 = e2)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4247, 317])).
% 0.70/0.87 tff(4249,plain,
% 0.70/0.87 ((e1 = e2) <=> (op(e3, e1) = e1)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4248])).
% 0.70/0.87 tff(4250,plain,
% 0.70/0.87 ((~(e1 = e2)) <=> (~(op(e3, e1) = e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4249])).
% 0.70/0.87 tff(4251,plain,
% 0.70/0.87 (~(op(e3, e1) = e1)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[324, 4250])).
% 0.70/0.87 tff(4252,plain,
% 0.70/0.87 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1651, 4251, 4246, 10])).
% 0.70/0.87 tff(4253,plain,
% 0.70/0.87 (op(e1, e0) = op(e1, op(e0, e1))),
% 0.70/0.87 inference(symmetry,[status(thm)],[4235])).
% 0.70/0.87 tff(4254,plain,
% 0.70/0.87 (op(e1, e0) = e1),
% 0.70/0.87 inference(transitivity,[status(thm)],[4253, 4239])).
% 0.70/0.87 tff(4255,plain,
% 0.70/0.87 ((op(e1, e0) = e2) <=> (e1 = e2)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4254])).
% 0.70/0.87 tff(4256,plain,
% 0.70/0.87 ((e1 = e2) <=> (op(e1, e0) = e2)),
% 0.70/0.87 inference(symmetry,[status(thm)],[4255])).
% 0.70/0.87 tff(4257,plain,
% 0.70/0.87 ((~(e1 = e2)) <=> (~(op(e1, e0) = e2))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4256])).
% 0.70/0.87 tff(4258,plain,
% 0.70/0.87 (~(op(e1, e0) = e2)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[324, 4257])).
% 0.70/0.87 tff(4259,plain,
% 0.70/0.87 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[205, 4258, 10, 74, 4210, 75, 12])).
% 0.70/0.87 tff(4260,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[681, 4259, 4252, 1798, 4187])).
% 0.70/0.87 tff(4261,plain,((op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e2, e0) = e2) | (op(e3, e3) = e2) | (~(op(e0, e1) = e0)) | (op(e3, e3) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(4262,plain,
% 0.70/0.87 (op(e1, e1) = e2),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[4261, 4062, 74, 75, 10, 63])).
% 0.70/0.87 tff(4263,plain,
% 0.70/0.87 ((op(e1, e1) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4262])).
% 0.70/0.87 tff(4264,plain,
% 0.70/0.87 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4263, 326])).
% 0.70/0.87 tff(4265,plain,
% 0.70/0.87 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4264])).
% 0.70/0.87 tff(4266,plain,
% 0.70/0.87 (~(op(e3, e1) = e2)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[348, 4265])).
% 0.70/0.87 tff(4267,plain,
% 0.70/0.87 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[455, 4266, 63, 433])).
% 0.70/0.87 tff(4268,plain,
% 0.70/0.87 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[681, 4267, 1798, 4187])).
% 0.70/0.87 tff(4269,plain,
% 0.70/0.87 (op(e2, op(e1, e2)) = e2),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[102, 4268])).
% 0.70/0.87 tff(4270,plain,
% 0.70/0.87 (op(e1, op(e1, e1)) = op(e1, e2)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4262])).
% 0.70/0.87 tff(4271,plain,
% 0.70/0.87 (op(e1, op(e1, e1)) = e1),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1315, 4268])).
% 0.70/0.87 tff(4272,plain,
% 0.70/0.87 (e1 = op(e1, op(e1, e1))),
% 0.70/0.87 inference(symmetry,[status(thm)],[4271])).
% 0.70/0.87 tff(4273,plain,
% 0.70/0.87 (e1 = op(e1, e2)),
% 0.70/0.87 inference(transitivity,[status(thm)],[4272, 4270])).
% 0.70/0.87 tff(4274,plain,
% 0.70/0.87 (op(e2, e1) = op(e2, op(e1, e2))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4273])).
% 0.70/0.87 tff(4275,plain,
% 0.70/0.87 (op(e2, e1) = e2),
% 0.70/0.87 inference(transitivity,[status(thm)],[4274, 4269])).
% 0.70/0.87 tff(4276,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[10, 4275])).
% 0.70/0.87 tff(4277,plain,((op(e0, e1) = e1) | (op(e2, e1) = e2) | (op(e3, e3) = e0) | (op(e2, e0) = e2) | (op(e3, e3) = e2) | (op(e0, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(4278,plain,
% 0.70/0.87 (op(e0, e1) = e3),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[4277, 4233, 63, 74, 75, 10])).
% 0.70/0.87 tff(4279,plain,
% 0.70/0.87 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1676, 4278, 63, 4233])).
% 0.70/0.87 tff(4280,plain,
% 0.70/0.87 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[681, 4279, 1798, 4187])).
% 0.70/0.87 tff(4281,plain,
% 0.70/0.87 (op(e2, op(e1, e2)) = e2),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[102, 4280])).
% 0.70/0.87 tff(4282,plain,
% 0.70/0.87 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e2)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4184])).
% 0.70/0.87 tff(4283,plain,
% 0.70/0.87 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e2))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4282])).
% 0.70/0.87 tff(4284,plain,
% 0.70/0.87 (~(op(e1, e3) = e2)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[944, 4283])).
% 0.70/0.87 tff(4285,plain,
% 0.70/0.87 ((op(e2, e2) = op(e2, e3)) <=> (op(e2, e2) = e2)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4184])).
% 0.70/0.87 tff(4286,plain,
% 0.70/0.87 ((~(op(e2, e2) = op(e2, e3))) <=> (~(op(e2, e2) = e2))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4285])).
% 0.70/0.87 tff(4287,plain,
% 0.70/0.87 (~(op(e2, e2) = e2)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[153, 4286])).
% 0.70/0.87 tff(4288,plain,
% 0.70/0.87 (~(op(e1, e2) = e2)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1269, 4281, 4287])).
% 0.70/0.87 tff(4289,plain,
% 0.70/0.87 (op(e0, op(e1, e0)) = e0),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[83, 4280])).
% 0.70/0.87 tff(4290,plain,
% 0.70/0.87 (op(e1, e0) = e2),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[135, 12, 766, 107])).
% 0.70/0.87 tff(4291,plain,
% 0.70/0.87 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e2)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4290])).
% 0.70/0.87 tff(4292,plain,
% 0.70/0.87 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e0, e0) = e2))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[4291])).
% 0.70/0.87 tff(4293,plain,
% 0.70/0.87 (~(op(e0, e0) = e2)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[1056, 4292])).
% 0.70/0.87 tff(4294,plain,
% 0.70/0.87 ((op(e0, e0) = e2) | (~(op(e0, op(e1, e0)) = e0)) | (op(e2, e0) = e2) | (op(e3, e0) = e2) | (op(e0, e3) = e2)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[1836, 1605])).
% 0.70/0.87 tff(4295,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[4294, 4293, 3983, 74, 104, 1832])).
% 0.70/0.87 tff(4296,plain,((op(e1, e1) = e2) | (op(e2, e0) = e2) | (op(e0, e3) = e2) | (~(op(e0, op(e1, e0)) = e0)) | (op(e1, e2) = e2) | (op(e1, e3) = e2) | (op(e2, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(4297,plain,
% 0.70/0.87 (op(e1, e1) = e2),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[4296, 4210, 74, 4289, 4288, 4284, 10])).
% 0.70/0.88 tff(4298,plain,
% 0.70/0.88 (e2 = op(e1, e1)),
% 0.70/0.88 inference(symmetry,[status(thm)],[4297])).
% 0.70/0.88 tff(4299,plain,
% 0.70/0.88 (op(e1, e2) = op(e1, op(e1, e1))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4298])).
% 0.70/0.88 tff(4300,plain,
% 0.70/0.88 (op(e1, op(e1, e1)) = op(e1, e2)),
% 0.70/0.88 inference(symmetry,[status(thm)],[4299])).
% 0.70/0.88 tff(4301,plain,
% 0.70/0.88 (op(e1, op(e1, e1)) = e1),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1315, 4280])).
% 0.70/0.88 tff(4302,plain,
% 0.70/0.88 (e1 = op(e1, op(e1, e1))),
% 0.70/0.88 inference(symmetry,[status(thm)],[4301])).
% 0.70/0.88 tff(4303,plain,
% 0.70/0.88 (e1 = op(e1, e2)),
% 0.70/0.88 inference(transitivity,[status(thm)],[4302, 4300])).
% 0.70/0.88 tff(4304,plain,
% 0.70/0.88 (op(e2, e1) = op(e2, op(e1, e2))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4303])).
% 0.70/0.88 tff(4305,plain,
% 0.70/0.88 (op(e2, e1) = e2),
% 0.70/0.88 inference(transitivity,[status(thm)],[4304, 4281])).
% 0.70/0.88 tff(4306,plain,
% 0.70/0.88 ($false),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[10, 4305])).
% 0.70/0.88 tff(4307,plain,((op(e3, e3) = e0) | (op(e2, e1) = e2) | (op(e2, e0) = e2) | (op(e3, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.88 tff(4308,plain,
% 0.70/0.88 (op(e3, e3) = e0),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[4307, 75, 74, 10])).
% 0.70/0.88 tff(4309,plain,
% 0.70/0.88 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1669, 4308])).
% 0.70/0.88 tff(4310,plain,
% 0.70/0.88 (op(e2, e3) = e2),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1765, 79, 74, 75, 10])).
% 0.70/0.88 tff(4311,plain,
% 0.70/0.88 ((op(e0, e3) = op(e2, e3)) <=> (op(e0, e3) = e2)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4310])).
% 0.70/0.88 tff(4312,plain,
% 0.70/0.88 ((op(e0, e3) = e2) <=> (op(e0, e3) = op(e2, e3))),
% 0.70/0.88 inference(symmetry,[status(thm)],[4311])).
% 0.70/0.88 tff(4313,plain,
% 0.70/0.88 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e0)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4308])).
% 0.70/0.88 tff(4314,plain,
% 0.70/0.88 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e0))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4313])).
% 0.70/0.88 tff(4315,plain,
% 0.70/0.88 (~(op(e1, e3) = e0)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[368, 4314])).
% 0.70/0.88 tff(4316,plain,
% 0.70/0.88 (op(e0, e3) = e2),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1320, 79, 10, 74, 4315, 75, 12])).
% 0.70/0.88 tff(4317,plain,
% 0.70/0.88 (op(e0, e3) = op(e2, e3)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[4316, 4312])).
% 0.70/0.88 tff(4318,plain,
% 0.70/0.88 ($false),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[2232, 4317])).
% 0.70/0.88 tff(4319,plain,(((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))) | (op(e2, e1) = e2) | (op(e2, e0) = e2) | (op(e3, e3) = e2) | (op(e1, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.88 tff(4320,plain,
% 0.70/0.88 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[4319, 12, 74, 75, 10])).
% 0.70/0.88 tff(4321,plain,
% 0.70/0.88 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[681, 4320, 1798, 4309])).
% 0.70/0.88 tff(4322,plain,
% 0.70/0.88 (op(e3, op(e2, e3)) = e3),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[471, 4321])).
% 0.70/0.88 tff(4323,plain,
% 0.70/0.88 (~(op(e2, e3) = e1)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[2043, 4322, 1607])).
% 0.70/0.88 tff(4324,plain,
% 0.70/0.88 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e0)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4308])).
% 0.70/0.88 tff(4325,plain,
% 0.70/0.88 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e0))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4324])).
% 0.70/0.88 tff(4326,plain,
% 0.70/0.88 (~(op(e2, e3) = e0)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[387, 4325])).
% 0.70/0.88 tff(4327,plain,
% 0.70/0.88 (~(op(e2, e3) = e2)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[4186, 4321, 74, 10])).
% 0.70/0.88 tff(4328,plain,
% 0.70/0.88 (op(e2, e3) = e3),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[2637, 4327, 4326, 4323])).
% 0.70/0.88 tff(4329,plain,
% 0.70/0.88 (op(e3, op(e2, e3)) = op(e3, e3)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4328])).
% 0.70/0.88 tff(4330,plain,
% 0.70/0.88 (op(e3, e3) = op(e3, op(e2, e3))),
% 0.70/0.88 inference(symmetry,[status(thm)],[4329])).
% 0.70/0.88 tff(4331,plain,
% 0.70/0.88 (e0 = op(e3, e3)),
% 0.70/0.88 inference(symmetry,[status(thm)],[4308])).
% 0.70/0.88 tff(4332,plain,
% 0.70/0.88 (e0 = e3),
% 0.70/0.88 inference(transitivity,[status(thm)],[4331, 4330, 4322])).
% 0.70/0.88 tff(4333,plain,
% 0.70/0.88 ($false),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[286, 4332])).
% 0.70/0.88 tff(4334,plain,((op(e1, e1) = e2) | (op(e2, e0) = e2) | (op(e2, e1) = e2) | (op(e3, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.88 tff(4335,plain,
% 0.70/0.88 (op(e1, e1) = e2),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[4334, 75, 10, 74])).
% 0.70/0.88 tff(4336,plain,
% 0.70/0.88 ((op(e1, e1) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4335])).
% 0.70/0.88 tff(4337,plain,
% 0.70/0.88 ((op(e1, e1) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.70/0.88 inference(transitivity,[status(thm)],[4336, 218])).
% 0.70/0.88 tff(4338,plain,
% 0.70/0.88 ((~(op(e1, e1) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4337])).
% 0.70/0.88 tff(4339,plain,
% 0.70/0.88 (~(op(e1, e3) = e2)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[838, 4338])).
% 0.70/0.88 tff(4340,plain,
% 0.70/0.88 (op(e1, op(e1, e1)) = op(e1, e2)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4166])).
% 0.70/0.88 tff(4341,plain,
% 0.70/0.88 (e1 = op(e1, e2)),
% 0.70/0.88 inference(transitivity,[status(thm)],[1317, 4340])).
% 0.70/0.88 tff(4342,plain,
% 0.70/0.88 (op(e2, e1) = op(e2, op(e1, e2))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4341])).
% 0.70/0.88 tff(4343,plain,
% 0.70/0.88 (op(e2, e1) = e2),
% 0.70/0.88 inference(transitivity,[status(thm)],[4342, 103])).
% 0.70/0.88 tff(4344,plain,
% 0.70/0.88 ($false),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[10, 4343])).
% 0.70/0.88 tff(4345,plain,(((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))) | (op(e2, e1) = e2) | (~(op(e1, e1) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.88 tff(4346,plain,
% 0.70/0.88 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[4345, 4335, 10])).
% 0.70/0.88 tff(4347,plain,
% 0.70/0.88 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[681, 4346, 1798, 4309])).
% 0.70/0.88 tff(4348,plain,
% 0.70/0.88 (~(op(e2, e3) = e2)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[4186, 4347, 74, 10])).
% 0.70/0.88 tff(4349,plain,
% 0.70/0.88 (op(e0, e3) = e2),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[147, 4348, 75, 4339])).
% 0.70/0.88 tff(4350,plain,
% 0.70/0.88 (op(e3, op(e2, e3)) = e3),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[471, 4347])).
% 0.70/0.88 tff(4351,plain,
% 0.70/0.88 (op(e2, op(e2, e2)) = e2),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[473, 4347])).
% 0.70/0.88 tff(4352,plain,
% 0.70/0.88 (~(op(e2, e2) = e1)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[488, 4351, 10])).
% 0.70/0.88 tff(4353,plain,
% 0.70/0.88 (op(e1, op(e2, e1)) = e1),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[546, 4347])).
% 0.70/0.88 tff(4354,plain,
% 0.70/0.88 (~(op(e2, e1) = e1)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[4170, 4353, 4335])).
% 0.70/0.88 tff(4355,plain,
% 0.70/0.88 ((op(e1, e1) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4335])).
% 0.70/0.88 tff(4356,plain,
% 0.70/0.88 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 0.70/0.88 inference(transitivity,[status(thm)],[4355, 326])).
% 0.70/0.88 tff(4357,plain,
% 0.70/0.88 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4356])).
% 0.70/0.88 tff(4358,plain,
% 0.70/0.88 (~(op(e3, e1) = e2)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[348, 4357])).
% 0.70/0.88 tff(4359,plain,
% 0.70/0.88 (op(e2, e2) = e2),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[524, 4348, 10, 74])).
% 0.70/0.88 tff(4360,plain,
% 0.70/0.88 ((op(e2, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4359])).
% 0.70/0.88 tff(4361,plain,
% 0.70/0.88 ((op(e2, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.70/0.88 inference(transitivity,[status(thm)],[4360, 469])).
% 0.70/0.88 tff(4362,plain,
% 0.70/0.88 ((~(op(e2, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4361])).
% 0.70/0.88 tff(4363,plain,
% 0.70/0.88 (~(op(e3, e2) = e2)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[504, 4362])).
% 0.70/0.88 tff(4364,plain,
% 0.70/0.88 (op(e3, e0) = e2),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[537, 4363, 4358, 75])).
% 0.70/0.88 tff(4365,plain,
% 0.70/0.88 (op(e3, op(e3, e3)) = op(e3, e0)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4308])).
% 0.70/0.88 tff(4366,plain,
% 0.70/0.88 (op(e3, op(e3, e3)) = e2),
% 0.70/0.88 inference(transitivity,[status(thm)],[4365, 4364])).
% 0.70/0.88 tff(4367,plain,
% 0.70/0.88 (op(op(e3, op(e3, e3)), op(e3, e3)) = op(e2, e0)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4366, 4308])).
% 0.70/0.88 tff(4368,plain,
% 0.70/0.88 ((e1 = op(op(e3, op(e3, e3)), op(e3, e3))) <=> (e1 = op(e2, e0))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4367])).
% 0.70/0.88 tff(4369,plain,
% 0.70/0.88 ((e1 = op(op(e3, op(e3, e3)), op(e3, e3))) <=> (op(e2, e0) = e1)),
% 0.70/0.88 inference(transitivity,[status(thm)],[4368, 1384])).
% 0.70/0.88 tff(4370,plain,
% 0.70/0.88 ((~(e1 = op(op(e3, op(e3, e3)), op(e3, e3)))) <=> (~(op(e2, e0) = e1))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4369])).
% 0.70/0.88 tff(4371,plain,
% 0.70/0.88 (e0 = op(e3, e3)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[4308, 1390])).
% 0.70/0.88 tff(4372,plain,
% 0.70/0.88 ((e2 = op(e3, op(e3, e3))) <=> (e2 = op(e3, e0))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4365])).
% 0.70/0.88 tff(4373,plain,
% 0.70/0.88 ((e2 = op(e3, op(e3, e3))) <=> (op(e3, e0) = e2)),
% 0.70/0.88 inference(transitivity,[status(thm)],[4372, 1223])).
% 0.70/0.88 tff(4374,plain,
% 0.70/0.88 ((op(e3, e0) = e2) <=> (e2 = op(e3, op(e3, e3)))),
% 0.70/0.88 inference(symmetry,[status(thm)],[4373])).
% 0.70/0.88 tff(4375,plain,
% 0.70/0.88 (e2 = op(e3, op(e3, e3))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[4364, 4374])).
% 0.70/0.88 tff(4376,plain,
% 0.70/0.88 (~(e1 = op(op(e3, op(e3, e3)), op(e3, e3)))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1405, 4375, 4371])).
% 0.70/0.88 tff(4377,plain,
% 0.70/0.88 (~(op(e2, e0) = e1)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[4376, 4370])).
% 0.70/0.88 tff(4378,plain,
% 0.70/0.88 (op(e2, e3) = e1),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[964, 4377, 4354, 4352])).
% 0.70/0.88 tff(4379,plain,
% 0.70/0.88 (e1 = op(e2, e3)),
% 0.70/0.88 inference(symmetry,[status(thm)],[4378])).
% 0.70/0.88 tff(4380,plain,
% 0.70/0.88 (op(e3, e1) = op(e3, op(e2, e3))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4379])).
% 0.70/0.88 tff(4381,plain,
% 0.70/0.88 (op(e3, e1) = e3),
% 0.70/0.88 inference(transitivity,[status(thm)],[4380, 4350])).
% 0.70/0.88 tff(4382,plain,
% 0.70/0.88 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e3)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4381])).
% 0.70/0.88 tff(4383,plain,
% 0.70/0.88 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e3))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4382])).
% 0.70/0.88 tff(4384,plain,
% 0.70/0.88 (~(op(e2, e1) = e3)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[576, 4383])).
% 0.70/0.88 tff(4385,plain,
% 0.70/0.88 ((op(e2, e2) = e3) <=> (e2 = e3)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4359])).
% 0.70/0.88 tff(4386,plain,
% 0.70/0.88 ((e2 = e3) <=> (op(e2, e2) = e3)),
% 0.70/0.88 inference(symmetry,[status(thm)],[4385])).
% 0.70/0.88 tff(4387,plain,
% 0.70/0.88 ((~(e2 = e3)) <=> (~(op(e2, e2) = e3))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4386])).
% 0.70/0.88 tff(4388,plain,
% 0.70/0.88 (~(op(e2, e2) = e3)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[462, 4387])).
% 0.70/0.88 tff(4389,plain,
% 0.70/0.88 ((op(e2, e3) = e3) <=> (e1 = e3)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4378])).
% 0.70/0.88 tff(4390,plain,
% 0.70/0.88 ((e1 = e3) <=> (op(e2, e3) = e3)),
% 0.70/0.88 inference(symmetry,[status(thm)],[4389])).
% 0.70/0.88 tff(4391,plain,
% 0.70/0.88 ((~(e1 = e3)) <=> (~(op(e2, e3) = e3))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4390])).
% 0.70/0.88 tff(4392,plain,
% 0.70/0.88 (~(op(e2, e3) = e3)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[591, 4391])).
% 0.70/0.88 tff(4393,plain,
% 0.70/0.88 (op(e2, e0) = e3),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[1498, 4392, 4388, 4384])).
% 0.70/0.88 tff(4394,plain,
% 0.70/0.88 (op(e0, op(e2, e0)) = op(e0, e3)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4393])).
% 0.70/0.88 tff(4395,plain,
% 0.70/0.88 (op(e0, op(e2, e0)) = e0),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[967, 4347])).
% 0.70/0.88 tff(4396,plain,
% 0.70/0.88 (e0 = op(e0, op(e2, e0))),
% 0.70/0.88 inference(symmetry,[status(thm)],[4395])).
% 0.70/0.88 tff(4397,plain,
% 0.70/0.88 (e0 = e2),
% 0.70/0.88 inference(transitivity,[status(thm)],[4396, 4394, 4349])).
% 0.70/0.88 tff(4398,plain,
% 0.70/0.88 ($false),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[238, 4397])).
% 0.70/0.88 tff(4399,plain,((op(e3, e3) = e2) | (op(e2, e1) = e2) | (op(e2, e0) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.88 tff(4400,plain,
% 0.70/0.88 (op(e3, e3) = e2),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[4399, 74, 10])).
% 0.70/0.88 tff(4401,plain,
% 0.70/0.88 (e2 = op(e3, e3)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[4400, 1736])).
% 0.70/0.88 tff(4402,plain,
% 0.70/0.88 (op(e3, op(e3, e3)) = op(e3, e2)),
% 0.70/0.88 inference(monotonicity,[status(thm)],[4400])).
% 0.70/0.88 tff(4403,plain,
% 0.73/0.88 ((e1 = op(e3, op(e3, e3))) <=> (e1 = op(e3, e2))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4402])).
% 0.73/0.88 tff(4404,plain,
% 0.73/0.88 ((e1 = op(e3, op(e3, e3))) <=> (op(e3, e2) = e1)),
% 0.73/0.88 inference(transitivity,[status(thm)],[4403, 1618])).
% 0.73/0.88 tff(4405,plain,
% 0.73/0.88 ((op(e3, e2) = e1) <=> (e1 = op(e3, op(e3, e3)))),
% 0.73/0.88 inference(symmetry,[status(thm)],[4404])).
% 0.73/0.88 tff(4406,plain,
% 0.73/0.88 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e2)),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4400])).
% 0.73/0.88 tff(4407,plain,
% 0.73/0.88 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e2))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4406])).
% 0.73/0.88 tff(4408,plain,
% 0.73/0.88 (~(op(e3, e1) = e2)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[399, 4407])).
% 0.73/0.88 tff(4409,plain,
% 0.73/0.88 (op(e1, e1) = e2),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[1606, 4408, 10])).
% 0.73/0.88 tff(4410,plain,
% 0.73/0.88 ((op(e1, e1) = e1) <=> (e2 = e1)),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4409])).
% 0.73/0.88 tff(4411,plain,
% 0.73/0.88 ((op(e1, e1) = e1) <=> (e1 = e2)),
% 0.73/0.88 inference(transitivity,[status(thm)],[4410, 317])).
% 0.73/0.88 tff(4412,plain,
% 0.73/0.88 ((e1 = e2) <=> (op(e1, e1) = e1)),
% 0.73/0.88 inference(symmetry,[status(thm)],[4411])).
% 0.73/0.88 tff(4413,plain,
% 0.73/0.88 ((~(e1 = e2)) <=> (~(op(e1, e1) = e1))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4412])).
% 0.73/0.88 tff(4414,plain,
% 0.73/0.88 (~(op(e1, e1) = e1)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[324, 4413])).
% 0.73/0.88 tff(4415,plain,
% 0.73/0.88 ((op(e1, e1) = e3) <=> (e2 = e3)),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4409])).
% 0.73/0.88 tff(4416,plain,
% 0.73/0.88 ((e2 = e3) <=> (op(e1, e1) = e3)),
% 0.73/0.88 inference(symmetry,[status(thm)],[4415])).
% 0.73/0.88 tff(4417,plain,
% 0.73/0.88 ((~(e2 = e3)) <=> (~(op(e1, e1) = e3))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4416])).
% 0.73/0.88 tff(4418,plain,
% 0.73/0.88 (~(op(e1, e1) = e3)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[462, 4417])).
% 0.73/0.88 tff(4419,plain,
% 0.73/0.88 ((op(e3, e3) = e3) <=> (e2 = e3)),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4400])).
% 0.73/0.88 tff(4420,plain,
% 0.73/0.88 ((e2 = e3) <=> (op(e3, e3) = e3)),
% 0.73/0.88 inference(symmetry,[status(thm)],[4419])).
% 0.73/0.88 tff(4421,plain,
% 0.73/0.88 ((~(e2 = e3)) <=> (~(op(e3, e3) = e3))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4420])).
% 0.73/0.88 tff(4422,plain,
% 0.73/0.88 (~(op(e3, e3) = e3)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[462, 4421])).
% 0.73/0.88 tff(4423,plain,
% 0.73/0.88 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[392, 4400])).
% 0.73/0.88 tff(4424,plain,
% 0.73/0.88 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[4345, 4409, 10])).
% 0.73/0.88 tff(4425,plain,
% 0.73/0.88 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[681, 4424, 1798, 4423])).
% 0.73/0.88 tff(4426,plain,
% 0.73/0.88 (op(e2, op(e2, e2)) = e2),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[473, 4425])).
% 0.73/0.88 tff(4427,plain,
% 0.73/0.88 (~(op(e2, e2) = e0)),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[481, 4426, 74])).
% 0.73/0.88 tff(4428,plain,
% 0.73/0.88 ((op(e0, e3) = op(e3, e3)) <=> (op(e0, e3) = e2)),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4400])).
% 0.73/0.88 tff(4429,plain,
% 0.73/0.88 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e0, e3) = e2))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4428])).
% 0.73/0.88 tff(4430,plain,
% 0.73/0.88 (~(op(e0, e3) = e2)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[725, 4429])).
% 0.73/0.88 tff(4431,plain,
% 0.73/0.88 ((op(e2, e3) = op(e3, e3)) <=> (op(e2, e3) = e2)),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4400])).
% 0.73/0.88 tff(4432,plain,
% 0.73/0.88 ((~(op(e2, e3) = op(e3, e3))) <=> (~(op(e2, e3) = e2))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4431])).
% 0.73/0.88 tff(4433,plain,
% 0.73/0.88 (~(op(e2, e3) = e2)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[387, 4432])).
% 0.73/0.88 tff(4434,plain,
% 0.73/0.88 (op(e2, e2) = e2),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[524, 4433, 10, 74])).
% 0.73/0.88 tff(4435,plain,
% 0.73/0.88 ((op(e0, e2) = op(e2, e2)) <=> (op(e0, e2) = e2)),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4434])).
% 0.73/0.88 tff(4436,plain,
% 0.73/0.88 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e0, e2) = e2))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4435])).
% 0.73/0.88 tff(4437,plain,
% 0.73/0.88 (~(op(e0, e2) = e2)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[816, 4436])).
% 0.73/0.88 tff(4438,plain,
% 0.73/0.88 (op(e0, e0) = e2),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[1792, 4437, 4430])).
% 0.73/0.88 tff(4439,plain,
% 0.73/0.88 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e2)),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4400])).
% 0.73/0.88 tff(4440,plain,
% 0.73/0.88 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e2))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4439])).
% 0.73/0.88 tff(4441,plain,
% 0.73/0.88 (~(op(e3, e0) = e2)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[257, 4440])).
% 0.73/0.88 tff(4442,plain,
% 0.73/0.88 ((op(e2, e2) = e3) <=> (e2 = e3)),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4434])).
% 0.73/0.88 tff(4443,plain,
% 0.73/0.88 ((e2 = e3) <=> (op(e2, e2) = e3)),
% 0.73/0.88 inference(symmetry,[status(thm)],[4442])).
% 0.73/0.88 tff(4444,plain,
% 0.73/0.88 ((~(e2 = e3)) <=> (~(op(e2, e2) = e3))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4443])).
% 0.73/0.88 tff(4445,plain,
% 0.73/0.88 (~(op(e2, e2) = e3)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[462, 4444])).
% 0.73/0.88 tff(4446,plain,
% 0.73/0.88 (op(e1, op(e2, e1)) = e1),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[546, 4425])).
% 0.73/0.88 tff(4447,plain,
% 0.73/0.88 (~(op(e2, e2) = e1)),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[488, 4426, 10])).
% 0.73/0.88 tff(4448,plain,
% 0.73/0.88 (~(op(e2, e1) = e1)),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[4170, 4446, 4409])).
% 0.73/0.88 tff(4449,plain,
% 0.73/0.88 (op(e3, op(e2, e3)) = e3),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[471, 4425])).
% 0.73/0.88 tff(4450,plain,
% 0.73/0.88 (op(e3, e1) = e1),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[450, 433, 1070, 1069])).
% 0.73/0.88 tff(4451,plain,
% 0.73/0.88 ((op(e3, e1) = e0) <=> (e1 = e0)),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4450])).
% 0.73/0.88 tff(4452,plain,
% 0.73/0.88 ((op(e3, e1) = e0) <=> (e0 = e1)),
% 0.73/0.88 inference(transitivity,[status(thm)],[4451, 635])).
% 0.73/0.88 tff(4453,plain,
% 0.73/0.88 ((e0 = e1) <=> (op(e3, e1) = e0)),
% 0.73/0.88 inference(symmetry,[status(thm)],[4452])).
% 0.73/0.88 tff(4454,plain,
% 0.73/0.88 ((~(e0 = e1)) <=> (~(op(e3, e1) = e0))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4453])).
% 0.73/0.88 tff(4455,plain,
% 0.73/0.88 (~(op(e3, e1) = e0)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[625, 4454])).
% 0.73/0.88 tff(4456,plain,
% 0.73/0.88 ((op(e3, e1) = e3) <=> (e1 = e3)),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4450])).
% 0.73/0.88 tff(4457,plain,
% 0.73/0.88 ((e1 = e3) <=> (op(e3, e1) = e3)),
% 0.73/0.88 inference(symmetry,[status(thm)],[4456])).
% 0.73/0.88 tff(4458,plain,
% 0.73/0.88 ((~(e1 = e3)) <=> (~(op(e3, e1) = e3))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4457])).
% 0.73/0.88 tff(4459,plain,
% 0.73/0.88 (~(op(e3, e1) = e3)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[591, 4458])).
% 0.73/0.88 tff(4460,assumption,(~(op(e2, e2) = e3)), introduced(assumption)).
% 0.73/0.88 tff(4461,plain,
% 0.73/0.88 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e1)),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4450])).
% 0.73/0.88 tff(4462,plain,
% 0.73/0.88 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e1))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4461])).
% 0.73/0.88 tff(4463,plain,
% 0.73/0.88 (~(op(e3, e0) = e1)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[1333, 4462])).
% 0.73/0.88 tff(4464,plain,
% 0.73/0.88 ((op(e0, e0) = e1) <=> (e2 = e1)),
% 0.73/0.88 inference(monotonicity,[status(thm)],[2954])).
% 0.73/0.88 tff(4465,plain,
% 0.73/0.88 ((op(e0, e0) = e1) <=> (e1 = e2)),
% 0.73/0.88 inference(transitivity,[status(thm)],[4464, 317])).
% 0.73/0.88 tff(4466,plain,
% 0.73/0.88 ((e1 = e2) <=> (op(e0, e0) = e1)),
% 0.73/0.88 inference(symmetry,[status(thm)],[4465])).
% 0.73/0.88 tff(4467,plain,
% 0.73/0.88 ((~(e1 = e2)) <=> (~(op(e0, e0) = e1))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4466])).
% 0.73/0.88 tff(4468,plain,
% 0.73/0.88 (~(op(e0, e0) = e1)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[324, 4467])).
% 0.73/0.88 tff(4469,plain,
% 0.73/0.88 (op(e2, e1) = e3),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[570, 544, 2683, 2808])).
% 0.73/0.88 tff(4470,plain,
% 0.73/0.88 (op(e1, e3) = e1),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[937, 4469, 551])).
% 0.73/0.88 tff(4471,plain,
% 0.73/0.88 ((op(e0, e3) = op(e1, e3)) <=> (op(e0, e3) = e1)),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4470])).
% 0.73/0.88 tff(4472,plain,
% 0.73/0.88 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e0, e3) = e1))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4471])).
% 0.73/0.88 tff(4473,plain,
% 0.73/0.88 (~(op(e0, e3) = e1)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[1755, 4472])).
% 0.73/0.88 tff(4474,plain,
% 0.73/0.88 (op(e0, e2) = e1),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[718, 4473, 4468, 433])).
% 0.73/0.88 tff(4475,plain,
% 0.73/0.88 (op(e0, op(e0, e0)) = op(e0, e2)),
% 0.73/0.88 inference(monotonicity,[status(thm)],[2954])).
% 0.73/0.88 tff(4476,plain,
% 0.73/0.88 (op(e0, op(e0, e0)) = e1),
% 0.73/0.88 inference(transitivity,[status(thm)],[4475, 4474])).
% 0.73/0.88 tff(4477,plain,
% 0.73/0.88 (op(op(e0, op(e0, e0)), op(e0, e0)) = op(e1, e2)),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4476, 2954])).
% 0.73/0.88 tff(4478,plain,
% 0.73/0.88 ((e3 = op(op(e0, op(e0, e0)), op(e0, e0))) <=> (e3 = op(e1, e2))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4477])).
% 0.73/0.88 tff(4479,plain,
% 0.73/0.88 ((e3 = op(op(e0, op(e0, e0)), op(e0, e0))) <=> (op(e1, e2) = e3)),
% 0.73/0.88 inference(transitivity,[status(thm)],[4478, 2877])).
% 0.73/0.88 tff(4480,plain,
% 0.73/0.88 ((~(e3 = op(op(e0, op(e0, e0)), op(e0, e0)))) <=> (~(op(e1, e2) = e3))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4479])).
% 0.73/0.88 tff(4481,plain,
% 0.73/0.88 (e2 = op(e0, e0)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[2954, 3695])).
% 0.73/0.88 tff(4482,plain,
% 0.73/0.88 ((e1 = op(e0, op(e0, e0))) <=> (e1 = op(e0, e2))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4475])).
% 0.73/0.88 tff(4483,plain,
% 0.73/0.88 ((e1 = op(e0, op(e0, e0))) <=> (op(e0, e2) = e1)),
% 0.73/0.88 inference(transitivity,[status(thm)],[4482, 4060])).
% 0.73/0.88 tff(4484,plain,
% 0.73/0.88 ((op(e0, e2) = e1) <=> (e1 = op(e0, op(e0, e0)))),
% 0.73/0.88 inference(symmetry,[status(thm)],[4483])).
% 0.73/0.88 tff(4485,plain,
% 0.73/0.88 (e1 = op(e0, op(e0, e0))),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[4474, 4484])).
% 0.73/0.88 tff(4486,plain,
% 0.73/0.88 (~(e3 = op(op(e0, op(e0, e0)), op(e0, e0)))),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[3708, 4485, 4481])).
% 0.73/0.88 tff(4487,plain,
% 0.73/0.88 (~(op(e1, e2) = e3)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[4486, 4480])).
% 0.73/0.88 tff(4488,plain,
% 0.73/0.88 ((e3 = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.73/0.88 inference(commutativity,[status(thm)],[])).
% 0.73/0.88 tff(4489,plain,
% 0.73/0.88 ((op(e0, e1) = op(e2, e1)) <=> (e0 = op(e2, e1))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4015])).
% 0.73/0.88 tff(4490,plain,
% 0.73/0.88 ((op(e0, e1) = op(e2, e1)) <=> (op(e2, e1) = e0)),
% 0.73/0.88 inference(transitivity,[status(thm)],[4489, 3142])).
% 0.73/0.88 tff(4491,plain,
% 0.73/0.88 ((~(op(e0, e1) = op(e2, e1))) <=> (~(op(e2, e1) = e0))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4490])).
% 0.73/0.88 tff(4492,plain,
% 0.73/0.88 (~(op(e2, e1) = e0)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[61, 4491])).
% 0.73/0.88 tff(4493,plain,
% 0.73/0.88 ((op(e1, e0) = op(e1, e3)) <=> (op(e1, e0) = e1)),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4470])).
% 0.73/0.88 tff(4494,plain,
% 0.73/0.88 ((~(op(e1, e0) = op(e1, e3))) <=> (~(op(e1, e0) = e1))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4493])).
% 0.73/0.88 tff(4495,plain,
% 0.73/0.88 (~(op(e1, e0) = e1)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[224, 4494])).
% 0.73/0.88 tff(4496,plain,
% 0.73/0.88 (op(e3, e0) = e3),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[3670, 4495, 1699, 1414, 4492, 496, 4468, 491])).
% 0.73/0.88 tff(4497,plain,
% 0.73/0.88 ((op(e3, e0) = op(e3, e2)) <=> (e3 = op(e3, e2))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4496])).
% 0.73/0.88 tff(4498,plain,
% 0.73/0.88 ((op(e3, e0) = op(e3, e2)) <=> (op(e3, e2) = e3)),
% 0.73/0.88 inference(transitivity,[status(thm)],[4497, 4488])).
% 0.73/0.88 tff(4499,plain,
% 0.73/0.88 ((~(op(e3, e0) = op(e3, e2))) <=> (~(op(e3, e2) = e3))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4498])).
% 0.73/0.88 tff(4500,plain,
% 0.73/0.88 (~(op(e3, e2) = e3)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[3176, 4499])).
% 0.73/0.88 tff(4501,plain,
% 0.73/0.88 ((op(e2, e1) = op(e2, e3)) <=> (e3 = op(e2, e3))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4469])).
% 0.73/0.88 tff(4502,plain,
% 0.73/0.88 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e3) = e3)),
% 0.73/0.88 inference(transitivity,[status(thm)],[4501, 2290])).
% 0.73/0.88 tff(4503,plain,
% 0.73/0.88 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e3) = e3))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4502])).
% 0.73/0.88 tff(4504,plain,
% 0.73/0.88 (~(op(e2, e3) = e3)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[1005, 4503])).
% 0.73/0.88 tff(4505,plain,
% 0.73/0.88 ((op(e1, e3) = e3) <=> (e1 = e3)),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4470])).
% 0.73/0.88 tff(4506,plain,
% 0.73/0.88 ((e1 = e3) <=> (op(e1, e3) = e3)),
% 0.73/0.88 inference(symmetry,[status(thm)],[4505])).
% 0.73/0.88 tff(4507,plain,
% 0.73/0.88 ((~(e1 = e3)) <=> (~(op(e1, e3) = e3))),
% 0.73/0.88 inference(monotonicity,[status(thm)],[4506])).
% 0.73/0.88 tff(4508,plain,
% 0.73/0.88 (~(op(e1, e3) = e3)),
% 0.73/0.88 inference(modus_ponens,[status(thm)],[591, 4507])).
% 0.73/0.88 tff(4509,plain,
% 0.73/0.88 (op(e0, e3) = e3),
% 0.73/0.88 inference(unit_resolution,[status(thm)],[2311, 4508, 797, 4504])).
% 0.73/0.88 tff(4510,plain,
% 0.73/0.88 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e3)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4509])).
% 0.73/0.89 tff(4511,plain,
% 0.73/0.89 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e3))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4510])).
% 0.73/0.89 tff(4512,plain,
% 0.73/0.89 (~(op(e0, e2) = e3)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[215, 4511])).
% 0.73/0.89 tff(4513,plain,
% 0.73/0.89 (op(e1, e2) = e3),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[3747, 4512, 4460, 4500])).
% 0.73/0.89 tff(4514,plain,
% 0.73/0.89 ($false),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[4513, 4487])).
% 0.73/0.89 tff(4515,plain,((op(e0, e1) = e3) | (~(op(e0, e0) = e2)) | (op(e2, e2) = e3) | (op(e3, e0) = e2) | (op(e3, e0) = e1) | (~(op(e3, op(e2, e3)) = e3)) | (op(e2, e2) = e0) | (op(e0, e1) = e1) | (op(e3, e3) = e3) | (~(op(e1, op(e2, e1)) = e1)) | (op(e3, e1) = e3) | (op(e1, e1) = e3)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.89 tff(4516,plain,
% 0.73/0.89 (op(e0, e1) = e3),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[4515, 4463, 4460, 1699, 2954, 496, 491, 433, 797, 551, 4459, 2808])).
% 0.73/0.89 tff(4517,plain,
% 0.73/0.89 (op(e2, e1) = e0),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[3977, 4516, 10, 551, 4455])).
% 0.73/0.89 tff(4518,plain,
% 0.73/0.89 (op(e1, e0) = e1),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[642, 4517, 551])).
% 0.73/0.89 tff(4519,plain,
% 0.73/0.89 ((op(e1, e0) = op(e2, e0)) <=> (e1 = op(e2, e0))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4518])).
% 0.73/0.89 tff(4520,plain,
% 0.73/0.89 ((op(e1, e0) = op(e2, e0)) <=> (op(e2, e0) = e1)),
% 0.73/0.89 inference(transitivity,[status(thm)],[4519, 1384])).
% 0.73/0.89 tff(4521,plain,
% 0.73/0.89 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e2, e0) = e1))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4520])).
% 0.73/0.89 tff(4522,plain,
% 0.73/0.89 (~(op(e2, e0) = e1)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1206, 4521])).
% 0.73/0.89 tff(4523,plain,
% 0.73/0.89 (op(e2, e3) = e1),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[964, 4522, 1069, 490])).
% 0.73/0.89 tff(4524,plain,
% 0.73/0.89 (op(e3, op(e2, e3)) = op(e3, e1)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4523])).
% 0.73/0.89 tff(4525,plain,
% 0.73/0.89 (op(e3, e1) = op(e3, op(e2, e3))),
% 0.73/0.89 inference(symmetry,[status(thm)],[4524])).
% 0.73/0.89 tff(4526,plain,
% 0.73/0.89 (e1 = op(e3, e1)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4450])).
% 0.73/0.89 tff(4527,plain,
% 0.73/0.89 (e1 = e3),
% 0.73/0.89 inference(transitivity,[status(thm)],[4526, 4525, 496])).
% 0.73/0.89 tff(4528,plain,
% 0.73/0.89 ($false),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[591, 4527])).
% 0.73/0.89 tff(4529,plain,((op(e0, e1) = e1) | (~(op(e3, op(e2, e3)) = e3)) | (op(e2, e1) = e1) | (op(e2, e2) = e1) | (~(op(e1, op(e2, e1)) = e1)) | (op(e2, e1) = e2) | (op(e2, e2) = e3) | (op(e3, e0) = e2) | (~(op(e0, e0) = e2)) | (op(e2, e2) = e0) | (op(e3, e3) = e3) | (op(e1, e1) = e3) | (op(e1, e1) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.89 tff(4530,plain,
% 0.73/0.89 (op(e0, e1) = e1),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[4529, 4449, 4448, 4447, 4446, 10, 4445, 4441, 4438, 4427, 4422, 4418, 4414])).
% 0.73/0.89 tff(4531,plain,
% 0.73/0.89 ((op(e0, e1) = op(e3, e1)) <=> (e1 = op(e3, e1))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4530])).
% 0.73/0.89 tff(4532,plain,
% 0.73/0.89 ((op(e0, e1) = op(e3, e1)) <=> (op(e3, e1) = e1)),
% 0.73/0.89 inference(transitivity,[status(thm)],[4531, 1640])).
% 0.73/0.89 tff(4533,plain,
% 0.73/0.89 ((~(op(e0, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e1))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4532])).
% 0.73/0.89 tff(4534,plain,
% 0.73/0.89 (~(op(e3, e1) = e1)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[332, 4533])).
% 0.73/0.89 tff(4535,plain,
% 0.73/0.89 (e2 = op(e3, e3)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4400])).
% 0.73/0.89 tff(4536,plain,
% 0.73/0.89 ((e1 = e2) <=> (e1 = op(e3, e3))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4535])).
% 0.73/0.89 tff(4537,plain,
% 0.73/0.89 ((e1 = e2) <=> (op(e3, e3) = e1)),
% 0.73/0.89 inference(transitivity,[status(thm)],[4536, 76])).
% 0.73/0.89 tff(4538,plain,
% 0.73/0.89 ((~(e1 = e2)) <=> (~(op(e3, e3) = e1))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4537])).
% 0.73/0.89 tff(4539,plain,
% 0.73/0.89 (~(op(e3, e3) = e1)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[324, 4538])).
% 0.73/0.89 tff(4540,plain,
% 0.73/0.89 ((op(e1, e1) = e0) <=> (e2 = e0)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4409])).
% 0.73/0.89 tff(4541,plain,
% 0.73/0.89 ((op(e1, e1) = e0) <=> (e0 = e2)),
% 0.73/0.89 inference(transitivity,[status(thm)],[4540, 217])).
% 0.73/0.89 tff(4542,plain,
% 0.73/0.89 ((e0 = e2) <=> (op(e1, e1) = e0)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4541])).
% 0.73/0.89 tff(4543,plain,
% 0.73/0.89 ((~(e0 = e2)) <=> (~(op(e1, e1) = e0))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4542])).
% 0.73/0.89 tff(4544,plain,
% 0.73/0.89 (~(op(e1, e1) = e0)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[238, 4543])).
% 0.73/0.89 tff(4545,plain,
% 0.73/0.89 ((op(e0, e1) = e0) <=> (e1 = e0)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4530])).
% 0.73/0.89 tff(4546,plain,
% 0.73/0.89 ((op(e0, e1) = e0) <=> (e0 = e1)),
% 0.73/0.89 inference(transitivity,[status(thm)],[4545, 635])).
% 0.73/0.89 tff(4547,plain,
% 0.73/0.89 ((e0 = e1) <=> (op(e0, e1) = e0)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4546])).
% 0.73/0.89 tff(4548,plain,
% 0.73/0.89 ((~(e0 = e1)) <=> (~(op(e0, e1) = e0))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4547])).
% 0.73/0.89 tff(4549,plain,
% 0.73/0.89 (~(op(e0, e1) = e0)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[625, 4548])).
% 0.73/0.89 tff(4550,plain,
% 0.73/0.89 (op(e0, op(e2, e0)) = e0),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[967, 4425])).
% 0.73/0.89 tff(4551,assumption,(op(e2, e0) = e1), introduced(assumption)).
% 0.73/0.89 tff(4552,plain,
% 0.73/0.89 (e1 = op(e2, e0)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4551])).
% 0.73/0.89 tff(4553,plain,
% 0.73/0.89 (op(e0, e1) = op(e0, op(e2, e0))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4552])).
% 0.73/0.89 tff(4554,plain,
% 0.73/0.89 (op(e0, op(e2, e0)) = op(e0, e1)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4553])).
% 0.73/0.89 tff(4555,plain,
% 0.73/0.89 (e0 = e1),
% 0.73/0.89 inference(transitivity,[status(thm)],[1897, 4554, 1132])).
% 0.73/0.89 tff(4556,plain,
% 0.73/0.89 ($false),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[625, 4555])).
% 0.73/0.89 tff(4557,plain,((~(op(e2, e0) = e1)) | (~(op(e0, e1) = e1)) | (~(op(e0, op(e2, e0)) = e0))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.89 tff(4558,plain,
% 0.73/0.89 (~(op(e2, e0) = e1)),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[4557, 4530, 4550])).
% 0.73/0.89 tff(4559,plain,
% 0.73/0.89 (op(e2, e3) = e1),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[964, 4558, 4448, 4447])).
% 0.73/0.89 tff(4560,plain,
% 0.73/0.89 (e1 = op(e2, e3)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4559])).
% 0.73/0.89 tff(4561,plain,
% 0.73/0.89 (op(e3, e1) = op(e3, op(e2, e3))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4560])).
% 0.73/0.89 tff(4562,plain,
% 0.73/0.89 (op(e3, e1) = e3),
% 0.73/0.89 inference(transitivity,[status(thm)],[4561, 4449])).
% 0.73/0.89 tff(4563,plain,
% 0.73/0.89 ((op(e3, e1) = e0) <=> (e3 = e0)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4562])).
% 0.73/0.89 tff(4564,plain,
% 0.73/0.89 ((op(e3, e1) = e0) <=> (e0 = e3)),
% 0.73/0.89 inference(transitivity,[status(thm)],[4563, 279])).
% 0.73/0.89 tff(4565,plain,
% 0.73/0.89 ((e0 = e3) <=> (op(e3, e1) = e0)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4564])).
% 0.73/0.89 tff(4566,plain,
% 0.73/0.89 ((~(e0 = e3)) <=> (~(op(e3, e1) = e0))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4565])).
% 0.73/0.89 tff(4567,plain,
% 0.73/0.89 (~(op(e3, e1) = e0)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[286, 4566])).
% 0.73/0.89 tff(4568,plain,
% 0.73/0.89 (op(e2, e1) = e0),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[619, 4567, 4549, 4544])).
% 0.73/0.89 tff(4569,plain,
% 0.73/0.89 (op(e1, e0) = e1),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[642, 4568, 4446])).
% 0.73/0.89 tff(4570,plain,
% 0.73/0.89 ((op(e1, e0) = op(e3, e0)) <=> (e1 = op(e3, e0))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4569])).
% 0.73/0.89 tff(4571,plain,
% 0.73/0.89 ((op(e1, e0) = op(e3, e0)) <=> (op(e3, e0) = e1)),
% 0.73/0.89 inference(transitivity,[status(thm)],[4570, 373])).
% 0.73/0.89 tff(4572,plain,
% 0.73/0.89 ((~(op(e1, e0) = op(e3, e0))) <=> (~(op(e3, e0) = e1))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4571])).
% 0.73/0.89 tff(4573,plain,
% 0.73/0.89 (~(op(e3, e0) = e1)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[420, 4572])).
% 0.73/0.89 tff(4574,plain,
% 0.73/0.89 (op(e3, e2) = e1),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[429, 4573, 4539, 4534])).
% 0.73/0.89 tff(4575,plain,
% 0.73/0.89 (e1 = op(e3, op(e3, e3))),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[4574, 4405])).
% 0.73/0.89 tff(4576,plain,
% 0.73/0.89 (op(e3, op(e3, e3)) = e1),
% 0.73/0.89 inference(transitivity,[status(thm)],[4402, 4574])).
% 0.73/0.89 tff(4577,plain,
% 0.73/0.89 (op(op(e3, op(e3, e3)), op(e3, e3)) = op(e1, e2)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4576, 4400])).
% 0.73/0.89 tff(4578,plain,
% 0.73/0.89 (op(e1, e2) = op(op(e3, op(e3, e3)), op(e3, e3))),
% 0.73/0.89 inference(symmetry,[status(thm)],[4577])).
% 0.73/0.89 tff(4579,plain,
% 0.73/0.89 ((op(e1, e0) = e0) <=> (e1 = e0)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4569])).
% 0.73/0.89 tff(4580,plain,
% 0.73/0.89 ((op(e1, e0) = e0) <=> (e0 = e1)),
% 0.73/0.89 inference(transitivity,[status(thm)],[4579, 635])).
% 0.73/0.89 tff(4581,plain,
% 0.73/0.89 ((e0 = e1) <=> (op(e1, e0) = e0)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4580])).
% 0.73/0.89 tff(4582,plain,
% 0.73/0.89 ((~(e0 = e1)) <=> (~(op(e1, e0) = e0))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4581])).
% 0.73/0.89 tff(4583,plain,
% 0.73/0.89 (~(op(e1, e0) = e0)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[625, 4582])).
% 0.73/0.89 tff(4584,plain,
% 0.73/0.89 ((op(e2, e3) = e3) <=> (e1 = e3)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4559])).
% 0.73/0.89 tff(4585,plain,
% 0.73/0.89 ((e1 = e3) <=> (op(e2, e3) = e3)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4584])).
% 0.73/0.89 tff(4586,plain,
% 0.73/0.89 ((~(e1 = e3)) <=> (~(op(e2, e3) = e3))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4585])).
% 0.73/0.89 tff(4587,plain,
% 0.73/0.89 (~(op(e2, e3) = e3)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[591, 4586])).
% 0.73/0.89 tff(4588,plain,
% 0.73/0.89 ((op(e2, e1) = op(e3, e1)) <=> (op(e2, e1) = e3)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4562])).
% 0.73/0.89 tff(4589,plain,
% 0.73/0.89 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e2, e1) = e3))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4588])).
% 0.73/0.89 tff(4590,plain,
% 0.73/0.89 (~(op(e2, e1) = e3)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[576, 4589])).
% 0.73/0.89 tff(4591,plain,
% 0.73/0.89 (op(e2, e0) = e3),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[1498, 4590, 4445, 4587])).
% 0.73/0.89 tff(4592,plain,
% 0.73/0.89 (e3 = op(e2, e0)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4591])).
% 0.73/0.89 tff(4593,plain,
% 0.73/0.89 (op(e0, e3) = op(e0, op(e2, e0))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4592])).
% 0.73/0.89 tff(4594,plain,
% 0.73/0.89 (op(e0, e3) = e0),
% 0.73/0.89 inference(transitivity,[status(thm)],[4593, 4550])).
% 0.73/0.89 tff(4595,plain,
% 0.73/0.89 ((op(e0, e3) = op(e1, e3)) <=> (e0 = op(e1, e3))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4594])).
% 0.73/0.89 tff(4596,plain,
% 0.73/0.89 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e0)),
% 0.73/0.89 inference(transitivity,[status(thm)],[4595, 2941])).
% 0.73/0.89 tff(4597,plain,
% 0.73/0.89 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e0))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4596])).
% 0.73/0.89 tff(4598,plain,
% 0.73/0.89 (~(op(e1, e3) = e0)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1755, 4597])).
% 0.73/0.89 tff(4599,plain,
% 0.73/0.89 (op(e1, e2) = e0),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[657, 4598, 4583, 4544])).
% 0.73/0.89 tff(4600,plain,
% 0.73/0.89 (e0 = op(e1, e2)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4599])).
% 0.73/0.89 tff(4601,plain,
% 0.73/0.89 (e0 = op(op(e3, op(e3, e3)), op(e3, e3))),
% 0.73/0.89 inference(transitivity,[status(thm)],[4600, 4578])).
% 0.73/0.89 tff(4602,plain,
% 0.73/0.89 ((~(~((~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(op(e3, op(e3, e3)), op(e3, e3))))))) <=> ((~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(op(e3, op(e3, e3)), op(e3, e3)))))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(4603,plain,
% 0.73/0.89 (((e2 = op(e3, e3)) & (e1 = op(e3, op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3)))) <=> (~((~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(op(e3, op(e3, e3)), op(e3, e3))))))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(4604,plain,
% 0.73/0.89 ((~((e2 = op(e3, e3)) & (e1 = op(e3, op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3))))) <=> (~(~((~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(op(e3, op(e3, e3)), op(e3, e3)))))))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4603])).
% 0.73/0.89 tff(4605,plain,
% 0.73/0.89 ((~((e2 = op(e3, e3)) & (e1 = op(e3, op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3))))) <=> ((~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(op(e3, op(e3, e3)), op(e3, e3)))))),
% 0.73/0.89 inference(transitivity,[status(thm)],[4604, 4602])).
% 0.73/0.89 tff(4606,plain,
% 0.73/0.89 ((~((e2 = op(e3, e3)) & (e1 = op(e3, op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3))))) <=> (~((e2 = op(e3, e3)) & (e1 = op(e3, op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3)))))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(4607,plain,
% 0.73/0.89 ((~(((e2 = op(e3, e3)) & (e1 = op(e3, op(e3, e3)))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3))))) <=> (~((e2 = op(e3, e3)) & (e1 = op(e3, op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3)))))),
% 0.73/0.89 inference(rewrite,[status(thm)],[])).
% 0.73/0.89 tff(4608,axiom,(~(((e2 = op(e3, e3)) & (e1 = op(e3, op(e3, e3)))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax21')).
% 0.73/0.89 tff(4609,plain,
% 0.73/0.89 (~((e2 = op(e3, e3)) & (e1 = op(e3, op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3))))),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[4608, 4607])).
% 0.73/0.89 tff(4610,plain,
% 0.73/0.89 (~((e2 = op(e3, e3)) & (e1 = op(e3, op(e3, e3))) & (e0 = op(op(e3, op(e3, e3)), op(e3, e3))))),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[4609, 4606])).
% 0.73/0.89 tff(4611,plain,
% 0.73/0.89 ((~(e2 = op(e3, e3))) | (~(e1 = op(e3, op(e3, e3)))) | (~(e0 = op(op(e3, op(e3, e3)), op(e3, e3))))),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[4610, 4605])).
% 0.73/0.89 tff(4612,plain,
% 0.73/0.89 ($false),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[4611, 4601, 4575, 4401])).
% 0.73/0.89 tff(4613,plain,((op(e2, e0) = e2) | (op(e2, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.89 tff(4614,plain,
% 0.73/0.89 (op(e2, e0) = e2),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[4613, 10])).
% 0.73/0.89 tff(4615,plain,
% 0.73/0.89 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e2)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4614])).
% 0.73/0.89 tff(4616,plain,
% 0.73/0.89 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e2))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4615])).
% 0.73/0.89 tff(4617,plain,
% 0.73/0.89 (~(op(e0, e0) = e2)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1827, 4616])).
% 0.73/0.89 tff(4618,plain,
% 0.73/0.89 (op(e3, e0) = op(e1, e2)),
% 0.73/0.89 inference(transitivity,[status(thm)],[1633, 1609, 1608])).
% 0.73/0.89 tff(4619,plain,
% 0.73/0.89 ((op(e3, e0) = e3) <=> (op(e1, e2) = e3)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4618])).
% 0.73/0.89 tff(4620,plain,
% 0.73/0.89 ((op(e1, e2) = e3) <=> (op(e3, e0) = e3)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4619])).
% 0.73/0.89 tff(4621,plain,
% 0.73/0.89 ((~(op(e1, e2) = e3)) <=> (~(op(e3, e0) = e3))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4620])).
% 0.73/0.89 tff(4622,plain,
% 0.73/0.89 ((e1 = e3) <=> (op(e1, e2) = e3)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[1610])).
% 0.73/0.89 tff(4623,plain,
% 0.73/0.89 ((~(e1 = e3)) <=> (~(op(e1, e2) = e3))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4622])).
% 0.73/0.89 tff(4624,plain,
% 0.73/0.89 (~(op(e1, e2) = e3)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[591, 4623])).
% 0.73/0.89 tff(4625,plain,
% 0.73/0.89 (~(op(e3, e0) = e3)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[4624, 4621])).
% 0.73/0.89 tff(4626,plain,
% 0.73/0.89 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e3)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[1687])).
% 0.73/0.89 tff(4627,plain,
% 0.73/0.89 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e3))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4626])).
% 0.73/0.89 tff(4628,plain,
% 0.73/0.89 (~(op(e1, e3) = e3)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[368, 4627])).
% 0.73/0.89 tff(4629,plain,
% 0.73/0.89 ((op(e0, e0) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e3, e2) = e3) | (op(e3, e0) = e3) | (op(e1, e1) = e1) | (op(e1, e3) = e3) | (op(e3, e3) = e2) | (op(e1, op(e0, e1)) = e1) | (~(op(e0, e3) = e1)) | (op(e0, e0) = e0) | (op(e0, e0) = e1)),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[2585, 1605])).
% 0.73/0.89 tff(4630,plain,
% 0.73/0.89 ($false),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[4629, 4628, 4625, 1798, 4617, 1735, 1686, 1695, 1690, 1682, 1639, 1617])).
% 0.73/0.89 tff(4631,plain,(((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (op(e1, e1) = e2) | (op(e2, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.89 tff(4632,plain,
% 0.73/0.89 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[4631, 12, 10])).
% 0.73/0.89 tff(4633,plain,
% 0.73/0.89 ((op(e2, e0) = e1) <=> (e2 = e1)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4614])).
% 0.73/0.89 tff(4634,plain,
% 0.73/0.89 ((op(e2, e0) = e1) <=> (e1 = e2)),
% 0.73/0.89 inference(transitivity,[status(thm)],[4633, 317])).
% 0.73/0.89 tff(4635,plain,
% 0.73/0.89 ((e1 = e2) <=> (op(e2, e0) = e1)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4634])).
% 0.73/0.89 tff(4636,plain,
% 0.73/0.89 ((~(e1 = e2)) <=> (~(op(e2, e0) = e1))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4635])).
% 0.73/0.89 tff(4637,plain,
% 0.73/0.89 (~(op(e2, e0) = e1)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[324, 4636])).
% 0.73/0.89 tff(4638,plain,
% 0.73/0.89 (op(e2, e1) = e1),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[2417, 470, 4637, 1146, 10])).
% 0.73/0.89 tff(4639,plain,
% 0.73/0.89 (e1 = op(e2, e1)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4638])).
% 0.73/0.89 tff(4640,plain,
% 0.73/0.89 (op(e1, e1) = op(e1, op(e2, e1))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4639])).
% 0.73/0.89 tff(4641,plain,
% 0.73/0.89 (op(e1, e1) = e1),
% 0.73/0.89 inference(transitivity,[status(thm)],[4640, 547])).
% 0.73/0.89 tff(4642,plain,
% 0.73/0.89 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e1)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4638])).
% 0.73/0.89 tff(4643,plain,
% 0.73/0.89 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e1))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4642])).
% 0.73/0.89 tff(4644,plain,
% 0.73/0.89 (~(op(e1, e1) = e1)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[633, 4643])).
% 0.73/0.89 tff(4645,plain,
% 0.73/0.89 ($false),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[4644, 4641])).
% 0.73/0.89 tff(4646,plain,(((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))) | (~(op(e3, e1) = e2)) | (op(e2, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.89 tff(4647,plain,
% 0.73/0.89 ((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[4646, 1607, 10])).
% 0.73/0.89 tff(4648,plain,
% 0.73/0.89 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[681, 4647, 1798, 4632])).
% 0.73/0.89 tff(4649,plain,
% 0.73/0.89 (op(e0, op(e1, e0)) = e0),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[83, 4648])).
% 0.73/0.89 tff(4650,plain,
% 0.73/0.89 ((op(e1, e0) = op(e2, e0)) <=> (op(e1, e0) = e2)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4614])).
% 0.73/0.89 tff(4651,plain,
% 0.73/0.89 ((~(op(e1, e0) = op(e2, e0))) <=> (~(op(e1, e0) = e2))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4650])).
% 0.73/0.89 tff(4652,plain,
% 0.73/0.89 (~(op(e1, e0) = e2)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1206, 4651])).
% 0.73/0.89 tff(4653,plain,
% 0.73/0.89 ((op(e2, e0) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4614])).
% 0.73/0.89 tff(4654,plain,
% 0.73/0.89 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.73/0.89 inference(transitivity,[status(thm)],[4653, 810])).
% 0.73/0.89 tff(4655,plain,
% 0.73/0.89 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4654])).
% 0.73/0.89 tff(4656,plain,
% 0.73/0.89 (~(op(e2, e2) = e2)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1200, 4655])).
% 0.73/0.89 tff(4657,plain,
% 0.73/0.89 (op(e2, op(e1, e2)) = e2),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[102, 4648])).
% 0.73/0.89 tff(4658,plain,
% 0.73/0.89 (~(op(e1, e2) = e2)),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[1269, 4657, 4656])).
% 0.73/0.89 tff(4659,plain,
% 0.73/0.89 (op(e1, e3) = e2),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[135, 4658, 4652, 12])).
% 0.73/0.89 tff(4660,plain,
% 0.73/0.89 ((op(e1, e3) = e3) <=> (e2 = e3)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4659])).
% 0.73/0.89 tff(4661,plain,
% 0.73/0.89 ((e2 = e3) <=> (op(e1, e3) = e3)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4660])).
% 0.73/0.89 tff(4662,plain,
% 0.73/0.89 ((~(e2 = e3)) <=> (~(op(e1, e3) = e3))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4661])).
% 0.73/0.89 tff(4663,plain,
% 0.73/0.89 (~(op(e1, e3) = e3)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[462, 4662])).
% 0.73/0.89 tff(4664,plain,
% 0.73/0.89 ((op(e2, e0) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4614])).
% 0.73/0.89 tff(4665,plain,
% 0.73/0.89 ((op(e2, e0) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.73/0.89 inference(transitivity,[status(thm)],[4664, 72])).
% 0.73/0.89 tff(4666,plain,
% 0.73/0.89 ((~(op(e2, e0) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4665])).
% 0.73/0.89 tff(4667,plain,
% 0.73/0.89 (~(op(e2, e3) = e2)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[979, 4666])).
% 0.73/0.89 tff(4668,plain,
% 0.73/0.89 (~(op(e1, e2) = e3)),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[773, 4657, 4667])).
% 0.73/0.89 tff(4669,plain,
% 0.73/0.89 (op(e1, op(e1, e1)) = e1),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[1315, 4648])).
% 0.73/0.89 tff(4670,assumption,(op(e1, e1) = e3), introduced(assumption)).
% 0.73/0.89 tff(4671,plain,
% 0.73/0.89 (op(e1, op(e1, e1)) = op(e1, e3)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4670])).
% 0.73/0.89 tff(4672,assumption,(op(e1, op(e1, e1)) = e1), introduced(assumption)).
% 0.73/0.89 tff(4673,plain,
% 0.73/0.89 (e1 = op(e1, op(e1, e1))),
% 0.73/0.89 inference(symmetry,[status(thm)],[4672])).
% 0.73/0.89 tff(4674,plain,
% 0.73/0.89 (e1 = e2),
% 0.73/0.89 inference(transitivity,[status(thm)],[4673, 4671, 548])).
% 0.73/0.89 tff(4675,plain,
% 0.73/0.89 ($false),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[324, 4674])).
% 0.73/0.89 tff(4676,plain,((~(op(e1, e1) = e3)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e1, e3) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.89 tff(4677,plain,
% 0.73/0.89 (~(op(e1, e1) = e3)),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[4676, 4669, 4659])).
% 0.73/0.89 tff(4678,plain,
% 0.73/0.89 (op(e1, e0) = e3),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[2136, 4677, 4668, 4663])).
% 0.73/0.89 tff(4679,plain,
% 0.73/0.89 (e3 = op(e1, e0)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4678])).
% 0.73/0.89 tff(4680,plain,
% 0.73/0.89 (op(e0, e3) = op(e0, op(e1, e0))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4679])).
% 0.73/0.89 tff(4681,plain,
% 0.73/0.89 (op(e0, e3) = e0),
% 0.73/0.89 inference(transitivity,[status(thm)],[4680, 4649])).
% 0.73/0.89 tff(4682,plain,
% 0.73/0.89 ((op(e0, e3) = op(e3, e3)) <=> (e0 = op(e3, e3))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4681])).
% 0.73/0.89 tff(4683,plain,
% 0.73/0.89 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e0)),
% 0.73/0.89 inference(transitivity,[status(thm)],[4682, 11])).
% 0.73/0.89 tff(4684,plain,
% 0.73/0.89 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e0))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4683])).
% 0.73/0.89 tff(4685,plain,
% 0.73/0.89 (~(op(e3, e3) = e0)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[725, 4684])).
% 0.73/0.89 tff(4686,plain,
% 0.73/0.89 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e0)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4681])).
% 0.73/0.89 tff(4687,plain,
% 0.73/0.89 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e0))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4686])).
% 0.73/0.89 tff(4688,plain,
% 0.73/0.89 (~(op(e0, e0) = e0)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[2178, 4687])).
% 0.73/0.89 tff(4689,plain,
% 0.73/0.89 ((e0 = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 0.73/0.89 inference(commutativity,[status(thm)],[])).
% 0.73/0.89 tff(4690,plain,
% 0.73/0.89 (~(op(e1, e2) = e2)),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[1269, 103, 4656])).
% 0.73/0.89 tff(4691,plain,
% 0.73/0.89 (op(e1, e3) = e2),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[135, 4690, 4652, 12])).
% 0.73/0.89 tff(4692,plain,
% 0.73/0.89 (e2 = op(e1, e3)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4691])).
% 0.73/0.89 tff(4693,plain,
% 0.73/0.89 (op(e3, e2) = op(e3, op(e1, e3))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4692])).
% 0.73/0.89 tff(4694,plain,
% 0.73/0.89 (op(e3, e2) = e3),
% 0.73/0.89 inference(transitivity,[status(thm)],[4693, 81])).
% 0.73/0.89 tff(4695,plain,
% 0.73/0.89 ((op(e3, e2) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4694])).
% 0.73/0.89 tff(4696,plain,
% 0.73/0.89 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.73/0.89 inference(transitivity,[status(thm)],[4695, 78])).
% 0.73/0.89 tff(4697,plain,
% 0.73/0.89 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4696])).
% 0.73/0.89 tff(4698,plain,
% 0.73/0.89 (~(op(e3, e3) = e3)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[1111, 4697])).
% 0.73/0.89 tff(4699,plain,
% 0.73/0.89 ((op(e3, e1) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[1607])).
% 0.73/0.89 tff(4700,plain,
% 0.73/0.89 ((op(e3, e1) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.73/0.89 inference(transitivity,[status(thm)],[4699, 469])).
% 0.73/0.89 tff(4701,plain,
% 0.73/0.89 ((~(op(e3, e1) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4700])).
% 0.73/0.89 tff(4702,plain,
% 0.73/0.89 (~(op(e3, e2) = e2)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[3824, 4701])).
% 0.73/0.89 tff(4703,plain,
% 0.73/0.89 (op(e0, e2) = e2),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[3388, 4690, 4656, 4702])).
% 0.73/0.89 tff(4704,plain,
% 0.73/0.89 ((op(e0, e2) = e1) <=> (e2 = e1)),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4703])).
% 0.73/0.89 tff(4705,plain,
% 0.73/0.89 ((op(e0, e2) = e1) <=> (e1 = e2)),
% 0.73/0.89 inference(transitivity,[status(thm)],[4704, 317])).
% 0.73/0.89 tff(4706,plain,
% 0.73/0.89 ((e1 = e2) <=> (op(e0, e2) = e1)),
% 0.73/0.89 inference(symmetry,[status(thm)],[4705])).
% 0.73/0.89 tff(4707,plain,
% 0.73/0.89 ((~(e1 = e2)) <=> (~(op(e0, e2) = e1))),
% 0.73/0.89 inference(monotonicity,[status(thm)],[4706])).
% 0.73/0.89 tff(4708,plain,
% 0.73/0.89 (~(op(e0, e2) = e1)),
% 0.73/0.89 inference(modus_ponens,[status(thm)],[324, 4707])).
% 0.73/0.89 tff(4709,plain,
% 0.73/0.89 ((~(op(e1, op(e0, e1)) = e1)) | (op(e1, e1) = e2) | (op(e2, e1) = e2) | (op(e0, e2) = e1) | (op(e3, e3) = e0) | (op(e3, e3) = e3)),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[1081, 1605])).
% 0.73/0.89 tff(4710,plain,
% 0.73/0.89 (~(op(e1, op(e0, e1)) = e1)),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[4709, 4708, 10, 4698, 63, 12])).
% 0.73/0.89 tff(4711,plain,
% 0.73/0.89 (~(op(e2, op(e0, e2)) = e2)),
% 0.73/0.89 inference(unit_resolution,[status(thm)],[819, 4703])).
% 0.73/0.89 tff(4712,plain,
% 0.73/0.89 ((op(e0, e2) = e1) | (op(e0, e1) = e1) | (op(e1, e1) = e2) | (op(e3, e3) = e0) | (op(e0, e0) = e0) | (op(e2, op(e0, e2)) = e2) | (op(e1, op(e0, e1)) = e1)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[3461, 1605])).
% 0.73/0.90 tff(4713,plain,
% 0.73/0.90 (op(e0, e0) = e0),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4712, 4708, 12, 63, 4711, 433, 4710])).
% 0.73/0.90 tff(4714,plain,
% 0.73/0.90 ((op(e0, e0) = op(e3, e0)) <=> (e0 = op(e3, e0))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4713])).
% 0.73/0.90 tff(4715,plain,
% 0.73/0.90 ((op(e0, e0) = op(e3, e0)) <=> (op(e3, e0) = e0)),
% 0.73/0.90 inference(transitivity,[status(thm)],[4714, 4689])).
% 0.73/0.90 tff(4716,plain,
% 0.73/0.90 ((op(e3, e0) = e0) <=> (op(e0, e0) = op(e3, e0))),
% 0.73/0.90 inference(symmetry,[status(thm)],[4715])).
% 0.73/0.90 tff(4717,plain,
% 0.73/0.90 ((op(e3, e2) = e0) <=> (e3 = e0)),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4694])).
% 0.73/0.90 tff(4718,plain,
% 0.73/0.90 ((op(e3, e2) = e0) <=> (e0 = e3)),
% 0.73/0.90 inference(transitivity,[status(thm)],[4717, 279])).
% 0.73/0.90 tff(4719,plain,
% 0.73/0.90 ((e0 = e3) <=> (op(e3, e2) = e0)),
% 0.73/0.90 inference(symmetry,[status(thm)],[4718])).
% 0.73/0.90 tff(4720,plain,
% 0.73/0.90 ((~(e0 = e3)) <=> (~(op(e3, e2) = e0))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4719])).
% 0.73/0.90 tff(4721,plain,
% 0.73/0.90 (~(op(e3, e2) = e0)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[286, 4720])).
% 0.73/0.90 tff(4722,plain,
% 0.73/0.90 (op(e3, e0) = e0),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[295, 4721, 63, 3965])).
% 0.73/0.90 tff(4723,plain,
% 0.73/0.90 (op(e0, e0) = op(e3, e0)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[4722, 4716])).
% 0.73/0.90 tff(4724,plain,
% 0.73/0.90 ($false),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1638, 4723])).
% 0.73/0.90 tff(4725,plain,(((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))) | (op(e3, e3) = e0) | (op(e1, e1) = e2) | (op(e0, e1) = e1) | (op(e2, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.90 tff(4726,plain,
% 0.73/0.90 (op(e0, e1) = e1),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4725, 4685, 12, 4648, 10])).
% 0.73/0.90 tff(4727,plain,
% 0.73/0.90 ($false),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[3899, 4726, 4688, 12, 4685])).
% 0.73/0.90 tff(4728,plain,((op(e1, e1) = e2) | (op(e2, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.90 tff(4729,plain,
% 0.73/0.90 (op(e1, e1) = e2),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4728, 10])).
% 0.73/0.90 tff(4730,plain,
% 0.73/0.90 ((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3))),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4345, 4729, 10])).
% 0.73/0.90 tff(4731,plain,
% 0.73/0.90 ((op(e1, e1) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4729])).
% 0.73/0.90 tff(4732,plain,
% 0.73/0.90 ((op(e1, e1) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 0.73/0.90 inference(transitivity,[status(thm)],[4731, 326])).
% 0.73/0.90 tff(4733,plain,
% 0.73/0.90 ((~(op(e1, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4732])).
% 0.73/0.90 tff(4734,plain,
% 0.73/0.90 (~(op(e3, e1) = e2)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[348, 4733])).
% 0.73/0.90 tff(4735,plain,
% 0.73/0.90 (~(op(e3, e3) = e0)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1335, 334, 374])).
% 0.73/0.90 tff(4736,plain,
% 0.73/0.90 ($false),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[455, 4735, 334, 374, 433])).
% 0.73/0.90 tff(4737,plain,(((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (op(e3, e1) = e2) | (op(e0, e1) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.90 tff(4738,plain,
% 0.73/0.90 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4737, 433, 4734])).
% 0.73/0.90 tff(4739,plain,
% 0.73/0.90 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[681, 4738, 1798, 4730])).
% 0.73/0.90 tff(4740,plain,
% 0.73/0.90 (op(e3, op(e2, e3)) = e3),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[471, 4739])).
% 0.73/0.90 tff(4741,plain,
% 0.73/0.90 (op(e1, op(e2, e1)) = e1),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[546, 4739])).
% 0.73/0.90 tff(4742,plain,
% 0.73/0.90 (~(op(e2, e1) = e1)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4170, 4741, 4729])).
% 0.73/0.90 tff(4743,plain,
% 0.73/0.90 (op(e2, op(e2, e2)) = e2),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[473, 4739])).
% 0.73/0.90 tff(4744,plain,
% 0.73/0.90 (~(op(e2, e2) = e1)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[488, 4743, 10])).
% 0.73/0.90 tff(4745,plain,
% 0.73/0.90 (op(e2, e3) = e1),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[964, 4744, 4637, 4742])).
% 0.73/0.90 tff(4746,plain,
% 0.73/0.90 (op(e3, op(e2, e3)) = op(e3, e1)),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4745])).
% 0.73/0.90 tff(4747,plain,
% 0.73/0.90 (op(e3, e1) = op(e3, op(e2, e3))),
% 0.73/0.90 inference(symmetry,[status(thm)],[4746])).
% 0.73/0.90 tff(4748,plain,
% 0.73/0.90 ((op(e1, e1) = e1) <=> (e2 = e1)),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4729])).
% 0.73/0.90 tff(4749,plain,
% 0.73/0.90 ((op(e1, e1) = e1) <=> (e1 = e2)),
% 0.73/0.90 inference(transitivity,[status(thm)],[4748, 317])).
% 0.73/0.90 tff(4750,plain,
% 0.73/0.90 ((e1 = e2) <=> (op(e1, e1) = e1)),
% 0.73/0.90 inference(symmetry,[status(thm)],[4749])).
% 0.73/0.90 tff(4751,plain,
% 0.73/0.90 ((~(e1 = e2)) <=> (~(op(e1, e1) = e1))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4750])).
% 0.73/0.90 tff(4752,plain,
% 0.73/0.90 (~(op(e1, e1) = e1)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[324, 4751])).
% 0.73/0.90 tff(4753,plain,
% 0.73/0.90 (op(e3, e1) = e1),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[450, 4742, 4752, 433])).
% 0.73/0.90 tff(4754,plain,
% 0.73/0.90 (e1 = op(e3, e1)),
% 0.73/0.90 inference(symmetry,[status(thm)],[4753])).
% 0.73/0.90 tff(4755,plain,
% 0.73/0.90 (e1 = e3),
% 0.73/0.90 inference(transitivity,[status(thm)],[4754, 4747, 4740])).
% 0.73/0.90 tff(4756,plain,
% 0.73/0.90 ($false),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[591, 4755])).
% 0.73/0.90 tff(4757,plain,((op(e0, e1) = e1) | (op(e2, e1) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.90 tff(4758,plain,
% 0.73/0.90 (op(e0, e1) = e1),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4757, 10])).
% 0.73/0.90 tff(4759,plain,
% 0.73/0.90 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1659, 4758, 10])).
% 0.73/0.90 tff(4760,plain,
% 0.73/0.90 (~((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3)))),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[681, 4759, 1798, 4730])).
% 0.73/0.90 tff(4761,plain,
% 0.73/0.90 (op(e2, op(e2, e2)) = e2),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[473, 4760])).
% 0.73/0.90 tff(4762,plain,
% 0.73/0.90 (~(op(e2, e2) = e1)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[488, 4761, 10])).
% 0.73/0.90 tff(4763,plain,
% 0.73/0.90 ((op(e2, e2) = op(e0, e2)) <=> (op(e0, e2) = op(e2, e2))),
% 0.73/0.90 inference(commutativity,[status(thm)],[])).
% 0.73/0.90 tff(4764,plain,
% 0.73/0.90 (op(e0, op(e2, e0)) = op(e0, e2)),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4614])).
% 0.73/0.90 tff(4765,plain,
% 0.73/0.90 (op(e0, op(e2, e0)) = e0),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[967, 4760])).
% 0.73/0.90 tff(4766,plain,
% 0.73/0.90 (e0 = op(e0, op(e2, e0))),
% 0.73/0.90 inference(symmetry,[status(thm)],[4765])).
% 0.73/0.90 tff(4767,plain,
% 0.73/0.90 (e0 = op(e0, e2)),
% 0.73/0.90 inference(transitivity,[status(thm)],[4766, 4764])).
% 0.73/0.90 tff(4768,plain,
% 0.73/0.90 ((op(e2, e2) = e0) <=> (op(e2, e2) = op(e0, e2))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4767])).
% 0.73/0.90 tff(4769,plain,
% 0.73/0.90 ((op(e2, e2) = e0) <=> (op(e0, e2) = op(e2, e2))),
% 0.73/0.90 inference(transitivity,[status(thm)],[4768, 4763])).
% 0.73/0.90 tff(4770,plain,
% 0.73/0.90 ((op(e0, e2) = op(e2, e2)) <=> (op(e2, e2) = e0)),
% 0.73/0.90 inference(symmetry,[status(thm)],[4769])).
% 0.73/0.90 tff(4771,plain,
% 0.73/0.90 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e0))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4770])).
% 0.73/0.90 tff(4772,plain,
% 0.73/0.90 (~(op(e2, e2) = e0)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[816, 4771])).
% 0.73/0.90 tff(4773,plain,
% 0.73/0.90 (op(e2, e2) = e3),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[513, 4772, 4656, 4762])).
% 0.73/0.90 tff(4774,plain,
% 0.73/0.90 (e3 = op(e2, e2)),
% 0.73/0.90 inference(symmetry,[status(thm)],[4773])).
% 0.73/0.90 tff(4775,plain,
% 0.73/0.90 (op(e2, e3) = op(e2, op(e2, e2))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4774])).
% 0.73/0.90 tff(4776,plain,
% 0.73/0.90 (op(e1, op(e2, e1)) = e1),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[546, 4760])).
% 0.73/0.90 tff(4777,plain,
% 0.73/0.90 (~(op(e2, e1) = e1)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4170, 4776, 4729])).
% 0.73/0.90 tff(4778,plain,
% 0.73/0.90 (op(e2, e3) = e1),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[964, 4762, 4637, 4777])).
% 0.73/0.90 tff(4779,plain,
% 0.73/0.90 (e1 = op(e2, e3)),
% 0.73/0.90 inference(symmetry,[status(thm)],[4778])).
% 0.73/0.90 tff(4780,plain,
% 0.73/0.90 (e1 = e2),
% 0.73/0.90 inference(transitivity,[status(thm)],[4779, 4775, 4761])).
% 0.73/0.90 tff(4781,plain,
% 0.73/0.90 ($false),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[324, 4780])).
% 0.73/0.90 tff(4782,plain,(op(e2, e1) = e2), inference(lemma,lemma(discharge,[]))).
% 0.73/0.90 tff(4783,plain,
% 0.73/0.90 ((op(e1, e1) = op(e2, e1)) <=> (op(e1, e1) = e2)),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4782])).
% 0.73/0.90 tff(4784,plain,
% 0.73/0.90 ((~(op(e1, e1) = op(e2, e1))) <=> (~(op(e1, e1) = e2))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4783])).
% 0.73/0.90 tff(4785,plain,
% 0.73/0.90 (~(op(e1, e1) = e2)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[633, 4784])).
% 0.73/0.90 tff(4786,plain,
% 0.73/0.90 ((~(op(e0, op(e0, e0)) = e0)) | (op(e1, e1) = e2) | (~(op(e3, op(e0, e3)) = e3)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e1, op(e0, e1)) = e1)) | (op(e0, e3) = e2)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1158, 1605])).
% 0.73/0.90 tff(4787,plain,
% 0.73/0.90 ((~(op(e0, op(e0, e0)) = e0)) | (~(op(e3, op(e0, e3)) = e3)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e1, op(e0, e1)) = e1)) | (op(e0, e3) = e2)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4786, 4785])).
% 0.73/0.90 tff(4788,plain,
% 0.73/0.90 (op(e0, e3) = e2),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4787, 9, 7, 5, 3])).
% 0.73/0.90 tff(4789,plain,
% 0.73/0.90 ((op(e0, e3) = e3) <=> (e2 = e3)),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4788])).
% 0.73/0.90 tff(4790,plain,
% 0.73/0.90 ((e2 = e3) <=> (op(e0, e3) = e3)),
% 0.73/0.90 inference(symmetry,[status(thm)],[4789])).
% 0.73/0.90 tff(4791,plain,
% 0.73/0.90 ((~(e2 = e3)) <=> (~(op(e0, e3) = e3))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4790])).
% 0.73/0.90 tff(4792,plain,
% 0.73/0.90 (~(op(e0, e3) = e3)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[462, 4791])).
% 0.73/0.90 tff(4793,plain,
% 0.73/0.90 ((op(e2, e1) = op(e2, e3)) <=> (e2 = op(e2, e3))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4782])).
% 0.73/0.90 tff(4794,plain,
% 0.73/0.90 ((op(e2, e1) = op(e2, e3)) <=> (op(e2, e3) = e2)),
% 0.73/0.90 inference(transitivity,[status(thm)],[4793, 72])).
% 0.73/0.90 tff(4795,plain,
% 0.73/0.90 ((~(op(e2, e1) = op(e2, e3))) <=> (~(op(e2, e3) = e2))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4794])).
% 0.73/0.90 tff(4796,plain,
% 0.73/0.90 (~(op(e2, e3) = e2)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[1005, 4795])).
% 0.73/0.90 tff(4797,plain,
% 0.73/0.90 ((~(op(e0, e2) = e3)) | (~(op(e2, op(e0, e2)) = e2))),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[908, 4796])).
% 0.73/0.90 tff(4798,plain,
% 0.73/0.90 (~(op(e0, e2) = e3)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4797, 9])).
% 0.73/0.90 tff(4799,plain,
% 0.73/0.90 (op(e0, e3) = e2),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4787, 7, 9, 5, 3])).
% 0.73/0.90 tff(4800,plain,
% 0.73/0.90 (op(e3, e2) = e3),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1120, 4799, 3])).
% 0.73/0.90 tff(4801,plain,
% 0.73/0.90 ((op(e2, e1) = op(e2, e2)) <=> (e2 = op(e2, e2))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4782])).
% 0.73/0.90 tff(4802,plain,
% 0.73/0.90 ((op(e2, e1) = op(e2, e2)) <=> (op(e2, e2) = e2)),
% 0.73/0.90 inference(transitivity,[status(thm)],[4801, 810])).
% 0.73/0.90 tff(4803,plain,
% 0.73/0.90 ((~(op(e2, e1) = op(e2, e2))) <=> (~(op(e2, e2) = e2))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4802])).
% 0.73/0.90 tff(4804,plain,
% 0.73/0.90 (~(op(e2, e2) = e2)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[1710, 4803])).
% 0.73/0.90 tff(4805,plain,
% 0.73/0.90 ((op(e0, e2) = e2) | (op(e1, e2) = e2) | (op(e3, e2) = e2)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[3388, 4804])).
% 0.73/0.90 tff(4806,plain,
% 0.73/0.90 (op(e3, e2) = e2),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4805, 1787, 766])).
% 0.73/0.90 tff(4807,plain,
% 0.73/0.90 (e2 = op(e3, e2)),
% 0.73/0.90 inference(symmetry,[status(thm)],[4806])).
% 0.73/0.90 tff(4808,plain,
% 0.73/0.90 (e2 = e3),
% 0.73/0.90 inference(transitivity,[status(thm)],[4807, 4800])).
% 0.73/0.90 tff(4809,plain,
% 0.73/0.90 ($false),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[462, 4808])).
% 0.73/0.90 tff(4810,plain,(((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))) | (op(e1, e2) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.90 tff(4811,plain,
% 0.73/0.90 (op(e1, e2) = e2),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4810, 1])).
% 0.73/0.90 tff(4812,plain,
% 0.73/0.90 ((op(e1, e2) = e0) <=> (e2 = e0)),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4811])).
% 0.73/0.90 tff(4813,plain,
% 0.73/0.90 ((op(e1, e2) = e0) <=> (e0 = e2)),
% 0.73/0.90 inference(transitivity,[status(thm)],[4812, 217])).
% 0.73/0.90 tff(4814,plain,
% 0.73/0.90 ((e0 = e2) <=> (op(e1, e2) = e0)),
% 0.73/0.90 inference(symmetry,[status(thm)],[4813])).
% 0.73/0.90 tff(4815,plain,
% 0.73/0.90 ((~(e0 = e2)) <=> (~(op(e1, e2) = e0))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4814])).
% 0.73/0.90 tff(4816,plain,
% 0.73/0.90 (~(op(e1, e2) = e0)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[238, 4815])).
% 0.73/0.90 tff(4817,plain,
% 0.73/0.90 ((op(e2, e0) = op(e2, e1)) <=> (op(e2, e0) = e2)),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4782])).
% 0.73/0.90 tff(4818,plain,
% 0.73/0.90 ((~(op(e2, e0) = op(e2, e1))) <=> (~(op(e2, e0) = e2))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4817])).
% 0.73/0.90 tff(4819,plain,
% 0.73/0.90 (~(op(e2, e0) = e2)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[997, 4818])).
% 0.73/0.90 tff(4820,plain,
% 0.73/0.90 ((~(op(e0, e2) = e0)) | (~(op(e2, op(e0, e2)) = e2))),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[901, 4819])).
% 0.73/0.90 tff(4821,plain,
% 0.73/0.90 (~(op(e0, e2) = e0)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4820, 9])).
% 0.73/0.90 tff(4822,plain,
% 0.73/0.90 (op(e3, e2) = e3),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1120, 3, 4788])).
% 0.73/0.90 tff(4823,plain,
% 0.73/0.90 ((op(e3, e2) = e0) <=> (e3 = e0)),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4822])).
% 0.73/0.90 tff(4824,plain,
% 0.73/0.90 ((op(e3, e2) = e0) <=> (e0 = e3)),
% 0.73/0.90 inference(transitivity,[status(thm)],[4823, 279])).
% 0.73/0.90 tff(4825,plain,
% 0.73/0.90 ((e0 = e3) <=> (op(e3, e2) = e0)),
% 0.73/0.90 inference(symmetry,[status(thm)],[4824])).
% 0.73/0.90 tff(4826,plain,
% 0.73/0.90 ((~(e0 = e3)) <=> (~(op(e3, e2) = e0))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4825])).
% 0.73/0.90 tff(4827,plain,
% 0.73/0.90 (~(op(e3, e2) = e0)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[286, 4826])).
% 0.73/0.90 tff(4828,plain,
% 0.73/0.90 (op(e2, e2) = e0),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[2741, 4827, 4821, 4816])).
% 0.73/0.90 tff(4829,plain,
% 0.73/0.90 ((op(e2, e0) = op(e2, e2)) <=> (op(e2, e0) = e0)),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4828])).
% 0.73/0.90 tff(4830,plain,
% 0.73/0.90 ((~(op(e2, e0) = op(e2, e2))) <=> (~(op(e2, e0) = e0))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4829])).
% 0.73/0.90 tff(4831,plain,
% 0.73/0.90 (~(op(e2, e0) = e0)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[1200, 4830])).
% 0.73/0.90 tff(4832,plain,
% 0.73/0.90 ((op(e3, e2) = op(e3, e3)) <=> (e3 = op(e3, e3))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4822])).
% 0.73/0.90 tff(4833,plain,
% 0.73/0.90 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e3) = e3)),
% 0.73/0.90 inference(transitivity,[status(thm)],[4832, 78])).
% 0.73/0.90 tff(4834,plain,
% 0.73/0.90 ((~(op(e3, e2) = op(e3, e3))) <=> (~(op(e3, e3) = e3))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4833])).
% 0.73/0.90 tff(4835,plain,
% 0.73/0.90 (~(op(e3, e3) = e3)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[1111, 4834])).
% 0.73/0.90 tff(4836,plain,
% 0.73/0.90 (((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))) | (op(e0, e2) = e2) | (op(e3, e3) = e0) | (op(e3, e3) = e3)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[919, 4819, 4796])).
% 0.73/0.90 tff(4837,plain,
% 0.73/0.90 (op(e3, e3) = e0),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4836, 4835, 1, 1787])).
% 0.73/0.90 tff(4838,plain,
% 0.73/0.90 ((op(e0, e3) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4788])).
% 0.73/0.90 tff(4839,plain,
% 0.73/0.90 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.73/0.90 inference(transitivity,[status(thm)],[4838, 1024])).
% 0.73/0.90 tff(4840,plain,
% 0.73/0.90 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4839])).
% 0.73/0.90 tff(4841,plain,
% 0.73/0.90 (~(op(e3, e3) = e2)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[725, 4840])).
% 0.73/0.90 tff(4842,plain,
% 0.73/0.90 ((op(e1, e2) = op(e3, e2)) <=> (e2 = op(e3, e2))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4811])).
% 0.73/0.90 tff(4843,plain,
% 0.73/0.90 ((op(e1, e2) = op(e3, e2)) <=> (op(e3, e2) = e2)),
% 0.73/0.90 inference(transitivity,[status(thm)],[4842, 469])).
% 0.73/0.90 tff(4844,plain,
% 0.73/0.90 ((~(op(e1, e2) = op(e3, e2))) <=> (~(op(e3, e2) = e2))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4843])).
% 0.73/0.90 tff(4845,plain,
% 0.73/0.90 (~(op(e3, e2) = e2)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[165, 4844])).
% 0.73/0.90 tff(4846,plain,
% 0.73/0.90 ((op(e2, e1) = op(e3, e1)) <=> (e2 = op(e3, e1))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4782])).
% 0.73/0.90 tff(4847,plain,
% 0.73/0.90 ((op(e2, e1) = op(e3, e1)) <=> (op(e3, e1) = e2)),
% 0.73/0.90 inference(transitivity,[status(thm)],[4846, 326])).
% 0.73/0.90 tff(4848,plain,
% 0.73/0.90 ((~(op(e2, e1) = op(e3, e1))) <=> (~(op(e3, e1) = e2))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4847])).
% 0.73/0.90 tff(4849,plain,
% 0.73/0.90 (~(op(e3, e1) = e2)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[576, 4848])).
% 0.73/0.90 tff(4850,plain,
% 0.73/0.90 ((op(e3, e0) = e2) | (op(e3, e2) = e2) | (op(e3, e3) = e2)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[537, 4849])).
% 0.73/0.90 tff(4851,plain,
% 0.73/0.90 (op(e3, e0) = e2),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4850, 4845, 4841])).
% 0.73/0.90 tff(4852,plain,
% 0.73/0.90 (op(e3, op(e3, e3)) = op(e3, e0)),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4837])).
% 0.73/0.90 tff(4853,plain,
% 0.73/0.90 (op(e3, op(e3, e3)) = e2),
% 0.73/0.90 inference(transitivity,[status(thm)],[4852, 4851])).
% 0.73/0.90 tff(4854,plain,
% 0.73/0.90 (op(op(e3, op(e3, e3)), op(e3, e3)) = op(e2, e0)),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4853, 4837])).
% 0.73/0.90 tff(4855,plain,
% 0.73/0.90 ((e1 = op(op(e3, op(e3, e3)), op(e3, e3))) <=> (e1 = op(e2, e0))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4854])).
% 0.73/0.90 tff(4856,plain,
% 0.73/0.90 ((e1 = op(op(e3, op(e3, e3)), op(e3, e3))) <=> (op(e2, e0) = e1)),
% 0.73/0.90 inference(transitivity,[status(thm)],[4855, 1384])).
% 0.73/0.90 tff(4857,plain,
% 0.73/0.90 ((~(e1 = op(op(e3, op(e3, e3)), op(e3, e3)))) <=> (~(op(e2, e0) = e1))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4856])).
% 0.73/0.90 tff(4858,plain,
% 0.73/0.90 (e0 = op(e3, e3)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[4837, 1390])).
% 0.73/0.90 tff(4859,plain,
% 0.73/0.90 (op(e3, e0) = op(e3, op(e3, e3))),
% 0.73/0.90 inference(symmetry,[status(thm)],[4852])).
% 0.73/0.90 tff(4860,plain,
% 0.73/0.90 (e2 = op(e3, e0)),
% 0.73/0.90 inference(symmetry,[status(thm)],[4851])).
% 0.73/0.90 tff(4861,plain,
% 0.73/0.90 (e2 = op(e3, op(e3, e3))),
% 0.73/0.90 inference(transitivity,[status(thm)],[4860, 4859])).
% 0.73/0.90 tff(4862,plain,
% 0.73/0.90 (~(e1 = op(op(e3, op(e3, e3)), op(e3, e3)))),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1405, 4861, 4858])).
% 0.73/0.90 tff(4863,plain,
% 0.73/0.90 (~(op(e2, e0) = e1)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[4862, 4857])).
% 0.73/0.90 tff(4864,plain,
% 0.73/0.90 ((op(e2, e0) = e0) | (op(e2, e0) = e1) | (op(e2, e0) = e3)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1909, 4819])).
% 0.73/0.90 tff(4865,plain,
% 0.73/0.90 (op(e2, e0) = e3),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4864, 4863, 4831])).
% 0.73/0.90 tff(4866,plain,
% 0.73/0.90 ((op(e0, e0) = op(e2, e0)) <=> (op(e0, e0) = e3)),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4865])).
% 0.73/0.90 tff(4867,plain,
% 0.73/0.90 ((~(op(e0, e0) = op(e2, e0))) <=> (~(op(e0, e0) = e3))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4866])).
% 0.73/0.90 tff(4868,plain,
% 0.73/0.90 (~(op(e0, e0) = e3)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[1827, 4867])).
% 0.73/0.90 tff(4869,plain,
% 0.73/0.90 ((op(e0, e2) = e1) | (~(op(e2, op(e0, e2)) = e2))),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1009, 4782])).
% 0.73/0.90 tff(4870,plain,
% 0.73/0.90 (op(e0, e2) = e1),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4869, 9])).
% 0.73/0.90 tff(4871,plain,
% 0.73/0.90 ((op(e0, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4870])).
% 0.73/0.90 tff(4872,plain,
% 0.73/0.90 ((op(e0, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 0.73/0.90 inference(transitivity,[status(thm)],[4871, 1949])).
% 0.73/0.90 tff(4873,plain,
% 0.73/0.90 ((~(op(e0, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4872])).
% 0.73/0.90 tff(4874,plain,
% 0.73/0.90 (~(op(e2, e2) = e1)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[816, 4873])).
% 0.73/0.90 tff(4875,plain,
% 0.73/0.90 ((op(e2, e1) = e1) <=> (e2 = e1)),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4782])).
% 0.73/0.90 tff(4876,plain,
% 0.73/0.90 ((op(e2, e1) = e1) <=> (e1 = e2)),
% 0.73/0.90 inference(transitivity,[status(thm)],[4875, 317])).
% 0.73/0.90 tff(4877,plain,
% 0.73/0.90 ((e1 = e2) <=> (op(e2, e1) = e1)),
% 0.73/0.90 inference(symmetry,[status(thm)],[4876])).
% 0.73/0.90 tff(4878,plain,
% 0.73/0.90 ((~(e1 = e2)) <=> (~(op(e2, e1) = e1))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4877])).
% 0.73/0.90 tff(4879,plain,
% 0.73/0.90 (~(op(e2, e1) = e1)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[324, 4878])).
% 0.73/0.90 tff(4880,plain,
% 0.73/0.90 ((op(e2, e0) = e1) | (op(e2, e2) = e1) | (op(e2, e3) = e1)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[964, 4879])).
% 0.73/0.90 tff(4881,plain,
% 0.73/0.90 (op(e2, e3) = e1),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4880, 4863, 4874])).
% 0.73/0.90 tff(4882,plain,
% 0.73/0.90 ((op(e1, e3) = op(e2, e3)) <=> (op(e1, e3) = e1)),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4881])).
% 0.73/0.90 tff(4883,plain,
% 0.73/0.90 ((~(op(e1, e3) = op(e2, e3))) <=> (~(op(e1, e3) = e1))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4882])).
% 0.73/0.90 tff(4884,plain,
% 0.73/0.90 (~(op(e1, e3) = e1)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[944, 4883])).
% 0.73/0.90 tff(4885,plain,
% 0.73/0.90 (~(op(e0, e1) = e3)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[846, 4884, 5])).
% 0.73/0.90 tff(4886,plain,
% 0.73/0.90 ($false),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1562, 4885, 4868, 4798, 4792])).
% 0.73/0.90 tff(4887,plain,((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.90 tff(4888,plain,
% 0.73/0.90 ((~(op(e2, e2) = e0)) | (~(op(e2, op(e2, e2)) = e2))),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[481, 4819])).
% 0.73/0.90 tff(4889,plain,
% 0.73/0.90 (~(op(e2, e2) = e0)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4888, 474])).
% 0.73/0.90 tff(4890,plain,
% 0.73/0.90 (e2 = op(e2, e1)),
% 0.73/0.90 inference(symmetry,[status(thm)],[4782])).
% 0.73/0.90 tff(4891,plain,
% 0.73/0.90 (op(e1, e2) = op(e1, op(e2, e1))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4890])).
% 0.73/0.90 tff(4892,plain,
% 0.73/0.90 (op(e1, e2) = e1),
% 0.73/0.90 inference(transitivity,[status(thm)],[4891, 547])).
% 0.73/0.90 tff(4893,plain,
% 0.73/0.90 ((op(e1, e2) = op(e2, e2)) <=> (e1 = op(e2, e2))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4892])).
% 0.73/0.90 tff(4894,plain,
% 0.73/0.90 ((op(e1, e2) = op(e2, e2)) <=> (op(e2, e2) = e1)),
% 0.73/0.90 inference(transitivity,[status(thm)],[4893, 1949])).
% 0.73/0.90 tff(4895,plain,
% 0.73/0.90 ((~(op(e1, e2) = op(e2, e2))) <=> (~(op(e2, e2) = e1))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4894])).
% 0.73/0.90 tff(4896,plain,
% 0.73/0.90 (~(op(e2, e2) = e1)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[764, 4895])).
% 0.73/0.90 tff(4897,plain,
% 0.73/0.90 ((op(e2, e2) = e0) | (op(e2, e2) = e1) | (op(e2, e2) = e3)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[513, 4804])).
% 0.73/0.90 tff(4898,plain,
% 0.73/0.90 (op(e2, e2) = e3),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4897, 4896, 4889])).
% 0.73/0.90 tff(4899,plain,
% 0.73/0.90 (e3 = op(e2, e2)),
% 0.73/0.90 inference(symmetry,[status(thm)],[4898])).
% 0.73/0.90 tff(4900,plain,
% 0.73/0.90 (op(e2, e3) = op(e2, op(e2, e2))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[4899])).
% 0.73/0.90 tff(4901,plain,
% 0.73/0.90 (op(e2, e3) = e2),
% 0.73/0.90 inference(transitivity,[status(thm)],[4900, 474])).
% 0.73/0.90 tff(4902,plain,
% 0.73/0.90 ($false),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4796, 4901])).
% 0.73/0.90 tff(4903,plain,((~(op(e0, op(e2, e0)) = e0)) | (~(op(e1, op(e2, e1)) = e1)) | (~(op(e2, op(e2, e2)) = e2)) | (~(op(e3, op(e2, e3)) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.90 tff(4904,plain,
% 0.73/0.90 (((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (op(e0, e1) = e1)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4737, 4849])).
% 0.73/0.90 tff(4905,plain,
% 0.73/0.90 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[4904, 433])).
% 0.73/0.90 tff(4906,plain,
% 0.73/0.90 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[681, 1221, 4903, 4905])).
% 0.73/0.90 tff(4907,plain,
% 0.73/0.90 (op(e2, op(e1, e2)) = e2),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[102, 4906])).
% 0.73/0.90 tff(4908,plain,
% 0.73/0.90 ((~(op(e1, e2) = e2)) | (~(op(e2, op(e1, e2)) = e2))),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[1269, 4804])).
% 0.73/0.91 tff(4909,plain,
% 0.73/0.91 (~(op(e1, e2) = e2)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4908, 4907])).
% 0.73/0.91 tff(4910,plain,
% 0.73/0.91 (op(e1, op(e1, e1)) = e1),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[1315, 4906])).
% 0.73/0.91 tff(4911,plain,
% 0.73/0.91 ((~(op(e1, e2) = e3)) | (~(op(e2, op(e1, e2)) = e2))),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[773, 4796])).
% 0.73/0.91 tff(4912,plain,
% 0.73/0.91 (~(op(e1, e2) = e3)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4911, 4907])).
% 0.73/0.91 tff(4913,assumption,(op(e1, e2) = e0), introduced(assumption)).
% 0.73/0.91 tff(4914,plain,
% 0.73/0.91 (e0 = op(e1, e2)),
% 0.73/0.91 inference(symmetry,[status(thm)],[4913])).
% 0.73/0.91 tff(4915,plain,
% 0.73/0.91 (op(e2, e0) = op(e2, op(e1, e2))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4914])).
% 0.73/0.91 tff(4916,plain,
% 0.73/0.91 (op(e2, e0) = e2),
% 0.73/0.91 inference(transitivity,[status(thm)],[4915, 106])).
% 0.73/0.91 tff(4917,plain,
% 0.73/0.91 ($false),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4819, 4916])).
% 0.73/0.91 tff(4918,plain,((~(op(e1, e2) = e0)) | (~(op(e2, op(e1, e2)) = e2))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.91 tff(4919,plain,
% 0.73/0.91 (~(op(e1, e2) = e0)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4918, 4907])).
% 0.73/0.91 tff(4920,plain,
% 0.73/0.91 (op(e1, e2) = e1),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[193, 4919, 4909, 4912])).
% 0.73/0.91 tff(4921,plain,
% 0.73/0.91 ((op(e1, e1) = op(e1, e2)) <=> (op(e1, e1) = e1)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4920])).
% 0.73/0.91 tff(4922,plain,
% 0.73/0.91 ((~(op(e1, e1) = op(e1, e2))) <=> (~(op(e1, e1) = e1))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4921])).
% 0.73/0.91 tff(4923,plain,
% 0.73/0.91 (~(op(e1, e1) = e1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[1616, 4922])).
% 0.73/0.91 tff(4924,plain,
% 0.73/0.91 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e0) = e1)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4920])).
% 0.73/0.91 tff(4925,plain,
% 0.73/0.91 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = e1))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4924])).
% 0.73/0.91 tff(4926,plain,
% 0.73/0.91 (~(op(e1, e0) = e1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[1428, 4925])).
% 0.73/0.91 tff(4927,plain,
% 0.73/0.91 (op(e1, e0) = e1),
% 0.73/0.91 inference(transitivity,[status(thm)],[2934, 4672])).
% 0.73/0.91 tff(4928,plain,
% 0.73/0.91 ($false),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[640, 4927])).
% 0.73/0.91 tff(4929,plain,((~(op(e1, e1) = e0)) | (op(e1, e0) = e1) | (~(op(e1, op(e1, e1)) = e1))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.91 tff(4930,plain,
% 0.73/0.91 (~(op(e1, e1) = e0)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4929, 4926, 4910])).
% 0.73/0.91 tff(4931,plain,
% 0.73/0.91 ((op(e1, e1) = e0) | (op(e1, e1) = e1) | (op(e1, e1) = e3)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[2603, 4785])).
% 0.73/0.91 tff(4932,plain,
% 0.73/0.91 (op(e1, e1) = e3),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4931, 4930, 4923])).
% 0.73/0.91 tff(4933,plain,
% 0.73/0.91 (~(op(e1, e3) = e2)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4676, 4932, 4910])).
% 0.73/0.91 tff(4934,plain,
% 0.73/0.91 ((op(e1, e0) = e2) | (op(e1, e2) = e2) | (op(e1, e3) = e2)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[135, 4785])).
% 0.73/0.91 tff(4935,plain,
% 0.73/0.91 (op(e1, e0) = e2),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4934, 4933, 4909])).
% 0.73/0.91 tff(4936,plain,
% 0.73/0.91 ((op(e0, e2) = op(e1, e2)) <=> (op(e0, e2) = e1)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4920])).
% 0.73/0.91 tff(4937,plain,
% 0.73/0.91 ((~(op(e0, e2) = op(e1, e2))) <=> (~(op(e0, e2) = e1))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4936])).
% 0.73/0.91 tff(4938,plain,
% 0.73/0.91 (~(op(e0, e2) = e1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[703, 4937])).
% 0.73/0.91 tff(4939,plain,
% 0.73/0.91 (op(e3, op(e1, e3)) = e3),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[80, 4906])).
% 0.73/0.91 tff(4940,plain,
% 0.73/0.91 (op(e0, op(e1, e0)) = e0),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[83, 4906])).
% 0.73/0.91 tff(4941,plain,
% 0.73/0.91 ((op(e0, e1) = e1) | (op(e1, e1) = e1) | (op(e3, e1) = e1)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[450, 4879])).
% 0.73/0.91 tff(4942,plain,
% 0.73/0.91 (op(e3, e1) = e1),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4941, 4923, 433])).
% 0.73/0.91 tff(4943,plain,
% 0.73/0.91 ((op(e3, e1) = op(e3, e3)) <=> (e1 = op(e3, e3))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4942])).
% 0.73/0.91 tff(4944,plain,
% 0.73/0.91 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e3) = e1)),
% 0.73/0.91 inference(transitivity,[status(thm)],[4943, 76])).
% 0.73/0.91 tff(4945,plain,
% 0.73/0.91 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e3) = e1))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4944])).
% 0.73/0.91 tff(4946,plain,
% 0.73/0.91 (~(op(e3, e3) = e1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[399, 4945])).
% 0.73/0.91 tff(4947,assumption,(op(e3, op(e1, e3)) = e3), introduced(assumption)).
% 0.73/0.91 tff(4948,plain,
% 0.73/0.91 (op(e3, e3) = e3),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[266, 75, 2668, 63])).
% 0.73/0.91 tff(4949,plain,
% 0.73/0.91 ((op(e3, e2) = op(e3, e3)) <=> (op(e3, e2) = e3)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4948])).
% 0.73/0.91 tff(4950,plain,
% 0.73/0.91 ((op(e3, e2) = e3) <=> (op(e3, e2) = op(e3, e3))),
% 0.73/0.91 inference(symmetry,[status(thm)],[4949])).
% 0.73/0.91 tff(4951,plain,
% 0.73/0.91 ((op(e0, e3) = e2) | (op(e1, e3) = e2) | (op(e3, e3) = e2)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[147, 4796])).
% 0.73/0.91 tff(4952,plain,
% 0.73/0.91 (op(e1, e3) = e2),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4951, 75, 104])).
% 0.73/0.91 tff(4953,plain,
% 0.73/0.91 (e2 = op(e1, e3)),
% 0.73/0.91 inference(symmetry,[status(thm)],[4952])).
% 0.73/0.91 tff(4954,plain,
% 0.73/0.91 (op(e3, e2) = op(e3, op(e1, e3))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4953])).
% 0.73/0.91 tff(4955,plain,
% 0.73/0.91 (op(e3, e2) = e3),
% 0.73/0.91 inference(transitivity,[status(thm)],[4954, 4947])).
% 0.73/0.91 tff(4956,plain,
% 0.73/0.91 (op(e3, e2) = op(e3, e3)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[4955, 4950])).
% 0.73/0.91 tff(4957,plain,
% 0.73/0.91 ($false),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[1111, 4956])).
% 0.73/0.91 tff(4958,plain,((op(e3, e3) = e2) | (~(op(e3, op(e1, e3)) = e3)) | (op(e3, e3) = e1) | (op(e3, e3) = e0) | (op(e0, e3) = e2)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.91 tff(4959,plain,
% 0.73/0.91 (op(e3, e3) = e2),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4958, 104, 2668, 63, 4947])).
% 0.73/0.91 tff(4960,plain,
% 0.73/0.91 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e2)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4959])).
% 0.73/0.91 tff(4961,plain,
% 0.73/0.91 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e2))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4960])).
% 0.73/0.91 tff(4962,plain,
% 0.73/0.91 (~(op(e1, e3) = e2)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[368, 4961])).
% 0.73/0.91 tff(4963,plain,
% 0.73/0.91 (op(e1, e0) = e2),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4934, 4962, 766])).
% 0.73/0.91 tff(4964,plain,
% 0.73/0.91 ((op(e0, e0) = op(e1, e0)) <=> (op(e0, e0) = e2)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4963])).
% 0.73/0.91 tff(4965,plain,
% 0.73/0.91 ((op(e0, e0) = e2) <=> (op(e0, e0) = op(e1, e0))),
% 0.73/0.91 inference(symmetry,[status(thm)],[4964])).
% 0.73/0.91 tff(4966,plain,
% 0.73/0.91 ((op(e3, e0) = op(e3, e3)) <=> (op(e3, e0) = e2)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4959])).
% 0.73/0.91 tff(4967,plain,
% 0.73/0.91 ((~(op(e3, e0) = op(e3, e3))) <=> (~(op(e3, e0) = e2))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4966])).
% 0.73/0.91 tff(4968,plain,
% 0.73/0.91 (~(op(e3, e0) = e2)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[257, 4967])).
% 0.73/0.91 tff(4969,plain,
% 0.73/0.91 ((op(e0, e0) = e2) | (~(op(e0, op(e1, e0)) = e0)) | (op(e3, e0) = e2) | (op(e0, e3) = e2)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4294, 4819])).
% 0.73/0.91 tff(4970,plain,
% 0.73/0.91 (op(e0, e0) = e2),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4969, 4968, 1832, 104])).
% 0.73/0.91 tff(4971,plain,
% 0.73/0.91 (op(e0, e0) = op(e1, e0)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[4970, 4965])).
% 0.73/0.91 tff(4972,plain,
% 0.73/0.91 ($false),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[1056, 4971])).
% 0.73/0.91 tff(4973,plain,((op(e0, e3) = e2) | (~(op(e0, op(e1, e0)) = e0)) | (op(e1, e2) = e2) | (op(e3, e3) = e1) | (op(e3, e3) = e0) | (~(op(e3, op(e1, e3)) = e3))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.91 tff(4974,plain,
% 0.73/0.91 (op(e0, e3) = e2),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4973, 63, 4909, 4946, 4940, 4939])).
% 0.73/0.91 tff(4975,plain,
% 0.73/0.91 ((op(e0, e3) = e1) <=> (e2 = e1)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4974])).
% 0.73/0.91 tff(4976,plain,
% 0.73/0.91 ((op(e0, e3) = e1) <=> (e1 = e2)),
% 0.73/0.91 inference(transitivity,[status(thm)],[4975, 317])).
% 0.73/0.91 tff(4977,plain,
% 0.73/0.91 ((e1 = e2) <=> (op(e0, e3) = e1)),
% 0.73/0.91 inference(symmetry,[status(thm)],[4976])).
% 0.73/0.91 tff(4978,plain,
% 0.73/0.91 ((~(e1 = e2)) <=> (~(op(e0, e3) = e1))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4977])).
% 0.73/0.91 tff(4979,plain,
% 0.73/0.91 (~(op(e0, e3) = e1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[324, 4978])).
% 0.73/0.91 tff(4980,plain,
% 0.73/0.91 (op(e0, e0) = e1),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[718, 4979, 433, 4938])).
% 0.73/0.91 tff(4981,plain,
% 0.73/0.91 ((op(e0, e0) = op(e2, e0)) <=> (e1 = op(e2, e0))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4980])).
% 0.73/0.91 tff(4982,plain,
% 0.73/0.91 ((op(e0, e0) = op(e2, e0)) <=> (op(e2, e0) = e1)),
% 0.73/0.91 inference(transitivity,[status(thm)],[4981, 1384])).
% 0.73/0.91 tff(4983,plain,
% 0.73/0.91 ((op(e2, e0) = e1) <=> (op(e0, e0) = op(e2, e0))),
% 0.73/0.91 inference(symmetry,[status(thm)],[4982])).
% 0.73/0.91 tff(4984,plain,
% 0.73/0.91 ((op(e0, e3) = e0) <=> (e2 = e0)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4974])).
% 0.73/0.91 tff(4985,plain,
% 0.73/0.91 ((op(e0, e3) = e0) <=> (e0 = e2)),
% 0.73/0.91 inference(transitivity,[status(thm)],[4984, 217])).
% 0.73/0.91 tff(4986,plain,
% 0.73/0.91 ((e0 = e2) <=> (op(e0, e3) = e0)),
% 0.73/0.91 inference(symmetry,[status(thm)],[4985])).
% 0.73/0.91 tff(4987,plain,
% 0.73/0.91 ((~(e0 = e2)) <=> (~(op(e0, e3) = e0))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4986])).
% 0.73/0.91 tff(4988,plain,
% 0.73/0.91 (~(op(e0, e3) = e0)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[238, 4987])).
% 0.73/0.91 tff(4989,plain,
% 0.73/0.91 ((op(e3, e0) = op(e3, e1)) <=> (op(e3, e0) = e1)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4942])).
% 0.73/0.91 tff(4990,plain,
% 0.73/0.91 ((~(op(e3, e0) = op(e3, e1))) <=> (~(op(e3, e0) = e1))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4989])).
% 0.73/0.91 tff(4991,plain,
% 0.73/0.91 (~(op(e3, e0) = e1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[1333, 4990])).
% 0.73/0.91 tff(4992,plain,
% 0.73/0.91 ((op(e0, e0) = op(e0, e3)) <=> (op(e0, e0) = e2)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4974])).
% 0.73/0.91 tff(4993,plain,
% 0.73/0.91 ((~(op(e0, e0) = op(e0, e3))) <=> (~(op(e0, e0) = e2))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4992])).
% 0.73/0.91 tff(4994,plain,
% 0.73/0.91 (~(op(e0, e0) = e2)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[2178, 4993])).
% 0.73/0.91 tff(4995,plain,
% 0.73/0.91 ((op(e0, e2) = op(e0, e3)) <=> (op(e0, e2) = e2)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4974])).
% 0.73/0.91 tff(4996,plain,
% 0.73/0.91 ((~(op(e0, e2) = op(e0, e3))) <=> (~(op(e0, e2) = e2))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4995])).
% 0.73/0.91 tff(4997,plain,
% 0.73/0.91 (~(op(e0, e2) = e2)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[215, 4996])).
% 0.73/0.91 tff(4998,plain,
% 0.73/0.91 ((op(e0, e3) = op(e1, e3)) <=> (e2 = op(e1, e3))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4974])).
% 0.73/0.91 tff(4999,plain,
% 0.73/0.91 ((op(e0, e3) = op(e1, e3)) <=> (op(e1, e3) = e2)),
% 0.73/0.91 inference(transitivity,[status(thm)],[4998, 218])).
% 0.73/0.91 tff(5000,plain,
% 0.73/0.91 ((~(op(e0, e3) = op(e1, e3))) <=> (~(op(e1, e3) = e2))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4999])).
% 0.73/0.91 tff(5001,plain,
% 0.73/0.91 (~(op(e1, e3) = e2)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[1755, 5000])).
% 0.73/0.91 tff(5002,plain,
% 0.73/0.91 ((op(e0, e3) = op(e3, e3)) <=> (e2 = op(e3, e3))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4974])).
% 0.73/0.91 tff(5003,plain,
% 0.73/0.91 ((op(e0, e3) = op(e3, e3)) <=> (op(e3, e3) = e2)),
% 0.73/0.91 inference(transitivity,[status(thm)],[5002, 1024])).
% 0.73/0.91 tff(5004,plain,
% 0.73/0.91 ((~(op(e0, e3) = op(e3, e3))) <=> (~(op(e3, e3) = e2))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5003])).
% 0.73/0.91 tff(5005,plain,
% 0.73/0.91 (~(op(e3, e3) = e2)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[725, 5004])).
% 0.73/0.91 tff(5006,plain,
% 0.73/0.91 ((op(e3, e1) = e2) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e3, e3) = e0) | (op(e0, e3) = e0) | (op(e0, e1) = e1) | (op(e2, e0) = e1) | (op(e0, e2) = e2) | (op(e1, e3) = e2) | (op(e0, e0) = e2) | (op(e3, e3) = e2) | (op(e1, e1) = e2) | (op(e2, e3) = e2) | (op(e3, e0) = e1) | (op(e1, e0) = e1)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[3404, 1605])).
% 0.73/0.91 tff(5007,plain,
% 0.73/0.91 ((~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e3, e3) = e0) | (op(e0, e3) = e0) | (op(e0, e1) = e1) | (op(e2, e0) = e1) | (op(e0, e2) = e2) | (op(e1, e3) = e2) | (op(e0, e0) = e2) | (op(e3, e3) = e2) | (op(e3, e0) = e1) | (op(e1, e0) = e1)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[5006, 4849, 4785, 4796])).
% 0.73/0.91 tff(5008,plain,
% 0.73/0.91 (op(e2, e0) = e1),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[5007, 5005, 63, 5001, 4997, 4994, 1221, 433, 4991, 4988, 4926])).
% 0.73/0.91 tff(5009,plain,
% 0.73/0.91 (op(e0, e0) = op(e2, e0)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[5008, 4983])).
% 0.73/0.91 tff(5010,plain,
% 0.73/0.91 ($false),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[1827, 5009])).
% 0.73/0.91 tff(5011,plain,((op(e3, e3) = e0) | (~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e0, e1) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.91 tff(5012,plain,
% 0.73/0.91 (op(e3, e3) = e0),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[5011, 1221, 433])).
% 0.73/0.91 tff(5013,plain,
% 0.73/0.91 ((op(e1, e3) = op(e3, e3)) <=> (op(e1, e3) = e0)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5012])).
% 0.73/0.91 tff(5014,plain,
% 0.73/0.91 ((~(op(e1, e3) = op(e3, e3))) <=> (~(op(e1, e3) = e0))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5013])).
% 0.73/0.91 tff(5015,plain,
% 0.73/0.91 (~(op(e1, e3) = e0)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[368, 5014])).
% 0.73/0.91 tff(5016,plain,
% 0.73/0.91 (op(e1, e0) = e0),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[657, 4930, 5015, 4919])).
% 0.73/0.91 tff(5017,plain,
% 0.73/0.91 (e0 = op(e1, e0)),
% 0.73/0.91 inference(symmetry,[status(thm)],[5016])).
% 0.73/0.91 tff(5018,plain,
% 0.73/0.91 (e0 = e2),
% 0.73/0.91 inference(transitivity,[status(thm)],[5017, 4935])).
% 0.73/0.91 tff(5019,plain,
% 0.73/0.91 ($false),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[238, 5018])).
% 0.73/0.91 tff(5020,plain,((~((~(op(e0, op(e0, e0)) = e0)) | (~(op(e1, op(e0, e1)) = e1)) | (~(op(e2, op(e0, e2)) = e2)) | (~(op(e3, op(e0, e3)) = e3)))) | (op(e0, e1) = e1)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.91 tff(5021,plain,
% 0.73/0.91 (op(e0, e1) = e1),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[5020, 4887])).
% 0.73/0.91 tff(5022,assumption,(op(e0, e0) = e0), introduced(assumption)).
% 0.73/0.91 tff(5023,plain,
% 0.73/0.91 ((op(e0, e0) = op(e0, e2)) <=> (e0 = op(e0, e2))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5022])).
% 0.73/0.91 tff(5024,plain,
% 0.73/0.91 ((op(e0, e0) = op(e0, e2)) <=> (op(e0, e2) = e0)),
% 0.73/0.91 inference(transitivity,[status(thm)],[5023, 988])).
% 0.73/0.91 tff(5025,plain,
% 0.73/0.91 ((~(op(e0, e0) = op(e0, e2))) <=> (~(op(e0, e2) = e0))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5024])).
% 0.73/0.91 tff(5026,plain,
% 0.73/0.91 (~(op(e0, e2) = e0)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[1190, 5025])).
% 0.73/0.91 tff(5027,plain,
% 0.73/0.91 (((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (~(op(e0, e1) = e1)) | (op(e3, e0) = e2)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[1720, 4785])).
% 0.73/0.91 tff(5028,plain,
% 0.73/0.91 (op(e3, e0) = e2),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[5027, 334, 5021])).
% 0.73/0.91 tff(5029,plain,
% 0.73/0.91 (e2 = op(e3, e0)),
% 0.73/0.91 inference(symmetry,[status(thm)],[5028])).
% 0.73/0.91 tff(5030,plain,
% 0.73/0.91 (op(e0, e2) = op(e0, op(e3, e0))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5029])).
% 0.73/0.91 tff(5031,plain,
% 0.73/0.91 (op(e0, e2) = e0),
% 0.73/0.91 inference(transitivity,[status(thm)],[5030, 1655])).
% 0.73/0.91 tff(5032,assumption,(~(op(e0, e2) = e0)), introduced(assumption)).
% 0.73/0.91 tff(5033,plain,
% 0.73/0.91 ($false),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[5032, 5031])).
% 0.73/0.91 tff(5034,plain,(((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))) | (op(e0, e2) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.91 tff(5035,plain,
% 0.73/0.91 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[5034, 5026])).
% 0.73/0.91 tff(5036,plain,
% 0.73/0.91 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[681, 5035, 4903, 4887])).
% 0.73/0.91 tff(5037,plain,
% 0.73/0.91 (op(e1, op(e1, e1)) = e1),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[1315, 5036])).
% 0.73/0.91 tff(5038,plain,
% 0.73/0.91 ((op(e0, e1) = op(e1, e1)) <=> (e1 = op(e1, e1))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5021])).
% 0.73/0.91 tff(5039,plain,
% 0.73/0.91 ((op(e0, e1) = op(e1, e1)) <=> (op(e1, e1) = e1)),
% 0.73/0.91 inference(transitivity,[status(thm)],[5038, 434])).
% 0.73/0.91 tff(5040,plain,
% 0.73/0.91 ((~(op(e0, e1) = op(e1, e1))) <=> (~(op(e1, e1) = e1))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5039])).
% 0.73/0.91 tff(5041,plain,
% 0.73/0.91 (~(op(e1, e1) = e1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[100, 5040])).
% 0.73/0.91 tff(5042,plain,
% 0.73/0.91 (op(e2, op(e1, e2)) = e2),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[102, 5036])).
% 0.73/0.91 tff(5043,plain,
% 0.73/0.91 (~(op(e1, e2) = e3)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4911, 5042])).
% 0.73/0.91 tff(5044,plain,
% 0.73/0.91 (~(op(e1, e2) = e0)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4918, 5042])).
% 0.73/0.91 tff(5045,plain,
% 0.73/0.91 (~(op(e1, e2) = e2)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4908, 5042])).
% 0.73/0.91 tff(5046,plain,
% 0.73/0.91 (op(e1, e2) = e1),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[193, 5045, 5044, 5043])).
% 0.73/0.91 tff(5047,plain,
% 0.73/0.91 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e0) = e1)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5046])).
% 0.73/0.91 tff(5048,plain,
% 0.73/0.91 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = e1))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5047])).
% 0.73/0.91 tff(5049,plain,
% 0.73/0.91 (~(op(e1, e0) = e1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[1428, 5048])).
% 0.73/0.91 tff(5050,plain,
% 0.73/0.91 (~(op(e1, e1) = e0)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4929, 5049, 5037])).
% 0.73/0.91 tff(5051,plain,
% 0.73/0.91 (op(e1, e1) = e3),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4931, 5050, 5041])).
% 0.73/0.91 tff(5052,plain,
% 0.73/0.91 (op(e1, op(e1, e1)) = op(e1, e3)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5051])).
% 0.73/0.91 tff(5053,plain,
% 0.73/0.91 (op(e1, e3) = op(e1, op(e1, e1))),
% 0.73/0.91 inference(symmetry,[status(thm)],[5052])).
% 0.73/0.91 tff(5054,plain,
% 0.73/0.91 ((op(e0, e0) = op(e1, e0)) <=> (e0 = op(e1, e0))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5022])).
% 0.73/0.91 tff(5055,plain,
% 0.73/0.91 ((op(e0, e0) = op(e1, e0)) <=> (op(e1, e0) = e0)),
% 0.73/0.91 inference(transitivity,[status(thm)],[5054, 1345])).
% 0.73/0.91 tff(5056,plain,
% 0.73/0.91 ((~(op(e0, e0) = op(e1, e0))) <=> (~(op(e1, e0) = e0))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5055])).
% 0.73/0.91 tff(5057,plain,
% 0.73/0.91 (~(op(e1, e0) = e0)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[1056, 5056])).
% 0.73/0.91 tff(5058,plain,
% 0.73/0.91 (op(e1, e3) = e0),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[657, 5050, 5057, 5044])).
% 0.73/0.91 tff(5059,plain,
% 0.73/0.91 (e0 = op(e1, e3)),
% 0.73/0.91 inference(symmetry,[status(thm)],[5058])).
% 0.73/0.91 tff(5060,plain,
% 0.73/0.91 (e0 = e1),
% 0.73/0.91 inference(transitivity,[status(thm)],[5059, 5053, 5037])).
% 0.73/0.91 tff(5061,plain,
% 0.73/0.91 ($false),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[625, 5060])).
% 0.73/0.91 tff(5062,plain,(~(op(e0, e0) = e0)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.91 tff(5063,plain,
% 0.73/0.91 ((~(op(e0, e1) = e1)) | (op(e0, e0) = e0) | (op(e3, e3) = e0)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[3899, 4785])).
% 0.73/0.91 tff(5064,plain,
% 0.73/0.91 (op(e3, e3) = e0),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[5063, 5062, 5021])).
% 0.73/0.91 tff(5065,plain,
% 0.73/0.91 ((~(op(e0, op(e3, e0)) = e0)) | (~(op(e1, op(e3, e1)) = e1)) | (~(op(e2, op(e3, e2)) = e2)) | (~(op(e3, op(e3, e3)) = e3))),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[1669, 5064])).
% 0.73/0.91 tff(5066,plain,
% 0.73/0.91 (~((~(op(e0, op(e1, e0)) = e0)) | (~(op(e1, op(e1, e1)) = e1)) | (~(op(e2, op(e1, e2)) = e2)) | (~(op(e3, op(e1, e3)) = e3)))),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[681, 5065, 4903, 4887])).
% 0.73/0.91 tff(5067,plain,
% 0.73/0.91 (op(e1, op(e1, e1)) = e1),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[1315, 5066])).
% 0.73/0.91 tff(5068,plain,
% 0.73/0.91 (op(e2, op(e1, e2)) = e2),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[102, 5066])).
% 0.73/0.91 tff(5069,plain,
% 0.73/0.91 (~(op(e1, e2) = e3)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4911, 5068])).
% 0.73/0.91 tff(5070,plain,
% 0.73/0.91 (~(op(e1, e2) = e0)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4918, 5068])).
% 0.73/0.91 tff(5071,plain,
% 0.73/0.91 (~(op(e1, e2) = e2)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[4908, 5068])).
% 0.73/0.91 tff(5072,plain,
% 0.73/0.91 (op(e1, e2) = e1),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[193, 5071, 5070, 5069])).
% 0.73/0.91 tff(5073,plain,
% 0.73/0.91 ((op(e1, e0) = op(e1, e2)) <=> (op(e1, e0) = e1)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5072])).
% 0.73/0.91 tff(5074,plain,
% 0.73/0.91 ((~(op(e1, e0) = op(e1, e2))) <=> (~(op(e1, e0) = e1))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5073])).
% 0.73/0.91 tff(5075,plain,
% 0.73/0.91 (~(op(e1, e0) = e1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[1428, 5074])).
% 0.73/0.91 tff(5076,plain,
% 0.73/0.91 ((op(e0, e1) = e0) <=> (e1 = e0)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5021])).
% 0.73/0.91 tff(5077,plain,
% 0.73/0.91 ((op(e0, e1) = e0) <=> (e0 = e1)),
% 0.73/0.91 inference(transitivity,[status(thm)],[5076, 635])).
% 0.73/0.91 tff(5078,plain,
% 0.73/0.91 ((e0 = e1) <=> (op(e0, e1) = e0)),
% 0.73/0.91 inference(symmetry,[status(thm)],[5077])).
% 0.73/0.91 tff(5079,plain,
% 0.73/0.91 ((~(e0 = e1)) <=> (~(op(e0, e1) = e0))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5078])).
% 0.73/0.91 tff(5080,plain,
% 0.73/0.91 (~(op(e0, e1) = e0)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[625, 5079])).
% 0.73/0.91 tff(5081,plain,
% 0.73/0.91 ((op(e3, e1) = op(e3, e3)) <=> (op(e3, e1) = e0)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5064])).
% 0.73/0.91 tff(5082,plain,
% 0.73/0.91 ((~(op(e3, e1) = op(e3, e3))) <=> (~(op(e3, e1) = e0))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5081])).
% 0.73/0.91 tff(5083,plain,
% 0.73/0.91 (~(op(e3, e1) = e0)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[399, 5082])).
% 0.73/0.91 tff(5084,plain,
% 0.73/0.91 ((op(e2, e1) = e0) <=> (e2 = e0)),
% 0.73/0.91 inference(monotonicity,[status(thm)],[4782])).
% 0.73/0.91 tff(5085,plain,
% 0.73/0.91 ((op(e2, e1) = e0) <=> (e0 = e2)),
% 0.73/0.91 inference(transitivity,[status(thm)],[5084, 217])).
% 0.73/0.91 tff(5086,plain,
% 0.73/0.91 ((e0 = e2) <=> (op(e2, e1) = e0)),
% 0.73/0.91 inference(symmetry,[status(thm)],[5085])).
% 0.73/0.91 tff(5087,plain,
% 0.73/0.91 ((~(e0 = e2)) <=> (~(op(e2, e1) = e0))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[5086])).
% 0.73/0.91 tff(5088,plain,
% 0.73/0.91 (~(op(e2, e1) = e0)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[238, 5087])).
% 0.73/0.91 tff(5089,plain,
% 0.73/0.91 ((op(e0, e1) = e0) | (op(e1, e1) = e0) | (op(e3, e1) = e0)),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[619, 5088])).
% 0.73/0.92 tff(5090,plain,
% 0.73/0.92 (op(e1, e1) = e0),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[5089, 5083, 5080])).
% 0.73/0.92 tff(5091,plain,
% 0.73/0.92 ($false),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[4929, 5090, 5075, 5067])).
% 0.73/0.92 % SZS output end Proof
% 0.73/0.92 % E exiting
%------------------------------------------------------------------------------