%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG045+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 : Thu Sep 24 11:47:52 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 95
% Syntax : Number of formulae : 452 ( 44 unt; 68 def)
% Number of atoms : 1290 ( 760 equ)
% Maximal formula atoms : 128 ( 2 avg)
% Number of connectives : 1400 ( 562 ~; 588 |; 180 &)
% ( 70 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 70 ( 68 usr; 69 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( ( op(e3,e3) = e3
| op(e3,e3) = e2
| op(e3,e3) = e1
| op(e3,e3) = e0 )
& ( op(e3,e2) = e3
| op(e3,e2) = e2
| op(e3,e2) = e1
| op(e3,e2) = e0 )
& ( op(e3,e1) = e3
| op(e3,e1) = e2
| op(e3,e1) = e1
| op(e3,e1) = e0 )
& ( op(e3,e0) = e3
| op(e3,e0) = e2
| op(e3,e0) = e1
| op(e3,e0) = e0 )
& ( op(e2,e3) = e3
| op(e2,e3) = e2
| op(e2,e3) = e1
| op(e2,e3) = e0 )
& ( op(e2,e2) = e3
| op(e2,e2) = e2
| op(e2,e2) = e1
| op(e2,e2) = e0 )
& ( op(e2,e1) = e3
| op(e2,e1) = e2
| op(e2,e1) = e1
| op(e2,e1) = e0 )
& ( op(e2,e0) = e3
| op(e2,e0) = e2
| op(e2,e0) = e1
| op(e2,e0) = e0 )
& ( op(e1,e3) = e3
| op(e1,e3) = e2
| op(e1,e3) = e1
| op(e1,e3) = e0 )
& ( op(e1,e2) = e3
| op(e1,e2) = e2
| op(e1,e2) = e1
| op(e1,e2) = e0 )
& ( op(e1,e1) = e3
| op(e1,e1) = e2
| op(e1,e1) = e1
| op(e1,e1) = e0 )
& ( op(e1,e0) = e3
| op(e1,e0) = e2
| op(e1,e0) = e1
| op(e1,e0) = e0 )
& ( op(e0,e3) = e3
| op(e0,e3) = e2
| op(e0,e3) = e1
| op(e0,e3) = e0 )
& ( op(e0,e2) = e3
| op(e0,e2) = e2
| op(e0,e2) = e1
| op(e0,e2) = e0 )
& ( op(e0,e1) = e3
| op(e0,e1) = e2
| op(e0,e1) = e1
| op(e0,e1) = e0 )
& ( op(e0,e0) = e3
| op(e0,e0) = e2
| op(e0,e0) = e1
| op(e0,e0) = e0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
( ( unit = e3
| unit = e2
| unit = e1
| unit = e0 )
& op(e3,unit) = e3
& op(unit,e3) = e3
& op(e2,unit) = e2
& op(unit,e2) = e2
& op(e1,unit) = e1
& op(unit,e1) = e1
& op(e0,unit) = e0
& op(unit,e0) = e0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( ( op(e3,e3) = e3
| op(e2,e3) = e3
| op(e1,e3) = e3
| op(e0,e3) = e3 )
& ( op(e3,e3) = e3
| op(e3,e2) = e3
| op(e3,e1) = e3
| op(e3,e0) = e3 )
& ( op(e3,e3) = e2
| op(e2,e3) = e2
| op(e1,e3) = e2
| op(e0,e3) = e2 )
& ( op(e3,e3) = e2
| op(e3,e2) = e2
| op(e3,e1) = e2
| op(e3,e0) = e2 )
& ( op(e3,e3) = e1
| op(e2,e3) = e1
| op(e1,e3) = e1
| op(e0,e3) = e1 )
& ( op(e3,e3) = e1
| op(e3,e2) = e1
| op(e3,e1) = e1
| op(e3,e0) = e1 )
& ( op(e3,e3) = e0
| op(e2,e3) = e0
| op(e1,e3) = e0
| op(e0,e3) = e0 )
& ( op(e3,e3) = e0
| op(e3,e2) = e0
| op(e3,e1) = e0
| op(e3,e0) = e0 )
& ( op(e3,e2) = e3
| op(e2,e2) = e3
| op(e1,e2) = e3
| op(e0,e2) = e3 )
& ( op(e2,e3) = e3
| op(e2,e2) = e3
| op(e2,e1) = e3
| op(e2,e0) = e3 )
& ( op(e3,e2) = e2
| op(e2,e2) = e2
| op(e1,e2) = e2
| op(e0,e2) = e2 )
& ( op(e2,e3) = e2
| op(e2,e2) = e2
| op(e2,e1) = e2
| op(e2,e0) = e2 )
& ( op(e3,e2) = e1
| op(e2,e2) = e1
| op(e1,e2) = e1
| op(e0,e2) = e1 )
& ( op(e2,e3) = e1
| op(e2,e2) = e1
| op(e2,e1) = e1
| op(e2,e0) = e1 )
& ( op(e3,e2) = e0
| op(e2,e2) = e0
| op(e1,e2) = e0
| op(e0,e2) = e0 )
& ( op(e2,e3) = e0
| op(e2,e2) = e0
| op(e2,e1) = e0
| op(e2,e0) = e0 )
& ( op(e3,e1) = e3
| op(e2,e1) = e3
| op(e1,e1) = e3
| op(e0,e1) = e3 )
& ( op(e1,e3) = e3
| op(e1,e2) = e3
| op(e1,e1) = e3
| op(e1,e0) = e3 )
& ( op(e3,e1) = e2
| op(e2,e1) = e2
| op(e1,e1) = e2
| op(e0,e1) = e2 )
& ( op(e1,e3) = e2
| op(e1,e2) = e2
| op(e1,e1) = e2
| op(e1,e0) = e2 )
& ( op(e3,e1) = e1
| op(e2,e1) = e1
| op(e1,e1) = e1
| op(e0,e1) = e1 )
& ( op(e1,e3) = e1
| op(e1,e2) = e1
| op(e1,e1) = e1
| op(e1,e0) = e1 )
& ( op(e3,e1) = e0
| op(e2,e1) = e0
| op(e1,e1) = e0
| op(e0,e1) = e0 )
& ( op(e1,e3) = e0
| op(e1,e2) = e0
| op(e1,e1) = e0
| op(e1,e0) = e0 )
& ( op(e3,e0) = e3
| op(e2,e0) = e3
| op(e1,e0) = e3
| op(e0,e0) = e3 )
& ( op(e0,e3) = e3
| op(e0,e2) = e3
| op(e0,e1) = e3
| op(e0,e0) = e3 )
& ( op(e3,e0) = e2
| op(e2,e0) = e2
| op(e1,e0) = e2
| op(e0,e0) = e2 )
& ( op(e0,e3) = e2
| op(e0,e2) = e2
| op(e0,e1) = e2
| op(e0,e0) = e2 )
& ( op(e3,e0) = e1
| op(e2,e0) = e1
| op(e1,e0) = e1
| op(e0,e0) = e1 )
& ( op(e0,e3) = e1
| op(e0,e2) = e1
| op(e0,e1) = e1
| op(e0,e0) = e1 )
& ( op(e3,e0) = e0
| op(e2,e0) = e0
| op(e1,e0) = e0
| op(e0,e0) = e0 )
& ( op(e0,e3) = e0
| op(e0,e2) = e0
| op(e0,e1) = e0
| op(e0,e0) = e0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
( op(e3,e2) != op(e3,e3)
& op(e3,e1) != op(e3,e3)
& op(e3,e1) != op(e3,e2)
& op(e3,e0) != op(e3,e3)
& op(e3,e0) != op(e3,e2)
& op(e3,e0) != op(e3,e1)
& op(e2,e2) != op(e2,e3)
& op(e2,e1) != op(e2,e3)
& op(e2,e1) != op(e2,e2)
& op(e2,e0) != op(e2,e3)
& op(e2,e0) != op(e2,e2)
& op(e2,e0) != op(e2,e1)
& op(e1,e2) != op(e1,e3)
& op(e1,e1) != op(e1,e3)
& op(e1,e1) != op(e1,e2)
& op(e1,e0) != op(e1,e3)
& op(e1,e0) != op(e1,e2)
& op(e1,e0) != op(e1,e1)
& op(e0,e2) != op(e0,e3)
& op(e0,e1) != op(e0,e3)
& op(e0,e1) != op(e0,e2)
& op(e0,e0) != op(e0,e3)
& op(e0,e0) != op(e0,e2)
& op(e0,e0) != op(e0,e1)
& op(e2,e3) != op(e3,e3)
& op(e1,e3) != op(e3,e3)
& op(e1,e3) != op(e2,e3)
& op(e0,e3) != op(e3,e3)
& op(e0,e3) != op(e2,e3)
& op(e0,e3) != op(e1,e3)
& op(e2,e2) != op(e3,e2)
& op(e1,e2) != op(e3,e2)
& op(e1,e2) != op(e2,e2)
& op(e0,e2) != op(e3,e2)
& op(e0,e2) != op(e2,e2)
& op(e0,e2) != op(e1,e2)
& op(e2,e1) != op(e3,e1)
& op(e1,e1) != op(e3,e1)
& op(e1,e1) != op(e2,e1)
& op(e0,e1) != op(e3,e1)
& op(e0,e1) != op(e2,e1)
& op(e0,e1) != op(e1,e1)
& op(e2,e0) != op(e3,e0)
& op(e1,e0) != op(e3,e0)
& op(e1,e0) != op(e2,e0)
& op(e0,e0) != op(e3,e0)
& op(e0,e0) != op(e2,e0)
& op(e0,e0) != op(e1,e0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
( e2 != e3
& e1 != e3
& e1 != e2
& e0 != e3
& e0 != e2
& e0 != e1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
( ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
~ ( e2 = op(e3,e1)
& e0 = op(e1,e1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ ( e1 = op(e3,e2)
& e0 = op(e2,e2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
~ ( e3 = op(e1,e2)
& e0 = op(e2,e2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ ( e1 = op(e2,e3)
& e0 = op(e3,e3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
~ ( e2 = op(e1,e3)
& e0 = op(e3,e3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
~ ( e2 = op(e3,e0)
& e1 = op(e0,e0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
~ ( e0 = op(e3,e2)
& e1 = op(e2,e2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
~ ( e3 = op(e0,e2)
& e1 = op(e2,e2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
~ ( e0 = op(e2,e3)
& e1 = op(e3,e3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
~ ( e2 = op(e0,e3)
& e1 = op(e3,e3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
~ ( e1 = op(e3,e0)
& e2 = op(e0,e0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
~ ( e3 = op(e1,e0)
& e2 = op(e0,e0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
~ ( e0 = op(e3,e1)
& e2 = op(e1,e1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
~ ( e0 = op(e1,e3)
& e2 = op(e3,e3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
~ ( e1 = op(e0,e3)
& e2 = op(e3,e3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
~ ( e1 = op(e2,e0)
& e3 = op(e0,e0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
~ ( e2 = op(e1,e0)
& e3 = op(e0,e0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
~ ( e0 = op(e2,e1)
& e3 = op(e1,e1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
~ ( e2 = op(e0,e1)
& e3 = op(e1,e1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
~ ( e0 = op(e1,e2)
& e3 = op(e2,e2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
~ ( e1 = op(e0,e2)
& e3 = op(e2,e2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,plain,
( op(e0,e2) = e3
| op(e0,e2) = e2
| op(e0,e2) = e1
| op(e0,e2) = e0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f38,plain,
( op(e1,e3) = e3
| op(e1,e3) = e2
| op(e1,e3) = e1
| op(e1,e3) = e0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f42,plain,
( op(e2,e3) = e3
| op(e2,e3) = e2
| op(e2,e3) = e1
| op(e2,e3) = e0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f43,plain,
( op(e3,e0) = e3
| op(e3,e0) = e2
| op(e3,e0) = e1
| op(e3,e0) = e0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f44,plain,
( op(e3,e1) = e3
| op(e3,e1) = e2
| op(e3,e1) = e1
| op(e3,e1) = e0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f45,plain,
( op(e3,e2) = e3
| op(e3,e2) = e2
| op(e3,e2) = e1
| op(e3,e2) = e0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f47,plain,
op(unit,e0) = e0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f48,plain,
op(e0,unit) = e0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f49,plain,
op(unit,e1) = e1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f50,plain,
op(e1,unit) = e1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f51,plain,
op(unit,e2) = e2,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f52,plain,
op(e2,unit) = e2,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f54,plain,
op(e3,unit) = e3,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f55,plain,
( unit = e3
| unit = e2
| unit = e1
| unit = e0 ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f58,plain,
( op(e0,e3) = e1
| op(e0,e2) = e1
| op(e0,e1) = e1
| op(e0,e0) = e1 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f60,plain,
( op(e0,e3) = e2
| op(e0,e2) = e2
| op(e0,e1) = e2
| op(e0,e0) = e2 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f61,plain,
( op(e3,e0) = e2
| op(e2,e0) = e2
| op(e1,e0) = e2
| op(e0,e0) = e2 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f64,plain,
( op(e1,e3) = e0
| op(e1,e2) = e0
| op(e1,e1) = e0
| op(e1,e0) = e0 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f65,plain,
( op(e3,e1) = e0
| op(e2,e1) = e0
| op(e1,e1) = e0
| op(e0,e1) = e0 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f70,plain,
( op(e1,e3) = e3
| op(e1,e2) = e3
| op(e1,e1) = e3
| op(e1,e0) = e3 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f73,plain,
( op(e3,e2) = e0
| op(e2,e2) = e0
| op(e1,e2) = e0
| op(e0,e2) = e0 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f75,plain,
( op(e3,e2) = e1
| op(e2,e2) = e1
| op(e1,e2) = e1
| op(e0,e2) = e1 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f79,plain,
( op(e3,e2) = e3
| op(e2,e2) = e3
| op(e1,e2) = e3
| op(e0,e2) = e3 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f80,plain,
( op(e3,e3) = e0
| op(e3,e2) = e0
| op(e3,e1) = e0
| op(e3,e0) = e0 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f81,plain,
( op(e3,e3) = e0
| op(e2,e3) = e0
| op(e1,e3) = e0
| op(e0,e3) = e0 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f82,plain,
( op(e3,e3) = e1
| op(e3,e2) = e1
| op(e3,e1) = e1
| op(e3,e0) = e1 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f83,plain,
( op(e3,e3) = e1
| op(e2,e3) = e1
| op(e1,e3) = e1
| op(e0,e3) = e1 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f88,plain,
op(e0,e0) != op(e1,e0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f89,plain,
op(e0,e0) != op(e2,e0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f91,plain,
op(e1,e0) != op(e2,e0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f92,plain,
op(e1,e0) != op(e3,e0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f93,plain,
op(e2,e0) != op(e3,e0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f94,plain,
op(e0,e1) != op(e1,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f95,plain,
op(e0,e1) != op(e2,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f96,plain,
op(e0,e1) != op(e3,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f97,plain,
op(e1,e1) != op(e2,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f98,plain,
op(e1,e1) != op(e3,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f100,plain,
op(e0,e2) != op(e1,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f102,plain,
op(e0,e2) != op(e3,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f104,plain,
op(e1,e2) != op(e3,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f109,plain,
op(e1,e3) != op(e2,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f111,plain,
op(e2,e3) != op(e3,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f112,plain,
op(e0,e0) != op(e0,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f113,plain,
op(e0,e0) != op(e0,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f114,plain,
op(e0,e0) != op(e0,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f115,plain,
op(e0,e1) != op(e0,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f116,plain,
op(e0,e1) != op(e0,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f117,plain,
op(e0,e2) != op(e0,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f119,plain,
op(e1,e0) != op(e1,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f120,plain,
op(e1,e0) != op(e1,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f121,plain,
op(e1,e1) != op(e1,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f122,plain,
op(e1,e1) != op(e1,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f123,plain,
op(e1,e2) != op(e1,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f124,plain,
op(e2,e0) != op(e2,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f126,plain,
op(e2,e0) != op(e2,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f131,plain,
op(e3,e0) != op(e3,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f133,plain,
op(e3,e1) != op(e3,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f134,plain,
op(e3,e1) != op(e3,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f135,plain,
op(e3,e2) != op(e3,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f136,plain,
e0 != e1,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f137,plain,
e0 != e2,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f139,plain,
e1 != e2,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f141,plain,
e2 != e3,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f142,definition,
( sP0_prd
<=> ( ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f143,plain,
( ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 )
| sP0_prd ),
inference(formula_renaming,[status(thm)],[f6,f142]) ).
fof(f144,plain,
( op(e0,e0) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f145,plain,
( op(e1,e1) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f146,plain,
( op(e2,e2) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f147,plain,
( op(e3,e3) = e3
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f148,plain,
( e2 != op(e3,e1)
| e0 != op(e1,e1) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f149,plain,
( e2 != op(e3,e1)
| e0 != op(e1,e1) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f152,plain,
( e1 != op(e3,e2)
| e0 != op(e2,e2) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f153,plain,
( e1 != op(e3,e2)
| e0 != op(e2,e2) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f154,plain,
( e3 != op(e1,e2)
| e0 != op(e2,e2) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f155,plain,
( e3 != op(e1,e2)
| e0 != op(e2,e2) ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f156,plain,
( e1 != op(e2,e3)
| e0 != op(e3,e3) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f157,plain,
( e1 != op(e2,e3)
| e0 != op(e3,e3) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f158,plain,
( e2 != op(e1,e3)
| e0 != op(e3,e3) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f159,plain,
( e2 != op(e1,e3)
| e0 != op(e3,e3) ),
inference(cnf_transformation,[status(thm)],[f158]) ).
fof(f160,plain,
( e2 != op(e3,e0)
| e1 != op(e0,e0) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f161,plain,
( e2 != op(e3,e0)
| e1 != op(e0,e0) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f164,plain,
( e0 != op(e3,e2)
| e1 != op(e2,e2) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f165,plain,
( e0 != op(e3,e2)
| e1 != op(e2,e2) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f166,plain,
( e3 != op(e0,e2)
| e1 != op(e2,e2) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f167,plain,
( e3 != op(e0,e2)
| e1 != op(e2,e2) ),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f168,plain,
( e0 != op(e2,e3)
| e1 != op(e3,e3) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f169,plain,
( e0 != op(e2,e3)
| e1 != op(e3,e3) ),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f170,plain,
( e2 != op(e0,e3)
| e1 != op(e3,e3) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f171,plain,
( e2 != op(e0,e3)
| e1 != op(e3,e3) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f172,plain,
( e1 != op(e3,e0)
| e2 != op(e0,e0) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f173,plain,
( e1 != op(e3,e0)
| e2 != op(e0,e0) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f174,plain,
( e3 != op(e1,e0)
| e2 != op(e0,e0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f175,plain,
( e3 != op(e1,e0)
| e2 != op(e0,e0) ),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f176,plain,
( e0 != op(e3,e1)
| e2 != op(e1,e1) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f177,plain,
( e0 != op(e3,e1)
| e2 != op(e1,e1) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f180,plain,
( e0 != op(e1,e3)
| e2 != op(e3,e3) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f181,plain,
( e0 != op(e1,e3)
| e2 != op(e3,e3) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f182,plain,
( e1 != op(e0,e3)
| e2 != op(e3,e3) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f183,plain,
( e1 != op(e0,e3)
| e2 != op(e3,e3) ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f184,plain,
( e1 != op(e2,e0)
| e3 != op(e0,e0) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f185,plain,
( e1 != op(e2,e0)
| e3 != op(e0,e0) ),
inference(cnf_transformation,[status(thm)],[f184]) ).
fof(f186,plain,
( e2 != op(e1,e0)
| e3 != op(e0,e0) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f187,plain,
( e2 != op(e1,e0)
| e3 != op(e0,e0) ),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f188,plain,
( e0 != op(e2,e1)
| e3 != op(e1,e1) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f189,plain,
( e0 != op(e2,e1)
| e3 != op(e1,e1) ),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f190,plain,
( e2 != op(e0,e1)
| e3 != op(e1,e1) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f191,plain,
( e2 != op(e0,e1)
| e3 != op(e1,e1) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f192,plain,
( e0 != op(e1,e2)
| e3 != op(e2,e2) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f193,plain,
( e0 != op(e1,e2)
| e3 != op(e2,e2) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f194,plain,
( e1 != op(e0,e2)
| e3 != op(e2,e2) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f195,plain,
( e1 != op(e0,e2)
| e3 != op(e2,e2) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f196,definition,
( sP1_prd
<=> ( ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f197,plain,
( sP0_prd
<=> ( ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| sP1_prd ) ),
inference(formula_renaming,[status(thm)],[f142,f196]) ).
fof(f198,plain,
( ( ( ( op(e3,e3) != e2
| op(e2,e2) != e2
| op(e1,e1) != e2
| op(e0,e0) != e2 )
& ~ sP1_prd )
| sP0_prd )
& ( ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 )
| sP1_prd
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f197]) ).
fof(f199,plain,
( op(e0,e0) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f200,plain,
( op(e1,e1) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f202,plain,
( op(e3,e3) = e2
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f205,definition,
( sP2_prd
<=> ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f206,plain,
( sP1_prd
<=> ( ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| sP2_prd ) ),
inference(formula_renaming,[status(thm)],[f196,f205]) ).
fof(f207,plain,
( ( ( ( op(e3,e3) != e1
| op(e2,e2) != e1
| op(e1,e1) != e1
| op(e0,e0) != e1 )
& ~ sP2_prd )
| sP1_prd )
& ( ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 )
| sP2_prd
| ~ sP1_prd ) ),
inference(NNF_transformation,[status(thm)],[f206]) ).
fof(f208,plain,
( op(e0,e0) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f207]) ).
fof(f209,plain,
( op(e1,e1) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f207]) ).
fof(f210,plain,
( op(e2,e2) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f207]) ).
fof(f211,plain,
( op(e3,e3) = e1
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f207]) ).
fof(f214,plain,
( ( op(e3,e3) != e0
| op(e2,e2) != e0
| op(e1,e1) != e0
| op(e0,e0) != e0
| sP2_prd )
& ( ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 )
| ~ sP2_prd ) ),
inference(NNF_transformation,[status(thm)],[f205]) ).
fof(f215,plain,
( op(e0,e0) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f216,plain,
( op(e1,e1) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f217,plain,
( op(e2,e2) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f218,plain,
( op(e3,e3) = e0
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f220,definition,
( sQ0_spl
<=> op(e0,e0) = e0 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f223,definition,
( sQ1_spl
<=> op(e0,e0) = e1 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f226,definition,
( sQ2_spl
<=> op(e0,e0) = e2 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f229,definition,
( sQ3_spl
<=> op(e0,e0) = e3 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f233,definition,
( sQ4_spl
<=> op(e0,e1) = e0 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f234,plain,
( ~ sQ4_spl
| op(e0,e1) = e0 ),
inference(component_clause,[status(thm)],[f233]) ).
fof(f236,definition,
( sQ5_spl
<=> op(e0,e1) = e1 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f237,plain,
( ~ sQ5_spl
| op(e0,e1) = e1 ),
inference(component_clause,[status(thm)],[f236]) ).
fof(f239,definition,
( sQ6_spl
<=> op(e0,e1) = e2 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f246,definition,
( sQ8_spl
<=> op(e0,e2) = e0 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( ~ sQ8_spl
| op(e0,e2) = e0 ),
inference(component_clause,[status(thm)],[f246]) ).
fof(f249,definition,
( sQ9_spl
<=> op(e0,e2) = e1 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f252,definition,
( sQ10_spl
<=> op(e0,e2) = e2 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f253,plain,
( ~ sQ10_spl
| op(e0,e2) = e2 ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f255,definition,
( sQ11_spl
<=> op(e0,e2) = e3 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( sQ11_spl
| sQ10_spl
| sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f33,f246,f249,f252,f255]) ).
fof(f259,definition,
( sQ12_spl
<=> op(e0,e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( ~ sQ12_spl
| op(e0,e3) = e0 ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,definition,
( sQ13_spl
<=> op(e0,e3) = e1 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f265,definition,
( sQ14_spl
<=> op(e0,e3) = e2 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f272,definition,
( sQ16_spl
<=> op(e1,e0) = e0 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( ~ sQ16_spl
| op(e1,e0) = e0 ),
inference(component_clause,[status(thm)],[f272]) ).
fof(f275,definition,
( sQ17_spl
<=> op(e1,e0) = e1 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f276,plain,
( ~ sQ17_spl
| op(e1,e0) = e1 ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f278,definition,
( sQ18_spl
<=> op(e1,e0) = e2 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f281,definition,
( sQ19_spl
<=> op(e1,e0) = e3 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f285,definition,
( sQ20_spl
<=> op(e1,e1) = e0 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f288,definition,
( sQ21_spl
<=> op(e1,e1) = e1 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f289,plain,
( ~ sQ21_spl
| op(e1,e1) = e1 ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f291,definition,
( sQ22_spl
<=> op(e1,e1) = e2 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f294,definition,
( sQ23_spl
<=> op(e1,e1) = e3 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f298,definition,
( sQ24_spl
<=> op(e1,e2) = e0 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f301,definition,
( sQ25_spl
<=> op(e1,e2) = e1 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f302,plain,
( ~ sQ25_spl
| op(e1,e2) = e1 ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f304,definition,
( sQ26_spl
<=> op(e1,e2) = e2 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f305,plain,
( ~ sQ26_spl
| op(e1,e2) = e2 ),
inference(component_clause,[status(thm)],[f304]) ).
fof(f307,definition,
( sQ27_spl
<=> op(e1,e2) = e3 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f311,definition,
( sQ28_spl
<=> op(e1,e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f314,definition,
( sQ29_spl
<=> op(e1,e3) = e1 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( ~ sQ29_spl
| op(e1,e3) = e1 ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f317,definition,
( sQ30_spl
<=> op(e1,e3) = e2 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f320,definition,
( sQ31_spl
<=> op(e1,e3) = e3 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f321,plain,
( ~ sQ31_spl
| op(e1,e3) = e3 ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f323,plain,
( sQ31_spl
| sQ30_spl
| sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f38,f311,f314,f317,f320]) ).
fof(f324,definition,
( sQ32_spl
<=> op(e2,e0) = e0 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f325,plain,
( ~ sQ32_spl
| op(e2,e0) = e0 ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f327,definition,
( sQ33_spl
<=> op(e2,e0) = e1 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f330,definition,
( sQ34_spl
<=> op(e2,e0) = e2 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f331,plain,
( ~ sQ34_spl
| op(e2,e0) = e2 ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f337,definition,
( sQ36_spl
<=> op(e2,e1) = e0 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f343,definition,
( sQ38_spl
<=> op(e2,e1) = e2 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f344,plain,
( ~ sQ38_spl
| op(e2,e1) = e2 ),
inference(component_clause,[status(thm)],[f343]) ).
fof(f350,definition,
( sQ40_spl
<=> op(e2,e2) = e0 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f353,definition,
( sQ41_spl
<=> op(e2,e2) = e1 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f359,definition,
( sQ43_spl
<=> op(e2,e2) = e3 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f363,definition,
( sQ44_spl
<=> op(e2,e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f366,definition,
( sQ45_spl
<=> op(e2,e3) = e1 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f369,definition,
( sQ46_spl
<=> op(e2,e3) = e2 ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f370,plain,
( ~ sQ46_spl
| op(e2,e3) = e2 ),
inference(component_clause,[status(thm)],[f369]) ).
fof(f372,definition,
( sQ47_spl
<=> op(e2,e3) = e3 ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f373,plain,
( ~ sQ47_spl
| op(e2,e3) = e3 ),
inference(component_clause,[status(thm)],[f372]) ).
fof(f375,plain,
( sQ47_spl
| sQ46_spl
| sQ45_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f42,f363,f366,f369,f372]) ).
fof(f376,definition,
( sQ48_spl
<=> op(e3,e0) = e0 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f379,definition,
( sQ49_spl
<=> op(e3,e0) = e1 ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f382,definition,
( sQ50_spl
<=> op(e3,e0) = e2 ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f385,definition,
( sQ51_spl
<=> op(e3,e0) = e3 ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f386,plain,
( ~ sQ51_spl
| op(e3,e0) = e3 ),
inference(component_clause,[status(thm)],[f385]) ).
fof(f388,plain,
( sQ51_spl
| sQ50_spl
| sQ49_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f43,f376,f379,f382,f385]) ).
fof(f389,definition,
( sQ52_spl
<=> op(e3,e1) = e0 ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f390,plain,
( ~ sQ52_spl
| op(e3,e1) = e0 ),
inference(component_clause,[status(thm)],[f389]) ).
fof(f392,definition,
( sQ53_spl
<=> op(e3,e1) = e1 ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f393,plain,
( ~ sQ53_spl
| op(e3,e1) = e1 ),
inference(component_clause,[status(thm)],[f392]) ).
fof(f395,definition,
( sQ54_spl
<=> op(e3,e1) = e2 ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f398,definition,
( sQ55_spl
<=> op(e3,e1) = e3 ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f399,plain,
( ~ sQ55_spl
| op(e3,e1) = e3 ),
inference(component_clause,[status(thm)],[f398]) ).
fof(f401,plain,
( sQ55_spl
| sQ54_spl
| sQ53_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f44,f389,f392,f395,f398]) ).
fof(f402,definition,
( sQ56_spl
<=> op(e3,e2) = e0 ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f403,plain,
( ~ sQ56_spl
| op(e3,e2) = e0 ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f405,definition,
( sQ57_spl
<=> op(e3,e2) = e1 ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f406,plain,
( ~ sQ57_spl
| op(e3,e2) = e1 ),
inference(component_clause,[status(thm)],[f405]) ).
fof(f408,definition,
( sQ58_spl
<=> op(e3,e2) = e2 ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f409,plain,
( ~ sQ58_spl
| op(e3,e2) = e2 ),
inference(component_clause,[status(thm)],[f408]) ).
fof(f411,definition,
( sQ59_spl
<=> op(e3,e2) = e3 ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f413,plain,
( sQ59_spl
| op(e3,e2) != e3 ),
inference(component_clause,[status(thm)],[f411]) ).
fof(f414,plain,
( sQ59_spl
| sQ58_spl
| sQ57_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f45,f402,f405,f408,f411]) ).
fof(f415,definition,
( sQ60_spl
<=> op(e3,e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f418,definition,
( sQ61_spl
<=> op(e3,e3) = e1 ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f421,definition,
( sQ62_spl
<=> op(e3,e3) = e2 ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f422,plain,
( ~ sQ62_spl
| op(e3,e3) = e2 ),
inference(component_clause,[status(thm)],[f421]) ).
fof(f424,definition,
( sQ63_spl
<=> op(e3,e3) = e3 ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f425,plain,
( ~ sQ63_spl
| op(e3,e3) = e3 ),
inference(component_clause,[status(thm)],[f424]) ).
fof(f428,definition,
( sQ64_spl
<=> unit = e0 ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f429,plain,
( ~ sQ64_spl
| unit = e0 ),
inference(component_clause,[status(thm)],[f428]) ).
fof(f431,definition,
( sQ65_spl
<=> unit = e1 ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f432,plain,
( ~ sQ65_spl
| unit = e1 ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f434,definition,
( sQ66_spl
<=> unit = e2 ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( ~ sQ66_spl
| unit = e2 ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,definition,
( sQ67_spl
<=> unit = e3 ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( ~ sQ67_spl
| unit = e3 ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f440,plain,
( sQ67_spl
| sQ66_spl
| sQ65_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f55,f428,f431,f434,f437]) ).
fof(f443,plain,
( sQ13_spl
| sQ9_spl
| sQ5_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f58,f223,f236,f249,f262]) ).
fof(f445,plain,
( sQ14_spl
| sQ10_spl
| sQ6_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f60,f226,f239,f252,f265]) ).
fof(f446,plain,
( sQ50_spl
| sQ34_spl
| sQ18_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f61,f226,f278,f330,f382]) ).
fof(f449,plain,
( sQ28_spl
| sQ24_spl
| sQ20_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f64,f272,f285,f298,f311]) ).
fof(f450,plain,
( sQ52_spl
| sQ36_spl
| sQ20_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f65,f233,f285,f337,f389]) ).
fof(f455,plain,
( sQ31_spl
| sQ27_spl
| sQ23_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f70,f281,f294,f307,f320]) ).
fof(f458,plain,
( sQ56_spl
| sQ40_spl
| sQ24_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f73,f246,f298,f350,f402]) ).
fof(f460,plain,
( sQ57_spl
| sQ41_spl
| sQ25_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f75,f249,f301,f353,f405]) ).
fof(f464,plain,
( sQ59_spl
| sQ43_spl
| sQ27_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f79,f255,f307,f359,f411]) ).
fof(f465,plain,
( sQ60_spl
| sQ56_spl
| sQ52_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f80,f376,f389,f402,f415]) ).
fof(f466,plain,
( sQ60_spl
| sQ44_spl
| sQ28_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f81,f259,f311,f363,f415]) ).
fof(f467,plain,
( sQ61_spl
| sQ57_spl
| sQ53_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f82,f379,f392,f405,f418]) ).
fof(f468,plain,
( sQ61_spl
| sQ45_spl
| sQ29_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f83,f262,f314,f366,f418]) ).
fof(f473,definition,
( sQ68_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f476,plain,
( sQ3_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f144,f473,f229]) ).
fof(f477,plain,
( sQ23_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f145,f473,f294]) ).
fof(f478,plain,
( sQ43_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f146,f473,f359]) ).
fof(f479,plain,
( sQ63_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f147,f473,f424]) ).
fof(f480,plain,
( ~ sQ54_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f149,f285,f395]) ).
fof(f482,plain,
( ~ sQ57_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f153,f350,f405]) ).
fof(f483,plain,
( ~ sQ27_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f155,f350,f307]) ).
fof(f484,plain,
( ~ sQ45_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f157,f415,f366]) ).
fof(f485,plain,
( ~ sQ30_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f159,f415,f317]) ).
fof(f486,plain,
( ~ sQ50_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f161,f223,f382]) ).
fof(f488,plain,
( ~ sQ56_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f165,f353,f402]) ).
fof(f489,plain,
( ~ sQ11_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f167,f353,f255]) ).
fof(f490,plain,
( ~ sQ44_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f169,f418,f363]) ).
fof(f491,plain,
( ~ sQ14_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f171,f418,f265]) ).
fof(f492,plain,
( ~ sQ49_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f173,f226,f379]) ).
fof(f493,plain,
( ~ sQ19_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f175,f226,f281]) ).
fof(f494,plain,
( ~ sQ52_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f177,f291,f389]) ).
fof(f496,plain,
( ~ sQ28_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f181,f421,f311]) ).
fof(f497,plain,
( ~ sQ13_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f183,f421,f262]) ).
fof(f498,plain,
( ~ sQ33_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f185,f229,f327]) ).
fof(f499,plain,
( ~ sQ18_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f187,f229,f278]) ).
fof(f500,plain,
( ~ sQ36_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f189,f294,f337]) ).
fof(f501,plain,
( ~ sQ6_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f191,f294,f239]) ).
fof(f502,plain,
( ~ sQ24_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f193,f359,f298]) ).
fof(f503,plain,
( ~ sQ9_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f195,f359,f249]) ).
fof(f504,definition,
( sQ69_spl
<=> sP1_prd ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f507,plain,
( sQ2_spl
| sQ69_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f199,f473,f504,f226]) ).
fof(f508,plain,
( sQ22_spl
| sQ69_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f200,f473,f504,f291]) ).
fof(f510,plain,
( sQ62_spl
| sQ69_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f202,f473,f504,f421]) ).
fof(f513,definition,
( sQ70_spl
<=> sP2_prd ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f516,plain,
( sQ1_spl
| sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f208,f504,f513,f223]) ).
fof(f517,plain,
( sQ21_spl
| sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f209,f504,f513,f288]) ).
fof(f518,plain,
( sQ41_spl
| sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f210,f504,f513,f353]) ).
fof(f519,plain,
( sQ61_spl
| sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f211,f504,f513,f418]) ).
fof(f522,plain,
( sQ0_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f215,f513,f220]) ).
fof(f523,plain,
( sQ20_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f216,f513,f285]) ).
fof(f524,plain,
( sQ40_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f217,f513,f350]) ).
fof(f525,plain,
( sQ60_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f218,f513,f415]) ).
fof(f529,plain,
( ~ sQ67_spl
| op(e2,e3) = e2 ),
inference(backward_demodulation,[status(thm)],[f438,f52]) ).
fof(f531,plain,
( ~ sQ67_spl
| op(e1,e3) = e1 ),
inference(backward_demodulation,[status(thm)],[f438,f50]) ).
fof(f532,plain,
( ~ sQ67_spl
| op(e3,e1) = e1 ),
inference(backward_demodulation,[status(thm)],[f438,f49]) ).
fof(f533,plain,
( ~ sQ67_spl
| op(e0,e3) = e0 ),
inference(backward_demodulation,[status(thm)],[f438,f48]) ).
fof(f543,plain,
( ~ sQ63_spl
| op(e2,e3) != e3 ),
inference(backward_demodulation,[status(thm)],[f425,f111]) ).
fof(f546,plain,
( ~ sQ25_spl
| e1 != op(e3,e2) ),
inference(backward_demodulation,[status(thm)],[f302,f104]) ).
fof(f548,plain,
( ~ sQ25_spl
| op(e0,e2) != e1 ),
inference(backward_demodulation,[status(thm)],[f302,f100]) ).
fof(f550,plain,
( ~ sQ38_spl
| op(e1,e1) != e2 ),
inference(backward_demodulation,[status(thm)],[f344,f97]) ).
fof(f551,plain,
( ~ sQ38_spl
| op(e0,e1) != e2 ),
inference(backward_demodulation,[status(thm)],[f344,f95]) ).
fof(f552,plain,
( ~ sQ26_spl
| ~ sQ25_spl
| e1 = e2 ),
inference(forward_demodulation,[status(thm)],[f302,f305]) ).
fof(f553,plain,
( ~ sQ26_spl
| ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f552,f139]) ).
fof(f554,plain,
( ~ sQ26_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f553]) ).
fof(f558,plain,
( ~ sQ5_spl
| e1 != op(e0,e3) ),
inference(backward_demodulation,[status(thm)],[f237,f116]) ).
fof(f559,plain,
( ~ sQ5_spl
| e1 != op(e0,e2) ),
inference(backward_demodulation,[status(thm)],[f237,f115]) ).
fof(f560,plain,
( ~ sQ5_spl
| op(e0,e0) != e1 ),
inference(backward_demodulation,[status(thm)],[f237,f112]) ).
fof(f561,plain,
( ~ sQ5_spl
| e1 != op(e3,e1) ),
inference(backward_demodulation,[status(thm)],[f237,f96]) ).
fof(f562,plain,
( ~ sQ5_spl
| e1 != op(e1,e1) ),
inference(backward_demodulation,[status(thm)],[f237,f94]) ).
fof(f563,plain,
( ~ sQ5_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f559,f249,f236]) ).
fof(f564,plain,
( ~ sQ5_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f560,f223,f236]) ).
fof(f565,plain,
( ~ sQ29_spl
| op(e1,e2) != e1 ),
inference(backward_demodulation,[status(thm)],[f315,f123]) ).
fof(f571,plain,
( ~ sQ53_spl
| op(e1,e1) != e1 ),
inference(backward_demodulation,[status(thm)],[f393,f98]) ).
fof(f573,plain,
( ~ sQ53_spl
| e1 != op(e3,e2) ),
inference(forward_demodulation,[status(thm)],[f393,f133]) ).
fof(f576,plain,
( ~ sQ16_spl
| e0 != op(e3,e0) ),
inference(backward_demodulation,[status(thm)],[f273,f92]) ).
fof(f577,plain,
( ~ sQ16_spl
| e0 != op(e2,e0) ),
inference(backward_demodulation,[status(thm)],[f273,f91]) ).
fof(f578,plain,
( ~ sQ16_spl
| op(e0,e0) != e0 ),
inference(backward_demodulation,[status(thm)],[f273,f88]) ).
fof(f580,plain,
( ~ sQ16_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f578,f220,f272]) ).
fof(f582,plain,
( ~ sQ57_spl
| ~ sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f406,f573]) ).
fof(f583,plain,
( ~ sQ57_spl
| ~ sQ53_spl ),
inference(contradiction_clause,[status(thm)],[f582]) ).
fof(f586,plain,
( ~ sQ63_spl
| op(e3,e1) != e3 ),
inference(forward_demodulation,[status(thm)],[f425,f134]) ).
fof(f587,plain,
( ~ sQ63_spl
| op(e3,e2) != e3 ),
inference(forward_demodulation,[status(thm)],[f425,f135]) ).
fof(f588,plain,
( ~ sQ12_spl
| op(e0,e2) != e0 ),
inference(backward_demodulation,[status(thm)],[f260,f117]) ).
fof(f589,plain,
( ~ sQ12_spl
| op(e0,e0) != e0 ),
inference(backward_demodulation,[status(thm)],[f260,f114]) ).
fof(f591,plain,
( ~ sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f589,f220,f259]) ).
fof(f592,plain,
( ~ sQ10_spl
| op(e0,e0) != e2 ),
inference(backward_demodulation,[status(thm)],[f253,f113]) ).
fof(f593,plain,
( ~ sQ10_spl
| e2 != op(e3,e2) ),
inference(backward_demodulation,[status(thm)],[f253,f102]) ).
fof(f599,plain,
( ~ sQ58_spl
| op(e3,e0) != e2 ),
inference(backward_demodulation,[status(thm)],[f409,f131]) ).
fof(f602,plain,
( ~ sQ32_spl
| e0 != op(e2,e1) ),
inference(backward_demodulation,[status(thm)],[f325,f124]) ).
fof(f603,plain,
( ~ sQ32_spl
| e0 != op(e3,e0) ),
inference(backward_demodulation,[status(thm)],[f325,f93]) ).
fof(f604,plain,
( ~ sQ32_spl
| op(e0,e0) != e0 ),
inference(backward_demodulation,[status(thm)],[f325,f89]) ).
fof(f606,plain,
( ~ sQ32_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f602,f337,f324]) ).
fof(f607,plain,
( ~ sQ32_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f604,f220,f324]) ).
fof(f615,plain,
( ~ sQ17_spl
| e1 != op(e1,e3) ),
inference(forward_demodulation,[status(thm)],[f276,f120]) ).
fof(f621,plain,
( ~ sQ47_spl
| ~ sQ46_spl
| e2 = e3 ),
inference(forward_demodulation,[status(thm)],[f370,f373]) ).
fof(f622,plain,
( ~ sQ47_spl
| ~ sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f621,f141]) ).
fof(f623,plain,
( ~ sQ47_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f622]) ).
fof(f624,plain,
( ~ sQ34_spl
| e2 != op(e2,e3) ),
inference(forward_demodulation,[status(thm)],[f331,f126]) ).
fof(f630,plain,
( ~ sQ21_spl
| e1 != op(e1,e2) ),
inference(backward_demodulation,[status(thm)],[f289,f121]) ).
fof(f634,plain,
( ~ sQ65_spl
| op(e3,e1) = e3 ),
inference(forward_demodulation,[status(thm)],[f432,f54]) ).
fof(f635,plain,
( ~ sQ65_spl
| ~ sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f634,f586]) ).
fof(f636,plain,
( ~ sQ65_spl
| ~ sQ63_spl ),
inference(contradiction_clause,[status(thm)],[f635]) ).
fof(f642,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| e0 = e2 ),
inference(forward_demodulation,[status(thm)],[f247,f253]) ).
fof(f643,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f642,f137]) ).
fof(f644,plain,
( ~ sQ10_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f643]) ).
fof(f645,plain,
( ~ sQ4_spl
| e0 != op(e0,e3) ),
inference(forward_demodulation,[status(thm)],[f234,f116]) ).
fof(f648,plain,
( ~ sQ64_spl
| op(e0,e0) = e0 ),
inference(backward_demodulation,[status(thm)],[f429,f47]) ).
fof(f650,plain,
( ~ sQ64_spl
| op(e0,e1) = e1 ),
inference(backward_demodulation,[status(thm)],[f429,f49]) ).
fof(f651,plain,
( ~ sQ64_spl
| op(e1,e0) = e1 ),
inference(backward_demodulation,[status(thm)],[f429,f50]) ).
fof(f652,plain,
( ~ sQ64_spl
| op(e0,e2) = e2 ),
inference(backward_demodulation,[status(thm)],[f429,f51]) ).
fof(f653,plain,
( ~ sQ64_spl
| op(e2,e0) = e2 ),
inference(backward_demodulation,[status(thm)],[f429,f52]) ).
fof(f655,plain,
( ~ sQ64_spl
| ~ sQ4_spl
| e0 = e1 ),
inference(forward_demodulation,[status(thm)],[f234,f650]) ).
fof(f656,plain,
( ~ sQ64_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f655,f136]) ).
fof(f657,plain,
( ~ sQ64_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f656]) ).
fof(f658,plain,
( ~ sQ34_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f624,f369,f330]) ).
fof(f659,plain,
( ~ sQ64_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f650,f236,f428]) ).
fof(f660,plain,
( ~ sQ5_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f558,f262,f236]) ).
fof(f661,plain,
( ~ sQ5_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f561,f392,f236]) ).
fof(f662,plain,
( ~ sQ58_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f599,f382,f408]) ).
fof(f663,plain,
( ~ sQ32_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f603,f376,f324]) ).
fof(f666,plain,
( ~ sQ10_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f593,f408,f252]) ).
fof(f668,plain,
( ~ sQ16_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f577,f324,f272]) ).
fof(f674,plain,
( ~ sQ66_spl
| op(e3,e2) = e3 ),
inference(forward_demodulation,[status(thm)],[f435,f54]) ).
fof(f675,plain,
( ~ sQ66_spl
| op(e0,e0) != e0 ),
inference(backward_demodulation,[status(thm)],[f680,f89]) ).
fof(f680,plain,
( ~ sQ66_spl
| op(e2,e0) = e0 ),
inference(forward_demodulation,[status(thm)],[f435,f47]) ).
fof(f681,plain,
( ~ sQ66_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f675,f220,f434]) ).
fof(f683,plain,
( sQ59_spl
| ~ sQ66_spl
| e3 != e3 ),
inference(forward_demodulation,[status(thm)],[f674,f413]) ).
fof(f684,plain,
( sQ59_spl
| ~ sQ66_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f683]) ).
fof(f685,plain,
( sQ59_spl
| ~ sQ66_spl ),
inference(contradiction_clause,[status(thm)],[f684]) ).
fof(f686,plain,
( ~ sQ21_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f630,f301,f288]) ).
fof(f687,plain,
( ~ sQ63_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f543,f372,f424]) ).
fof(f688,plain,
( ~ sQ64_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f648,f220,f428]) ).
fof(f690,plain,
( ~ sQ64_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f652,f252,f428]) ).
fof(f694,plain,
( ~ sQ65_spl
| e0 != op(e1,e1) ),
inference(backward_demodulation,[status(thm)],[f698,f94]) ).
fof(f695,plain,
( ~ sQ65_spl
| e0 != op(e3,e1) ),
inference(backward_demodulation,[status(thm)],[f698,f96]) ).
fof(f696,plain,
( ~ sQ65_spl
| op(e0,e0) != e0 ),
inference(backward_demodulation,[status(thm)],[f698,f112]) ).
fof(f697,plain,
( ~ sQ65_spl
| e0 != op(e0,e2) ),
inference(backward_demodulation,[status(thm)],[f698,f115]) ).
fof(f698,plain,
( ~ sQ65_spl
| op(e0,e1) = e0 ),
inference(forward_demodulation,[status(thm)],[f432,f48]) ).
fof(f699,plain,
( ~ sQ65_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f694,f285,f431]) ).
fof(f700,plain,
( ~ sQ65_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f696,f220,f431]) ).
fof(f701,plain,
( ~ sQ65_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f697,f246,f431]) ).
fof(f702,plain,
( ~ sQ66_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f680,f324,f434]) ).
fof(f704,plain,
( ~ sQ63_spl
| ~ sQ59_spl ),
inference(split_clause,[status(thm)],[f587,f411,f424]) ).
fof(f705,plain,
( ~ sQ29_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f565,f301,f314]) ).
fof(f708,plain,
( ~ sQ65_spl
| op(e2,e1) = e2 ),
inference(backward_demodulation,[status(thm)],[f432,f52]) ).
fof(f713,plain,
( ~ sQ65_spl
| e0 != op(e1,e3) ),
inference(backward_demodulation,[status(thm)],[f718,f120]) ).
fof(f717,plain,
( ~ sQ65_spl
| e0 != op(e1,e2) ),
inference(backward_demodulation,[status(thm)],[f718,f119]) ).
fof(f718,plain,
( ~ sQ65_spl
| op(e1,e0) = e0 ),
inference(forward_demodulation,[status(thm)],[f432,f47]) ).
fof(f719,plain,
( ~ sQ65_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f717,f298,f431]) ).
fof(f720,plain,
( ~ sQ55_spl
| e3 != op(e3,e2) ),
inference(backward_demodulation,[status(thm)],[f399,f133]) ).
fof(f723,plain,
( ~ sQ55_spl
| op(e1,e1) != e3 ),
inference(backward_demodulation,[status(thm)],[f399,f98]) ).
fof(f726,plain,
( ~ sQ55_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f723,f294,f398]) ).
fof(f732,plain,
( ~ sQ56_spl
| op(e1,e2) != e0 ),
inference(backward_demodulation,[status(thm)],[f403,f104]) ).
fof(f739,plain,
( ~ sQ57_spl
| ~ sQ56_spl
| e0 = e1 ),
inference(forward_demodulation,[status(thm)],[f403,f406]) ).
fof(f740,plain,
( ~ sQ57_spl
| ~ sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f739,f136]) ).
fof(f741,plain,
( ~ sQ57_spl
| ~ sQ56_spl ),
inference(contradiction_clause,[status(thm)],[f740]) ).
fof(f742,plain,
( ~ sQ67_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f529,f369,f437]) ).
fof(f743,plain,
( ~ sQ67_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f532,f392,f437]) ).
fof(f744,plain,
( ~ sQ67_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f533,f259,f437]) ).
fof(f759,plain,
( ~ sQ52_spl
| e0 != op(e3,e3) ),
inference(forward_demodulation,[status(thm)],[f390,f134]) ).
fof(f760,plain,
( ~ sQ17_spl
| e1 != op(e1,e2) ),
inference(backward_demodulation,[status(thm)],[f276,f119]) ).
fof(f762,plain,
( ~ sQ17_spl
| e1 != op(e3,e0) ),
inference(backward_demodulation,[status(thm)],[f276,f92]) ).
fof(f767,plain,
( ~ sQ17_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f760,f301,f275]) ).
fof(f768,plain,
( ~ sQ17_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f762,f379,f275]) ).
fof(f769,plain,
( ~ sQ65_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f708,f343,f431]) ).
fof(f770,plain,
( ~ sQ65_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f713,f311,f431]) ).
fof(f772,plain,
( ~ sQ64_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f651,f275,f428]) ).
fof(f773,plain,
( ~ sQ64_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f653,f330,f428]) ).
fof(f776,plain,
( ~ sQ52_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f759,f415,f389]) ).
fof(f777,plain,
( ~ sQ38_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f551,f239,f343]) ).
fof(f778,plain,
( ~ sQ5_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f562,f288,f236]) ).
fof(f779,plain,
( ~ sQ12_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f588,f246,f259]) ).
fof(f780,plain,
( ~ sQ4_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f645,f259,f233]) ).
fof(f781,plain,
( ~ sQ10_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f592,f226,f252]) ).
fof(f783,plain,
( ~ sQ38_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f550,f291,f343]) ).
fof(f784,plain,
( ~ sQ55_spl
| ~ sQ59_spl ),
inference(split_clause,[status(thm)],[f720,f411,f398]) ).
fof(f787,plain,
( ~ sQ53_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f571,f288,f392]) ).
fof(f789,plain,
( ~ sQ31_spl
| e3 != op(e2,e3) ),
inference(backward_demodulation,[status(thm)],[f321,f109]) ).
fof(f791,plain,
( ~ sQ31_spl
| op(e1,e1) != e3 ),
inference(backward_demodulation,[status(thm)],[f321,f122]) ).
fof(f794,plain,
( ~ sQ66_spl
| op(e1,e2) = e1 ),
inference(backward_demodulation,[status(thm)],[f435,f50]) ).
fof(f801,plain,
( ~ sQ66_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f794,f301,f434]) ).
fof(f802,plain,
( ~ sQ65_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f634,f398,f431]) ).
fof(f804,plain,
( ~ sQ65_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f695,f389,f431]) ).
fof(f807,plain,
( ~ sQ67_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f531,f314,f437]) ).
fof(f812,plain,
( ~ sQ25_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f548,f249,f301]) ).
fof(f813,plain,
( ~ sQ16_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f576,f376,f272]) ).
fof(f814,plain,
( ~ sQ31_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f791,f294,f320]) ).
fof(f822,plain,
( ~ sQ51_spl
| e3 != op(e3,e2) ),
inference(backward_demodulation,[status(thm)],[f386,f131]) ).
fof(f827,plain,
( ~ sQ51_spl
| ~ sQ59_spl ),
inference(split_clause,[status(thm)],[f822,f411,f385]) ).
fof(f828,plain,
( ~ sQ17_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f615,f314,f275]) ).
fof(f831,plain,
( ~ sQ56_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f732,f298,f402]) ).
fof(f844,plain,
( ~ sQ62_spl
| op(e2,e3) != e2 ),
inference(backward_demodulation,[status(thm)],[f422,f111]) ).
fof(f846,plain,
( ~ sQ62_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f844,f369,f421]) ).
fof(f847,plain,
( ~ sQ25_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f546,f405,f301]) ).
fof(f849,plain,
( ~ sQ31_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f789,f372,f320]) ).
fof(f851,plain,
$false,
inference(sat_refutation,[status(thm)],[f258,f323,f375,f388,f401,f414,f440,f443,f445,f446,f449,f450,f455,f458,f460,f464,f465,f466,f467,f468,f476,f477,f478,f479,f480,f482,f483,f484,f485,f486,f488,f489,f490,f491,f492,f493,f494,f496,f497,f498,f499,f500,f501,f502,f503,f507,f508,f510,f516,f517,f518,f519,f522,f523,f524,f525,f554,f563,f564,f580,f583,f591,f606,f607,f623,f636,f644,f657,f658,f659,f660,f661,f662,f663,f666,f668,f681,f685,f686,f687,f688,f690,f699,f700,f701,f702,f704,f705,f719,f726,f741,f742,f743,f744,f767,f768,f769,f770,f772,f773,f776,f777,f778,f779,f780,f781,f783,f784,f787,f801,f802,f804,f807,f812,f813,f814,f827,f828,f831,f846,f847,f849]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG045+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 12:54:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.058618 seconds
% 0.13/0.42 % CPU time: 0.270615 seconds
% 0.13/0.42 % Total memory used: 14.115 MB
% 0.13/0.42 % Net memory used: 13.952 MB
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