%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG067+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 12:53:20 PM UTC 2026
% Result : Theorem 0.92s 7.01s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 25
% Syntax : Number of formulae : 193 ( 1 unt; 24 def)
% Number of atoms : 1017 ( 752 equ)
% Maximal formula atoms : 125 ( 5 avg)
% Number of connectives : 1285 ( 461 ~; 476 |; 348 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 55 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 26 ( 24 usr; 25 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,conjecture,
~ ( ( ( op(e4,e4) != e4
& op(e4,e4) = e4
& op(e4,e4) = e4 )
| ( op(e4,e3) != e4
& op(e3,e3) = e4
& op(e4,e4) = e3 )
| ( op(e4,e2) != e4
& op(e2,e2) = e4
& op(e4,e4) = e2 )
| ( op(e4,e1) != e4
& op(e1,e1) = e4
& op(e4,e4) = e1 )
| ( op(e4,e0) != e4
& op(e0,e0) = e4
& op(e4,e4) = e0 )
| ( op(e3,e4) != e3
& op(e4,e4) = e3
& op(e3,e3) = e4 )
| ( op(e3,e3) != e3
& op(e3,e3) = e3
& op(e3,e3) = e3 )
| ( op(e3,e2) != e3
& op(e2,e2) = e3
& op(e3,e3) = e2 )
| ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 )
| ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 )
| ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 )
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 )
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) )
& ( op(e4,e4) = e4
| op(e4,e4) != e4 )
& ( op(e4,e3) = e4
| op(e4,e4) != e3 )
& ( op(e4,e2) = e4
| op(e4,e4) != e2 )
& ( op(e4,e1) = e4
| op(e4,e4) != e1 )
& ( op(e4,e0) = e4
| op(e4,e4) != e0 )
& ( op(e3,e4) = e3
| op(e3,e3) != e4 )
& ( op(e3,e3) = e3
| op(e3,e3) != e3 )
& ( op(e3,e2) = e3
| op(e3,e3) != e2 )
& ( op(e3,e1) = e3
| op(e3,e3) != e1 )
& ( op(e3,e0) = e3
| op(e3,e3) != e0 )
& ( op(e2,e4) = e2
| op(e2,e2) != e4 )
& ( op(e2,e3) = e2
| op(e2,e2) != e3 )
& ( op(e2,e2) = e2
| op(e2,e2) != e2 )
& ( op(e2,e1) = e2
| op(e2,e2) != e1 )
& ( op(e2,e0) = e2
| op(e2,e2) != e0 )
& ( op(e1,e4) = e1
| op(e1,e1) != e4 )
& ( op(e1,e3) = e1
| op(e1,e1) != e3 )
& ( op(e1,e2) = e1
| op(e1,e1) != e2 )
& ( op(e1,e1) = e1
| op(e1,e1) != e1 )
& ( op(e1,e0) = e1
| op(e1,e1) != e0 )
& ( op(e0,e4) = e0
| op(e0,e0) != e4 )
& ( op(e0,e3) = e0
| op(e0,e0) != e3 )
& ( op(e0,e2) = e0
| op(e0,e0) != e2 )
& ( op(e0,e1) = e0
| op(e0,e0) != e1 )
& ( op(e0,e0) = e0
| op(e0,e0) != e0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f8,negated_conjecture,
~ ~ ( ( ( op(e4,e4) != e4
& op(e4,e4) = e4
& op(e4,e4) = e4 )
| ( op(e4,e3) != e4
& op(e3,e3) = e4
& op(e4,e4) = e3 )
| ( op(e4,e2) != e4
& op(e2,e2) = e4
& op(e4,e4) = e2 )
| ( op(e4,e1) != e4
& op(e1,e1) = e4
& op(e4,e4) = e1 )
| ( op(e4,e0) != e4
& op(e0,e0) = e4
& op(e4,e4) = e0 )
| ( op(e3,e4) != e3
& op(e4,e4) = e3
& op(e3,e3) = e4 )
| ( op(e3,e3) != e3
& op(e3,e3) = e3
& op(e3,e3) = e3 )
| ( op(e3,e2) != e3
& op(e2,e2) = e3
& op(e3,e3) = e2 )
| ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 )
| ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 )
| ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 )
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 )
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) )
& ( op(e4,e4) = e4
| op(e4,e4) != e4 )
& ( op(e4,e3) = e4
| op(e4,e4) != e3 )
& ( op(e4,e2) = e4
| op(e4,e4) != e2 )
& ( op(e4,e1) = e4
| op(e4,e4) != e1 )
& ( op(e4,e0) = e4
| op(e4,e4) != e0 )
& ( op(e3,e4) = e3
| op(e3,e3) != e4 )
& ( op(e3,e3) = e3
| op(e3,e3) != e3 )
& ( op(e3,e2) = e3
| op(e3,e3) != e2 )
& ( op(e3,e1) = e3
| op(e3,e3) != e1 )
& ( op(e3,e0) = e3
| op(e3,e3) != e0 )
& ( op(e2,e4) = e2
| op(e2,e2) != e4 )
& ( op(e2,e3) = e2
| op(e2,e2) != e3 )
& ( op(e2,e2) = e2
| op(e2,e2) != e2 )
& ( op(e2,e1) = e2
| op(e2,e2) != e1 )
& ( op(e2,e0) = e2
| op(e2,e2) != e0 )
& ( op(e1,e4) = e1
| op(e1,e1) != e4 )
& ( op(e1,e3) = e1
| op(e1,e1) != e3 )
& ( op(e1,e2) = e1
| op(e1,e1) != e2 )
& ( op(e1,e1) = e1
| op(e1,e1) != e1 )
& ( op(e1,e0) = e1
| op(e1,e1) != e0 )
& ( op(e0,e4) = e0
| op(e0,e0) != e4 )
& ( op(e0,e3) = e0
| op(e0,e0) != e3 )
& ( op(e0,e2) = e0
| op(e0,e0) != e2 )
& ( op(e0,e1) = e0
| op(e0,e0) != e1 )
& ( op(e0,e0) = e0
| op(e0,e0) != e0 ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
( ( ( op(e4,e4) != e4
& op(e4,e4) = e4
& op(e4,e4) = e4 )
| ( op(e4,e3) != e4
& op(e3,e3) = e4
& op(e4,e4) = e3 )
| ( op(e4,e2) != e4
& op(e2,e2) = e4
& op(e4,e4) = e2 )
| ( op(e4,e1) != e4
& op(e1,e1) = e4
& op(e4,e4) = e1 )
| ( op(e4,e0) != e4
& op(e0,e0) = e4
& op(e4,e4) = e0 )
| ( op(e3,e4) != e3
& op(e4,e4) = e3
& op(e3,e3) = e4 )
| ( op(e3,e3) != e3
& op(e3,e3) = e3
& op(e3,e3) = e3 )
| ( op(e3,e2) != e3
& op(e2,e2) = e3
& op(e3,e3) = e2 )
| ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 )
| ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 )
| ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 )
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 )
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) )
& ( op(e4,e4) = e4
| op(e4,e4) != e4 )
& ( op(e4,e3) = e4
| op(e4,e4) != e3 )
& ( op(e4,e2) = e4
| op(e4,e4) != e2 )
& ( op(e4,e1) = e4
| op(e4,e4) != e1 )
& ( op(e4,e0) = e4
| op(e4,e4) != e0 )
& ( op(e3,e4) = e3
| op(e3,e3) != e4 )
& ( op(e3,e3) = e3
| op(e3,e3) != e3 )
& ( op(e3,e2) = e3
| op(e3,e3) != e2 )
& ( op(e3,e1) = e3
| op(e3,e3) != e1 )
& ( op(e3,e0) = e3
| op(e3,e3) != e0 )
& ( op(e2,e4) = e2
| op(e2,e2) != e4 )
& ( op(e2,e3) = e2
| op(e2,e2) != e3 )
& ( op(e2,e2) = e2
| op(e2,e2) != e2 )
& ( op(e2,e1) = e2
| op(e2,e2) != e1 )
& ( op(e2,e0) = e2
| op(e2,e2) != e0 )
& ( op(e1,e4) = e1
| op(e1,e1) != e4 )
& ( op(e1,e3) = e1
| op(e1,e1) != e3 )
& ( op(e1,e2) = e1
| op(e1,e1) != e2 )
& ( op(e1,e1) = e1
| op(e1,e1) != e1 )
& ( op(e1,e0) = e1
| op(e1,e1) != e0 )
& ( op(e0,e4) = e0
| op(e0,e0) != e4 )
& ( op(e0,e3) = e0
| op(e0,e0) != e3 )
& ( op(e0,e2) = e0
| op(e0,e0) != e2 )
& ( op(e0,e1) = e0
| op(e0,e0) != e1 )
& ( op(e0,e0) = e0
| op(e0,e0) != e0 ) ),
inference(flattening,[],[f8]) ).
fof(f35,plain,
( ~ sP23
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f36,plain,
( ~ sP22
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f37,plain,
( ~ sP21
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f38,plain,
( ~ sP20
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f39,plain,
( ~ sP19
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f40,plain,
( ~ sP18
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f41,plain,
( ~ sP17
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f42,plain,
( ~ sP16
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f43,plain,
( ~ sP15
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f44,plain,
( ~ sP14
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f45,plain,
( ~ sP13
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f46,plain,
( ~ sP12
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f47,plain,
( ~ sP11
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f48,plain,
( ~ sP10
| ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f49,plain,
( ~ sP9
| ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f50,plain,
( ~ sP8
| ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f51,plain,
( ~ sP7
| ( op(e3,e2) != e3
& op(e2,e2) = e3
& op(e3,e3) = e2 ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f52,plain,
( ~ sP6
| ( op(e3,e3) != e3
& op(e3,e3) = e3
& op(e3,e3) = e3 ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f53,plain,
( ~ sP5
| ( op(e3,e4) != e3
& op(e4,e4) = e3
& op(e3,e3) = e4 ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f54,plain,
( ~ sP4
| ( op(e4,e0) != e4
& op(e0,e0) = e4
& op(e4,e4) = e0 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f55,plain,
( ~ sP3
| ( op(e4,e1) != e4
& op(e1,e1) = e4
& op(e4,e4) = e1 ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f56,plain,
( ~ sP2
| ( op(e4,e2) != e4
& op(e2,e2) = e4
& op(e4,e4) = e2 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f57,plain,
( ~ sP1
| ( op(e4,e3) != e4
& op(e3,e3) = e4
& op(e4,e4) = e3 ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f258,plain,
( ~ sP23
| e0 != op(e0,e1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f260,plain,
( ~ sP23
| op(e0,e0) = e1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f261,plain,
( ~ sP22
| e0 != op(e0,e2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f263,plain,
( ~ sP22
| op(e0,e0) = e2 ),
inference(cnf_transformation,[],[f36]) ).
fof(f264,plain,
( ~ sP21
| e0 != op(e0,e3) ),
inference(cnf_transformation,[],[f37]) ).
fof(f266,plain,
( ~ sP21
| op(e0,e0) = e3 ),
inference(cnf_transformation,[],[f37]) ).
fof(f267,plain,
( ~ sP20
| e0 != op(e0,e4) ),
inference(cnf_transformation,[],[f38]) ).
fof(f269,plain,
( ~ sP20
| op(e0,e0) = e4 ),
inference(cnf_transformation,[],[f38]) ).
fof(f270,plain,
( ~ sP19
| e1 != op(e1,e0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f272,plain,
( ~ sP19
| e0 = op(e1,e1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f273,plain,
( ~ sP18
| e1 != op(e1,e1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f274,plain,
( ~ sP18
| e1 = op(e1,e1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f276,plain,
( ~ sP17
| e1 != op(e1,e2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f278,plain,
( ~ sP17
| e2 = op(e1,e1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f279,plain,
( ~ sP16
| e1 != op(e1,e3) ),
inference(cnf_transformation,[],[f42]) ).
fof(f281,plain,
( ~ sP16
| e3 = op(e1,e1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f282,plain,
( ~ sP15
| e1 != op(e1,e4) ),
inference(cnf_transformation,[],[f43]) ).
fof(f284,plain,
( ~ sP15
| e4 = op(e1,e1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f285,plain,
( ~ sP14
| e2 != op(e2,e0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f287,plain,
( ~ sP14
| e0 = op(e2,e2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f288,plain,
( ~ sP13
| e2 != op(e2,e1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f290,plain,
( ~ sP13
| e1 = op(e2,e2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f291,plain,
( ~ sP12
| e2 != op(e2,e2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f292,plain,
( ~ sP12
| e2 = op(e2,e2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f294,plain,
( ~ sP11
| e2 != op(e2,e3) ),
inference(cnf_transformation,[],[f47]) ).
fof(f296,plain,
( ~ sP11
| e3 = op(e2,e2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f297,plain,
( ~ sP10
| e2 != op(e2,e4) ),
inference(cnf_transformation,[],[f48]) ).
fof(f299,plain,
( ~ sP10
| e4 = op(e2,e2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f300,plain,
( ~ sP9
| e3 != op(e3,e0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f302,plain,
( ~ sP9
| e0 = op(e3,e3) ),
inference(cnf_transformation,[],[f49]) ).
fof(f303,plain,
( ~ sP8
| e3 != op(e3,e1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f305,plain,
( ~ sP8
| e1 = op(e3,e3) ),
inference(cnf_transformation,[],[f50]) ).
fof(f306,plain,
( ~ sP7
| e3 != op(e3,e2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f308,plain,
( ~ sP7
| e2 = op(e3,e3) ),
inference(cnf_transformation,[],[f51]) ).
fof(f309,plain,
( ~ sP6
| e3 != op(e3,e3) ),
inference(cnf_transformation,[],[f52]) ).
fof(f310,plain,
( ~ sP6
| e3 = op(e3,e3) ),
inference(cnf_transformation,[],[f52]) ).
fof(f312,plain,
( ~ sP5
| e3 != op(e3,e4) ),
inference(cnf_transformation,[],[f53]) ).
fof(f314,plain,
( ~ sP5
| e4 = op(e3,e3) ),
inference(cnf_transformation,[],[f53]) ).
fof(f315,plain,
( ~ sP4
| e4 != op(e4,e0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f317,plain,
( ~ sP4
| e0 = op(e4,e4) ),
inference(cnf_transformation,[],[f54]) ).
fof(f318,plain,
( ~ sP3
| e4 != op(e4,e1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f320,plain,
( ~ sP3
| e1 = op(e4,e4) ),
inference(cnf_transformation,[],[f55]) ).
fof(f321,plain,
( ~ sP2
| e4 != op(e4,e2) ),
inference(cnf_transformation,[],[f56]) ).
fof(f323,plain,
( ~ sP2
| e2 = op(e4,e4) ),
inference(cnf_transformation,[],[f56]) ).
fof(f324,plain,
( ~ sP1
| e4 != op(e4,e3) ),
inference(cnf_transformation,[],[f57]) ).
fof(f326,plain,
( ~ sP1
| e3 = op(e4,e4) ),
inference(cnf_transformation,[],[f57]) ).
fof(f330,plain,
( sP0
| sP1
| sP2
| sP3
| sP4
| sP5
| sP6
| sP7
| sP8
| sP9
| sP10
| sP11
| sP12
| sP13
| sP14
| sP15
| sP16
| sP17
| sP18
| sP19
| sP20
| sP21
| sP22
| sP23
| e0 != op(e0,e0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f331,plain,
( sP0
| sP1
| sP2
| sP3
| sP4
| sP5
| sP6
| sP7
| sP8
| sP9
| sP10
| sP11
| sP12
| sP13
| sP14
| sP15
| sP16
| sP17
| sP18
| sP19
| sP20
| sP21
| sP22
| sP23
| e0 = op(e0,e0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f334,plain,
( e4 = op(e4,e3)
| e3 != op(e4,e4) ),
inference(cnf_transformation,[],[f34]) ).
fof(f335,plain,
( e4 = op(e4,e2)
| e2 != op(e4,e4) ),
inference(cnf_transformation,[],[f34]) ).
fof(f336,plain,
( e4 = op(e4,e1)
| e1 != op(e4,e4) ),
inference(cnf_transformation,[],[f34]) ).
fof(f337,plain,
( e4 = op(e4,e0)
| e0 != op(e4,e4) ),
inference(cnf_transformation,[],[f34]) ).
fof(f338,plain,
( e3 = op(e3,e4)
| e4 != op(e3,e3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f340,plain,
( e3 = op(e3,e2)
| e2 != op(e3,e3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f341,plain,
( e3 = op(e3,e1)
| e1 != op(e3,e3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f342,plain,
( e3 = op(e3,e0)
| e0 != op(e3,e3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f343,plain,
( e2 = op(e2,e4)
| e4 != op(e2,e2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f344,plain,
( e2 = op(e2,e3)
| e3 != op(e2,e2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f346,plain,
( e2 = op(e2,e1)
| e1 != op(e2,e2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f347,plain,
( e2 = op(e2,e0)
| e0 != op(e2,e2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f348,plain,
( e1 = op(e1,e4)
| e4 != op(e1,e1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f349,plain,
( e1 = op(e1,e3)
| e3 != op(e1,e1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f350,plain,
( e1 = op(e1,e2)
| e2 != op(e1,e1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f352,plain,
( e1 = op(e1,e0)
| e0 != op(e1,e1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f353,plain,
( e0 = op(e0,e4)
| op(e0,e0) != e4 ),
inference(cnf_transformation,[],[f34]) ).
fof(f354,plain,
( e0 = op(e0,e3)
| op(e0,e0) != e3 ),
inference(cnf_transformation,[],[f34]) ).
fof(f355,plain,
( e0 = op(e0,e2)
| op(e0,e0) != e2 ),
inference(cnf_transformation,[],[f34]) ).
fof(f356,plain,
( e0 = op(e0,e1)
| op(e0,e0) != e1 ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_248,plain,
( ( op(e0,e0) = e1 )
| ~ sP23 ),
inference(cnf_transformation,[],[f260]) ).
tcf(c_250,plain,
( ~ sP23
| ( op(e0,e1) != e0 ) ),
inference(cnf_transformation,[],[f258]) ).
tcf(c_251,plain,
( ( op(e0,e0) = e2 )
| ~ sP22 ),
inference(cnf_transformation,[],[f263]) ).
tcf(c_253,plain,
( ~ sP22
| ( op(e0,e2) != e0 ) ),
inference(cnf_transformation,[],[f261]) ).
tcf(c_254,plain,
( ( op(e0,e0) = e3 )
| ~ sP21 ),
inference(cnf_transformation,[],[f266]) ).
tcf(c_256,plain,
( ~ sP21
| ( op(e0,e3) != e0 ) ),
inference(cnf_transformation,[],[f264]) ).
tcf(c_257,plain,
( ( op(e0,e0) = e4 )
| ~ sP20 ),
inference(cnf_transformation,[],[f269]) ).
tcf(c_259,plain,
( ~ sP20
| ( op(e0,e4) != e0 ) ),
inference(cnf_transformation,[],[f267]) ).
tcf(c_260,plain,
( ( op(e1,e1) = e0 )
| ~ sP19 ),
inference(cnf_transformation,[],[f272]) ).
tcf(c_262,plain,
( ~ sP19
| ( op(e1,e0) != e1 ) ),
inference(cnf_transformation,[],[f270]) ).
tcf(c_264,plain,
( ( op(e1,e1) = e1 )
| ~ sP18 ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_265,plain,
( ~ sP18
| ( op(e1,e1) != e1 ) ),
inference(cnf_transformation,[],[f273]) ).
tcf(c_266,plain,
( ( op(e1,e1) = e2 )
| ~ sP17 ),
inference(cnf_transformation,[],[f278]) ).
tcf(c_268,plain,
( ~ sP17
| ( op(e1,e2) != e1 ) ),
inference(cnf_transformation,[],[f276]) ).
tcf(c_269,plain,
( ( op(e1,e1) = e3 )
| ~ sP16 ),
inference(cnf_transformation,[],[f281]) ).
tcf(c_271,plain,
( ~ sP16
| ( op(e1,e3) != e1 ) ),
inference(cnf_transformation,[],[f279]) ).
tcf(c_272,plain,
( ( op(e1,e1) = e4 )
| ~ sP15 ),
inference(cnf_transformation,[],[f284]) ).
tcf(c_274,plain,
( ~ sP15
| ( op(e1,e4) != e1 ) ),
inference(cnf_transformation,[],[f282]) ).
tcf(c_275,plain,
( ( op(e2,e2) = e0 )
| ~ sP14 ),
inference(cnf_transformation,[],[f287]) ).
tcf(c_277,plain,
( ~ sP14
| ( op(e2,e0) != e2 ) ),
inference(cnf_transformation,[],[f285]) ).
tcf(c_278,plain,
( ( op(e2,e2) = e1 )
| ~ sP13 ),
inference(cnf_transformation,[],[f290]) ).
tcf(c_280,plain,
( ~ sP13
| ( op(e2,e1) != e2 ) ),
inference(cnf_transformation,[],[f288]) ).
tcf(c_282,plain,
( ( op(e2,e2) = e2 )
| ~ sP12 ),
inference(cnf_transformation,[],[f292]) ).
tcf(c_283,plain,
( ~ sP12
| ( op(e2,e2) != e2 ) ),
inference(cnf_transformation,[],[f291]) ).
tcf(c_284,plain,
( ( op(e2,e2) = e3 )
| ~ sP11 ),
inference(cnf_transformation,[],[f296]) ).
tcf(c_286,plain,
( ~ sP11
| ( op(e2,e3) != e2 ) ),
inference(cnf_transformation,[],[f294]) ).
tcf(c_287,plain,
( ( op(e2,e2) = e4 )
| ~ sP10 ),
inference(cnf_transformation,[],[f299]) ).
tcf(c_289,plain,
( ~ sP10
| ( op(e2,e4) != e2 ) ),
inference(cnf_transformation,[],[f297]) ).
tcf(c_290,plain,
( ( op(e3,e3) = e0 )
| ~ sP9 ),
inference(cnf_transformation,[],[f302]) ).
tcf(c_292,plain,
( ~ sP9
| ( op(e3,e0) != e3 ) ),
inference(cnf_transformation,[],[f300]) ).
tcf(c_293,plain,
( ( op(e3,e3) = e1 )
| ~ sP8 ),
inference(cnf_transformation,[],[f305]) ).
tcf(c_295,plain,
( ~ sP8
| ( op(e3,e1) != e3 ) ),
inference(cnf_transformation,[],[f303]) ).
tcf(c_296,plain,
( ( op(e3,e3) = e2 )
| ~ sP7 ),
inference(cnf_transformation,[],[f308]) ).
tcf(c_298,plain,
( ~ sP7
| ( op(e3,e2) != e3 ) ),
inference(cnf_transformation,[],[f306]) ).
tcf(c_300,plain,
( ( op(e3,e3) = e3 )
| ~ sP6 ),
inference(cnf_transformation,[],[f310]) ).
tcf(c_301,plain,
( ~ sP6
| ( op(e3,e3) != e3 ) ),
inference(cnf_transformation,[],[f309]) ).
tcf(c_302,plain,
( ( op(e3,e3) = e4 )
| ~ sP5 ),
inference(cnf_transformation,[],[f314]) ).
tcf(c_304,plain,
( ~ sP5
| ( op(e3,e4) != e3 ) ),
inference(cnf_transformation,[],[f312]) ).
tcf(c_305,plain,
( ( op(e4,e4) = e0 )
| ~ sP4 ),
inference(cnf_transformation,[],[f317]) ).
tcf(c_307,plain,
( ~ sP4
| ( op(e4,e0) != e4 ) ),
inference(cnf_transformation,[],[f315]) ).
tcf(c_308,plain,
( ( op(e4,e4) = e1 )
| ~ sP3 ),
inference(cnf_transformation,[],[f320]) ).
tcf(c_310,plain,
( ~ sP3
| ( op(e4,e1) != e4 ) ),
inference(cnf_transformation,[],[f318]) ).
tcf(c_311,plain,
( ( op(e4,e4) = e2 )
| ~ sP2 ),
inference(cnf_transformation,[],[f323]) ).
tcf(c_313,plain,
( ~ sP2
| ( op(e4,e2) != e4 ) ),
inference(cnf_transformation,[],[f321]) ).
tcf(c_314,plain,
( ( op(e4,e4) = e3 )
| ~ sP1 ),
inference(cnf_transformation,[],[f326]) ).
tcf(c_316,plain,
( ~ sP1
| ( op(e4,e3) != e4 ) ),
inference(cnf_transformation,[],[f324]) ).
tcf(c_320,negated_conjecture,
( ( op(e0,e1) = e0 )
| ( op(e0,e0) != e1 ) ),
inference(cnf_transformation,[],[f356]) ).
tcf(c_321,negated_conjecture,
( ( op(e0,e2) = e0 )
| ( op(e0,e0) != e2 ) ),
inference(cnf_transformation,[],[f355]) ).
tcf(c_322,negated_conjecture,
( ( op(e0,e3) = e0 )
| ( op(e0,e0) != e3 ) ),
inference(cnf_transformation,[],[f354]) ).
tcf(c_323,negated_conjecture,
( ( op(e0,e4) = e0 )
| ( op(e0,e0) != e4 ) ),
inference(cnf_transformation,[],[f353]) ).
tcf(c_324,negated_conjecture,
( ( op(e1,e0) = e1 )
| ( op(e1,e1) != e0 ) ),
inference(cnf_transformation,[],[f352]) ).
tcf(c_325,negated_conjecture,
( ( op(e1,e2) = e1 )
| ( op(e1,e1) != e2 ) ),
inference(cnf_transformation,[],[f350]) ).
tcf(c_326,negated_conjecture,
( ( op(e1,e3) = e1 )
| ( op(e1,e1) != e3 ) ),
inference(cnf_transformation,[],[f349]) ).
tcf(c_327,negated_conjecture,
( ( op(e1,e4) = e1 )
| ( op(e1,e1) != e4 ) ),
inference(cnf_transformation,[],[f348]) ).
tcf(c_328,negated_conjecture,
( ( op(e2,e0) = e2 )
| ( op(e2,e2) != e0 ) ),
inference(cnf_transformation,[],[f347]) ).
tcf(c_329,negated_conjecture,
( ( op(e2,e1) = e2 )
| ( op(e2,e2) != e1 ) ),
inference(cnf_transformation,[],[f346]) ).
tcf(c_330,negated_conjecture,
( ( op(e2,e3) = e2 )
| ( op(e2,e2) != e3 ) ),
inference(cnf_transformation,[],[f344]) ).
tcf(c_331,negated_conjecture,
( ( op(e2,e4) = e2 )
| ( op(e2,e2) != e4 ) ),
inference(cnf_transformation,[],[f343]) ).
tcf(c_332,negated_conjecture,
( ( op(e3,e0) = e3 )
| ( op(e3,e3) != e0 ) ),
inference(cnf_transformation,[],[f342]) ).
tcf(c_333,negated_conjecture,
( ( op(e3,e1) = e3 )
| ( op(e3,e3) != e1 ) ),
inference(cnf_transformation,[],[f341]) ).
tcf(c_334,negated_conjecture,
( ( op(e3,e2) = e3 )
| ( op(e3,e3) != e2 ) ),
inference(cnf_transformation,[],[f340]) ).
tcf(c_335,negated_conjecture,
( ( op(e3,e4) = e3 )
| ( op(e3,e3) != e4 ) ),
inference(cnf_transformation,[],[f338]) ).
tcf(c_336,negated_conjecture,
( ( op(e4,e0) = e4 )
| ( op(e4,e4) != e0 ) ),
inference(cnf_transformation,[],[f337]) ).
tcf(c_337,negated_conjecture,
( ( op(e4,e1) = e4 )
| ( op(e4,e4) != e1 ) ),
inference(cnf_transformation,[],[f336]) ).
tcf(c_338,negated_conjecture,
( ( op(e4,e2) = e4 )
| ( op(e4,e4) != e2 ) ),
inference(cnf_transformation,[],[f335]) ).
tcf(c_339,negated_conjecture,
( ( op(e4,e3) = e4 )
| ( op(e4,e4) != e3 ) ),
inference(cnf_transformation,[],[f334]) ).
tcf(c_341,negated_conjecture,
( sP0
| sP1
| sP2
| sP3
| sP4
| sP5
| sP6
| sP7
| sP8
| sP9
| sP10
| sP11
| sP12
| sP13
| sP14
| sP15
| sP16
| sP17
| sP18
| sP19
| sP20
| sP21
| sP22
| sP23
| ( op(e0,e0) = e0 ) ),
inference(cnf_transformation,[],[f331]) ).
tcf(c_342,negated_conjecture,
( sP0
| sP1
| sP2
| sP3
| sP4
| sP5
| sP6
| sP7
| sP8
| sP9
| sP10
| sP11
| sP12
| sP13
| sP14
| sP15
| sP16
| sP17
| sP18
| sP19
| sP20
| sP21
| sP22
| sP23
| ( op(e0,e0) != e0 ) ),
inference(cnf_transformation,[],[f330]) ).
fof(f10,definition,
( ~ sP0
| ( op(e4,e4) != e4
& op(e4,e4) = e4
& op(e4,e4) = e4 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f11,definition,
( ~ sP1
| ( op(e4,e3) != e4
& op(e3,e3) = e4
& op(e4,e4) = e3 ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f12,definition,
( ~ sP2
| ( op(e4,e2) != e4
& op(e2,e2) = e4
& op(e4,e4) = e2 ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f13,definition,
( ~ sP3
| ( op(e4,e1) != e4
& op(e1,e1) = e4
& op(e4,e4) = e1 ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f14,definition,
( ~ sP4
| ( op(e4,e0) != e4
& op(e0,e0) = e4
& op(e4,e4) = e0 ) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f15,definition,
( ~ sP5
| ( op(e3,e4) != e3
& op(e4,e4) = e3
& op(e3,e3) = e4 ) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f16,definition,
( ~ sP6
| ( op(e3,e3) != e3
& op(e3,e3) = e3
& op(e3,e3) = e3 ) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f17,definition,
( ~ sP7
| ( op(e3,e2) != e3
& op(e2,e2) = e3
& op(e3,e3) = e2 ) ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f18,definition,
( ~ sP8
| ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 ) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f19,definition,
( ~ sP9
| ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 ) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f20,definition,
( ~ sP10
| ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 ) ),
introduced(definition,[new_symbols(definition,[sP10])],[predicate_definition_introduction]) ).
fof(f21,definition,
( ~ sP11
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 ) ),
introduced(definition,[new_symbols(definition,[sP11])],[predicate_definition_introduction]) ).
fof(f22,definition,
( ~ sP12
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 ) ),
introduced(definition,[new_symbols(definition,[sP12])],[predicate_definition_introduction]) ).
fof(f23,definition,
( ~ sP13
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 ) ),
introduced(definition,[new_symbols(definition,[sP13])],[predicate_definition_introduction]) ).
fof(f24,definition,
( ~ sP14
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 ) ),
introduced(definition,[new_symbols(definition,[sP14])],[predicate_definition_introduction]) ).
fof(f25,definition,
( ~ sP15
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 ) ),
introduced(definition,[new_symbols(definition,[sP15])],[predicate_definition_introduction]) ).
fof(f26,definition,
( ~ sP16
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 ) ),
introduced(definition,[new_symbols(definition,[sP16])],[predicate_definition_introduction]) ).
fof(f27,definition,
( ~ sP17
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 ) ),
introduced(definition,[new_symbols(definition,[sP17])],[predicate_definition_introduction]) ).
fof(f28,definition,
( ~ sP18
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 ) ),
introduced(definition,[new_symbols(definition,[sP18])],[predicate_definition_introduction]) ).
fof(f29,definition,
( ~ sP19
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 ) ),
introduced(definition,[new_symbols(definition,[sP19])],[predicate_definition_introduction]) ).
fof(f30,definition,
( ~ sP20
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 ) ),
introduced(definition,[new_symbols(definition,[sP20])],[predicate_definition_introduction]) ).
fof(f31,definition,
( ~ sP21
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 ) ),
introduced(definition,[new_symbols(definition,[sP21])],[predicate_definition_introduction]) ).
fof(f32,definition,
( ~ sP22
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 ) ),
introduced(definition,[new_symbols(definition,[sP22])],[predicate_definition_introduction]) ).
fof(f33,definition,
( ~ sP23
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 ) ),
introduced(definition,[new_symbols(definition,[sP23])],[predicate_definition_introduction]) ).
fof(f34,plain,
( ( sP0
| sP1
| sP2
| sP3
| sP4
| sP5
| sP6
| sP7
| sP8
| sP9
| sP10
| sP11
| sP12
| sP13
| sP14
| sP15
| sP16
| sP17
| sP18
| sP19
| sP20
| sP21
| sP22
| sP23
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) )
& ( op(e4,e4) = e4
| op(e4,e4) != e4 )
& ( op(e4,e3) = e4
| op(e4,e4) != e3 )
& ( op(e4,e2) = e4
| op(e4,e4) != e2 )
& ( op(e4,e1) = e4
| op(e4,e4) != e1 )
& ( op(e4,e0) = e4
| op(e4,e4) != e0 )
& ( op(e3,e4) = e3
| op(e3,e3) != e4 )
& ( op(e3,e3) = e3
| op(e3,e3) != e3 )
& ( op(e3,e2) = e3
| op(e3,e3) != e2 )
& ( op(e3,e1) = e3
| op(e3,e3) != e1 )
& ( op(e3,e0) = e3
| op(e3,e3) != e0 )
& ( op(e2,e4) = e2
| op(e2,e2) != e4 )
& ( op(e2,e3) = e2
| op(e2,e2) != e3 )
& ( op(e2,e2) = e2
| op(e2,e2) != e2 )
& ( op(e2,e1) = e2
| op(e2,e2) != e1 )
& ( op(e2,e0) = e2
| op(e2,e2) != e0 )
& ( op(e1,e4) = e1
| op(e1,e1) != e4 )
& ( op(e1,e3) = e1
| op(e1,e1) != e3 )
& ( op(e1,e2) = e1
| op(e1,e1) != e2 )
& ( op(e1,e1) = e1
| op(e1,e1) != e1 )
& ( op(e1,e0) = e1
| op(e1,e1) != e0 )
& ( op(e0,e4) = e0
| op(e0,e0) != e4 )
& ( op(e0,e3) = e0
| op(e0,e0) != e3 )
& ( op(e0,e2) = e0
| op(e0,e0) != e2 )
& ( op(e0,e1) = e0
| op(e0,e0) != e1 )
& ( op(e0,e0) = e0
| op(e0,e0) != e0 ) ),
inference(definition_folding,[],[f9,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13,f12,f11,f10]) ).
fof(f58,plain,
( ~ sP0
| ( op(e4,e4) != e4
& op(e4,e4) = e4
& op(e4,e4) = e4 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f327,plain,
( ~ sP0
| e4 != op(e4,e4) ),
inference(cnf_transformation,[],[f58]) ).
fof(f328,plain,
( ~ sP0
| e4 = op(e4,e4) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_318,plain,
( ( op(e4,e4) = e4 )
| ~ sP0 ),
inference(cnf_transformation,[],[f328]) ).
tcf(c_319,plain,
( ~ sP0
| ( op(e4,e4) != e4 ) ),
inference(cnf_transformation,[],[f327]) ).
tcf(c_343,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_342,c_341,c_320,c_321,c_322,c_323,c_324,c_325,c_326,c_327,c_328,c_329,c_330,c_331,c_332,c_333,c_334,c_335,c_336,c_337,c_338,c_339,c_250,c_253,c_256,c_259,c_262,c_265,c_268,c_271,c_274,c_277,c_280,c_283,c_286,c_289,c_292,c_295,c_298,c_301,c_304,c_307,c_310,c_313,c_316,c_319,c_248,c_251,c_254,c_257,c_260,c_264,c_266,c_269,c_272,c_275,c_278,c_282,c_284,c_287,c_290,c_293,c_296,c_300,c_302,c_305,c_308,c_311,c_314,c_318]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG067+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/6.35 % Computer : n012.cluster.edu
% 0.04/6.35 % Model : x86_64 x86_64
% 0.04/6.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/6.35 % Memory : 8046.5625MB
% 0.04/6.35 % OS : Linux 6.8.0-71-generic
% 0.04/6.35 % CPULimit : 300
% 0.04/6.35 % WCLimit : 300
% 0.04/6.35 % DateTime : Fri Sep 25 04:41:15 UTC 2026
% 0.04/6.35 % CPUTime :
% 0.04/6.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/6.37 Running first-order theorem proving
% 0.04/6.37 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/6.38
% 0.04/6.38 % ======== iProver multi-core TPTP/SMT =========
% 0.04/6.38
% 0.04/6.38 % Detected problem language: tptp
% 0.04/6.39 % Proving...
% 0.92/7.01 % SZS status Started for theBenchmark.p
% 0.92/7.01 % SZS status Theorem for theBenchmark.p
% 0.92/7.01
% 0.92/7.01 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.92/7.01
% 0.92/7.01 % ------ iProver source info
% 0.92/7.01
% 0.92/7.01 % git: date: 2026-07-19 20:42:38 +0200
% 0.92/7.01 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.92/7.01 % git: non_committed_changes: false
% 0.92/7.01
% 0.92/7.01 % ------ Parsing...
% 0.92/7.01 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.92/7.01
% 0.92/7.01 % ------ Preprocessing...%
% 0.92/7.01
% 0.92/7.01 % SZS status Theorem for theBenchmark.p
% 0.92/7.01
% 0.92/7.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.92/7.02
% 0.92/7.02
%------------------------------------------------------------------------------