%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG139+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 12:53:34 PM UTC 2026
% Result : Unsatisfiable 2.07s 1.28s
% Output : CNFRefutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 21
% Syntax : Number of formulae : 251 ( 60 unt; 4 def)
% Number of atoms : 1003 ( 939 equ)
% Maximal formula atoms : 128 ( 3 avg)
% Number of connectives : 1102 ( 350 ~; 588 |; 164 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 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/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f2,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/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f3,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/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
( e2 != e3
& e1 != e3
& e1 != e2
& e0 != e3
& e0 != e2
& e0 != e1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f5,axiom,
( ( ( op(e3,e3) != e3
& op(e3,e3) = e3 )
| ( op(e3,e3) != e2
& op(e2,e2) = e3 )
| ( op(e3,e3) != e1
& op(e1,e1) = e3 )
| ( op(e3,e3) != e0
& op(e0,e0) = e3 ) )
& ( ( op(e2,e2) != e3
& op(e3,e3) = e2 )
| ( op(e2,e2) != e2
& op(e2,e2) = e2 )
| ( op(e2,e2) != e1
& op(e1,e1) = e2 )
| ( op(e2,e2) != e0
& op(e0,e0) = e2 ) )
& ( ( op(e1,e1) != e3
& op(e3,e3) = e1 )
| ( op(e1,e1) != e2
& op(e2,e2) = e1 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1 )
| ( op(e1,e1) != e0
& op(e0,e0) = e1 ) )
& ( ( op(e0,e0) != e3
& op(e3,e3) = e0 )
| ( op(e0,e0) != e2
& op(e2,e2) = e0 )
| ( op(e0,e0) != e1
& op(e1,e1) = e0 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
fof(f9,axiom,
~ ( e1 = op(e3,e3)
& e2 = op(op(e3,e3),op(e3,e3))
& e0 = op(op(e3,e3),e3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9) ).
fof(f14,axiom,
~ ( e3 = op(e0,e0)
& e2 = op(op(e0,e0),op(e0,e0))
& e1 = op(op(e0,e0),e0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14) ).
fof(f15,axiom,
~ ( e0 = op(e3,e3)
& e2 = op(op(e3,e3),op(e3,e3))
& e1 = op(op(e3,e3),e3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f16,axiom,
~ ( e2 = op(e0,e0)
& e3 = op(op(e0,e0),op(e0,e0))
& e1 = op(op(e0,e0),e0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f21,axiom,
~ ( e0 = op(e3,e3)
& e1 = op(op(e3,e3),op(e3,e3))
& e2 = op(op(e3,e3),e3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f22,axiom,
~ ( e1 = op(e0,e0)
& e3 = op(op(e0,e0),op(e0,e0))
& e2 = op(op(e0,e0),e0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
fof(f23,axiom,
~ ( e0 = op(e1,e1)
& e3 = op(op(e1,e1),op(e1,e1))
& e2 = op(op(e1,e1),e1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
fof(f24,axiom,
~ ( e2 = op(e1,e1)
& e0 = op(op(e1,e1),op(e1,e1))
& e3 = op(op(e1,e1),e1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
fof(f26,axiom,
~ ( e2 = op(e0,e0)
& e1 = op(op(e0,e0),op(e0,e0))
& e3 = op(op(e0,e0),e0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f27,axiom,
~ ( e0 = op(e2,e2)
& e1 = op(op(e2,e2),op(e2,e2))
& e3 = op(op(e2,e2),e2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).
fof(f28,axiom,
~ ( e1 = op(e0,e0)
& e2 = op(op(e0,e0),op(e0,e0))
& e3 = op(op(e0,e0),e0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f29,axiom,
~ ( e0 = op(e1,e1)
& e2 = op(op(e1,e1),op(e1,e1))
& e3 = op(op(e1,e1),e1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).
fof(f33,plain,
( e1 != op(e3,e3)
| e2 != op(op(e3,e3),op(e3,e3))
| e0 != op(op(e3,e3),e3) ),
inference(ennf_transformation,[],[f9]) ).
fof(f38,plain,
( op(e0,e0) != e3
| e2 != op(op(e0,e0),op(e0,e0))
| e1 != op(op(e0,e0),e0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f39,plain,
( e0 != op(e3,e3)
| e2 != op(op(e3,e3),op(e3,e3))
| e1 != op(op(e3,e3),e3) ),
inference(ennf_transformation,[],[f15]) ).
fof(f40,plain,
( op(e0,e0) != e2
| e3 != op(op(e0,e0),op(e0,e0))
| e1 != op(op(e0,e0),e0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f45,plain,
( e0 != op(e3,e3)
| e1 != op(op(e3,e3),op(e3,e3))
| e2 != op(op(e3,e3),e3) ),
inference(ennf_transformation,[],[f21]) ).
fof(f46,plain,
( op(e0,e0) != e1
| e3 != op(op(e0,e0),op(e0,e0))
| e2 != op(op(e0,e0),e0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f47,plain,
( e0 != op(e1,e1)
| e3 != op(op(e1,e1),op(e1,e1))
| e2 != op(op(e1,e1),e1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f48,plain,
( e2 != op(e1,e1)
| e0 != op(op(e1,e1),op(e1,e1))
| e3 != op(op(e1,e1),e1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f50,plain,
( op(e0,e0) != e2
| e1 != op(op(e0,e0),op(e0,e0))
| e3 != op(op(e0,e0),e0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f51,plain,
( e0 != op(e2,e2)
| e1 != op(op(e2,e2),op(e2,e2))
| e3 != op(op(e2,e2),e2) ),
inference(ennf_transformation,[],[f27]) ).
fof(f52,plain,
( op(e0,e0) != e1
| e2 != op(op(e0,e0),op(e0,e0))
| e3 != op(op(e0,e0),e0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f53,plain,
( e0 != op(e1,e1)
| e2 != op(op(e1,e1),op(e1,e1))
| e3 != op(op(e1,e1),e1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f59,plain,
( ~ sP3
| ( op(e0,e0) != e3
& op(e3,e3) = e0 ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f60,plain,
( ~ sP2
| ( op(e1,e1) != e3
& op(e3,e3) = e1 ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f61,plain,
( ~ sP1
| ( op(e2,e2) != e3
& op(e3,e3) = e2 ) ),
inference(nnf_transformation,[],[f55]) ).
fof(f63,plain,
( e3 = op(e3,e3)
| e2 = op(e3,e3)
| e1 = op(e3,e3)
| e0 = op(e3,e3) ),
inference(cnf_transformation,[],[f1]) ).
fof(f66,plain,
( e3 = op(e3,e0)
| e2 = op(e3,e0)
| e1 = op(e3,e0)
| e0 = op(e3,e0) ),
inference(cnf_transformation,[],[f1]) ).
fof(f70,plain,
( e3 = op(e2,e0)
| e2 = op(e2,e0)
| e1 = op(e2,e0)
| e0 = op(e2,e0) ),
inference(cnf_transformation,[],[f1]) ).
fof(f71,plain,
( e3 = op(e1,e3)
| e2 = op(e1,e3)
| e1 = op(e1,e3)
| e0 = op(e1,e3) ),
inference(cnf_transformation,[],[f1]) ).
fof(f75,plain,
( e3 = op(e0,e3)
| e2 = op(e0,e3)
| e1 = op(e0,e3)
| e0 = op(e0,e3) ),
inference(cnf_transformation,[],[f1]) ).
fof(f76,plain,
( e3 = op(e0,e2)
| e2 = op(e0,e2)
| e1 = op(e0,e2)
| e0 = op(e0,e2) ),
inference(cnf_transformation,[],[f1]) ).
fof(f88,plain,
( e3 = op(e2,e3)
| e3 = op(e2,e2)
| e3 = op(e2,e1)
| e3 = op(e2,e0) ),
inference(cnf_transformation,[],[f2]) ).
fof(f93,plain,
( e0 = op(e3,e2)
| e0 = op(e2,e2)
| e0 = op(e1,e2)
| e0 = op(e0,e2) ),
inference(cnf_transformation,[],[f2]) ).
fof(f95,plain,
( e3 = op(e3,e1)
| e3 = op(e2,e1)
| e3 = op(e1,e1)
| e3 = op(e0,e1) ),
inference(cnf_transformation,[],[f2]) ).
fof(f96,plain,
( e3 = op(e1,e3)
| e3 = op(e1,e2)
| e3 = op(e1,e1)
| e3 = op(e1,e0) ),
inference(cnf_transformation,[],[f2]) ).
fof(f98,plain,
( e2 = op(e1,e3)
| e2 = op(e1,e2)
| e2 = op(e1,e1)
| e2 = op(e1,e0) ),
inference(cnf_transformation,[],[f2]) ).
fof(f104,plain,
( e3 = op(e0,e3)
| e3 = op(e0,e2)
| e3 = op(e0,e1)
| op(e0,e0) = e3 ),
inference(cnf_transformation,[],[f2]) ).
fof(f106,plain,
( e2 = op(e0,e3)
| e2 = op(e0,e2)
| e2 = op(e0,e1)
| op(e0,e0) = e2 ),
inference(cnf_transformation,[],[f2]) ).
fof(f107,plain,
( e1 = op(e3,e0)
| e1 = op(e2,e0)
| e1 = op(e1,e0)
| op(e0,e0) = e1 ),
inference(cnf_transformation,[],[f2]) ).
fof(f114,plain,
op(e3,e0) != op(e3,e3),
inference(cnf_transformation,[],[f3]) ).
fof(f115,plain,
op(e3,e0) != op(e3,e2),
inference(cnf_transformation,[],[f3]) ).
fof(f116,plain,
op(e3,e0) != op(e3,e1),
inference(cnf_transformation,[],[f3]) ).
fof(f117,plain,
op(e2,e2) != op(e2,e3),
inference(cnf_transformation,[],[f3]) ).
fof(f119,plain,
op(e2,e1) != op(e2,e2),
inference(cnf_transformation,[],[f3]) ).
fof(f121,plain,
op(e2,e0) != op(e2,e2),
inference(cnf_transformation,[],[f3]) ).
fof(f124,plain,
op(e1,e1) != op(e1,e3),
inference(cnf_transformation,[],[f3]) ).
fof(f125,plain,
op(e1,e1) != op(e1,e2),
inference(cnf_transformation,[],[f3]) ).
fof(f132,plain,
op(e0,e0) != op(e0,e3),
inference(cnf_transformation,[],[f3]) ).
fof(f133,plain,
op(e0,e0) != op(e0,e2),
inference(cnf_transformation,[],[f3]) ).
fof(f136,plain,
op(e1,e3) != op(e3,e3),
inference(cnf_transformation,[],[f3]) ).
fof(f137,plain,
op(e1,e3) != op(e2,e3),
inference(cnf_transformation,[],[f3]) ).
fof(f138,plain,
op(e0,e3) != op(e3,e3),
inference(cnf_transformation,[],[f3]) ).
fof(f139,plain,
op(e0,e3) != op(e2,e3),
inference(cnf_transformation,[],[f3]) ).
fof(f140,plain,
op(e0,e3) != op(e1,e3),
inference(cnf_transformation,[],[f3]) ).
fof(f143,plain,
op(e1,e2) != op(e2,e2),
inference(cnf_transformation,[],[f3]) ).
fof(f145,plain,
op(e0,e2) != op(e2,e2),
inference(cnf_transformation,[],[f3]) ).
fof(f146,plain,
op(e0,e2) != op(e1,e2),
inference(cnf_transformation,[],[f3]) ).
fof(f149,plain,
op(e1,e1) != op(e2,e1),
inference(cnf_transformation,[],[f3]) ).
fof(f153,plain,
op(e2,e0) != op(e3,e0),
inference(cnf_transformation,[],[f3]) ).
fof(f154,plain,
op(e1,e0) != op(e3,e0),
inference(cnf_transformation,[],[f3]) ).
fof(f156,plain,
op(e0,e0) != op(e3,e0),
inference(cnf_transformation,[],[f3]) ).
fof(f157,plain,
op(e0,e0) != op(e2,e0),
inference(cnf_transformation,[],[f3]) ).
fof(f159,plain,
e2 != e3,
inference(cnf_transformation,[],[f4]) ).
fof(f160,plain,
e1 != e3,
inference(cnf_transformation,[],[f4]) ).
fof(f161,plain,
e1 != e2,
inference(cnf_transformation,[],[f4]) ).
fof(f162,plain,
e0 != e3,
inference(cnf_transformation,[],[f4]) ).
fof(f163,plain,
e0 != e2,
inference(cnf_transformation,[],[f4]) ).
fof(f164,plain,
e0 != e1,
inference(cnf_transformation,[],[f4]) ).
fof(f165,plain,
( ~ sP3
| op(e0,e0) != e3 ),
inference(cnf_transformation,[],[f59]) ).
fof(f166,plain,
( ~ sP3
| e0 = op(e3,e3) ),
inference(cnf_transformation,[],[f59]) ).
fof(f168,plain,
( ~ sP2
| e1 = op(e3,e3) ),
inference(cnf_transformation,[],[f60]) ).
fof(f169,plain,
( ~ sP1
| e3 != op(e2,e2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f170,plain,
( ~ sP1
| e2 = op(e3,e3) ),
inference(cnf_transformation,[],[f61]) ).
fof(f175,plain,
( sP0
| e2 != op(e3,e3)
| e3 = op(e1,e1)
| e0 != op(e3,e3) ),
inference(cnf_transformation,[],[f58]) ).
fof(f176,plain,
( sP0
| e3 = op(e2,e2)
| e3 = op(e1,e1)
| e0 != op(e3,e3) ),
inference(cnf_transformation,[],[f58]) ).
fof(f178,plain,
( sP0
| e3 = op(e2,e2)
| e1 != op(e3,e3)
| op(e0,e0) = e3 ),
inference(cnf_transformation,[],[f58]) ).
fof(f179,plain,
( sP0
| e2 != op(e3,e3)
| e3 = op(e1,e1)
| op(e0,e0) = e3 ),
inference(cnf_transformation,[],[f58]) ).
fof(f180,plain,
( sP0
| e3 = op(e2,e2)
| e3 = op(e1,e1)
| op(e0,e0) = e3 ),
inference(cnf_transformation,[],[f58]) ).
fof(f187,plain,
( sP1
| e2 != op(e2,e2)
| e2 = op(e1,e1)
| op(e0,e0) = e2 ),
inference(cnf_transformation,[],[f58]) ).
fof(f188,plain,
( sP1
| e2 = op(e2,e2)
| e2 = op(e1,e1)
| op(e0,e0) = e2 ),
inference(cnf_transformation,[],[f58]) ).
fof(f194,plain,
( sP2
| e1 = op(e2,e2)
| e1 != op(e1,e1)
| op(e0,e0) = e1 ),
inference(cnf_transformation,[],[f58]) ).
fof(f196,plain,
( sP2
| e1 = op(e2,e2)
| e1 = op(e1,e1)
| op(e0,e0) = e1 ),
inference(cnf_transformation,[],[f58]) ).
fof(f198,plain,
( sP3
| e0 = op(e2,e2)
| op(e0,e0) != e1
| e0 != op(e0,e0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f200,plain,
( sP3
| e0 = op(e2,e2)
| e0 = op(e1,e1)
| e0 != op(e0,e0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f202,plain,
( sP3
| e0 = op(e2,e2)
| op(e0,e0) != e1
| e0 = op(e0,e0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f204,plain,
( sP3
| e0 = op(e2,e2)
| e0 = op(e1,e1)
| e0 = op(e0,e0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f208,plain,
( e1 != op(e3,e3)
| e2 != op(op(e3,e3),op(e3,e3))
| e0 != op(op(e3,e3),e3) ),
inference(cnf_transformation,[],[f33]) ).
fof(f213,plain,
( op(e0,e0) != e3
| e2 != op(op(e0,e0),op(e0,e0))
| e1 != op(op(e0,e0),e0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f214,plain,
( e0 != op(e3,e3)
| e2 != op(op(e3,e3),op(e3,e3))
| e1 != op(op(e3,e3),e3) ),
inference(cnf_transformation,[],[f39]) ).
fof(f215,plain,
( op(e0,e0) != e2
| e3 != op(op(e0,e0),op(e0,e0))
| e1 != op(op(e0,e0),e0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f220,plain,
( e0 != op(e3,e3)
| e1 != op(op(e3,e3),op(e3,e3))
| e2 != op(op(e3,e3),e3) ),
inference(cnf_transformation,[],[f45]) ).
fof(f221,plain,
( op(e0,e0) != e1
| e3 != op(op(e0,e0),op(e0,e0))
| e2 != op(op(e0,e0),e0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f222,plain,
( e0 != op(e1,e1)
| e3 != op(op(e1,e1),op(e1,e1))
| e2 != op(op(e1,e1),e1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f223,plain,
( e2 != op(e1,e1)
| e0 != op(op(e1,e1),op(e1,e1))
| e3 != op(op(e1,e1),e1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f225,plain,
( op(e0,e0) != e2
| e1 != op(op(e0,e0),op(e0,e0))
| e3 != op(op(e0,e0),e0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f226,plain,
( e0 != op(e2,e2)
| e1 != op(op(e2,e2),op(e2,e2))
| e3 != op(op(e2,e2),e2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f227,plain,
( op(e0,e0) != e1
| e2 != op(op(e0,e0),op(e0,e0))
| e3 != op(op(e0,e0),e0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f228,plain,
( e0 != op(e1,e1)
| e2 != op(op(e1,e1),op(e1,e1))
| e3 != op(op(e1,e1),e1) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_51,plain,
( ( op(e0,e2) = e3 )
| ( op(e0,e2) = e2 )
| ( op(e0,e2) = e1 )
| ( op(e0,e2) = e0 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_52,plain,
( ( op(e0,e3) = e3 )
| ( op(e0,e3) = e2 )
| ( op(e0,e3) = e1 )
| ( op(e0,e3) = e0 ) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_56,plain,
( ( op(e1,e3) = e3 )
| ( op(e1,e3) = e2 )
| ( op(e1,e3) = e1 )
| ( op(e1,e3) = e0 ) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_57,plain,
( ( op(e2,e0) = e3 )
| ( op(e2,e0) = e2 )
| ( op(e2,e0) = e1 )
| ( op(e2,e0) = e0 ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_61,plain,
( ( op(e3,e0) = e3 )
| ( op(e3,e0) = e2 )
| ( op(e3,e0) = e1 )
| ( op(e3,e0) = e0 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_64,plain,
( ( op(e3,e3) = e3 )
| ( op(e3,e3) = e2 )
| ( op(e3,e3) = e1 )
| ( op(e3,e3) = e0 ) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_68,plain,
( ( op(e3,e0) = e1 )
| ( op(e2,e0) = e1 )
| ( op(e1,e0) = e1 )
| ( op(e0,e0) = e1 ) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_69,plain,
( ( op(e0,e3) = e2 )
| ( op(e0,e2) = e2 )
| ( op(e0,e1) = e2 )
| ( op(e0,e0) = e2 ) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_71,plain,
( ( op(e0,e3) = e3 )
| ( op(e0,e2) = e3 )
| ( op(e0,e1) = e3 )
| ( op(e0,e0) = e3 ) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_77,plain,
( ( op(e1,e3) = e2 )
| ( op(e1,e2) = e2 )
| ( op(e1,e1) = e2 )
| ( op(e1,e0) = e2 ) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_79,plain,
( ( op(e1,e3) = e3 )
| ( op(e1,e2) = e3 )
| ( op(e1,e1) = e3 )
| ( op(e1,e0) = e3 ) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_80,plain,
( ( op(e3,e1) = e3 )
| ( op(e2,e1) = e3 )
| ( op(e1,e1) = e3 )
| ( op(e0,e1) = e3 ) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_82,plain,
( ( op(e3,e2) = e0 )
| ( op(e2,e2) = e0 )
| ( op(e1,e2) = e0 )
| ( op(e0,e2) = e0 ) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_87,plain,
( ( op(e2,e3) = e3 )
| ( op(e2,e2) = e3 )
| ( op(e2,e1) = e3 )
| ( op(e2,e0) = e3 ) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_98,plain,
op(e0,e0) != op(e2,e0),
inference(cnf_transformation,[],[f157]) ).
tcf(c_99,plain,
op(e0,e0) != op(e3,e0),
inference(cnf_transformation,[],[f156]) ).
tcf(c_101,plain,
op(e1,e0) != op(e3,e0),
inference(cnf_transformation,[],[f154]) ).
tcf(c_102,plain,
op(e2,e0) != op(e3,e0),
inference(cnf_transformation,[],[f153]) ).
tcf(c_106,plain,
op(e1,e1) != op(e2,e1),
inference(cnf_transformation,[],[f149]) ).
tcf(c_109,plain,
op(e0,e2) != op(e1,e2),
inference(cnf_transformation,[],[f146]) ).
tcf(c_110,plain,
op(e0,e2) != op(e2,e2),
inference(cnf_transformation,[],[f145]) ).
tcf(c_112,plain,
op(e1,e2) != op(e2,e2),
inference(cnf_transformation,[],[f143]) ).
tcf(c_115,plain,
op(e0,e3) != op(e1,e3),
inference(cnf_transformation,[],[f140]) ).
tcf(c_116,plain,
op(e0,e3) != op(e2,e3),
inference(cnf_transformation,[],[f139]) ).
tcf(c_117,plain,
op(e0,e3) != op(e3,e3),
inference(cnf_transformation,[],[f138]) ).
tcf(c_118,plain,
op(e1,e3) != op(e2,e3),
inference(cnf_transformation,[],[f137]) ).
tcf(c_119,plain,
op(e1,e3) != op(e3,e3),
inference(cnf_transformation,[],[f136]) ).
tcf(c_122,plain,
op(e0,e0) != op(e0,e2),
inference(cnf_transformation,[],[f133]) ).
tcf(c_123,plain,
op(e0,e0) != op(e0,e3),
inference(cnf_transformation,[],[f132]) ).
tcf(c_130,plain,
op(e1,e1) != op(e1,e2),
inference(cnf_transformation,[],[f125]) ).
tcf(c_131,plain,
op(e1,e1) != op(e1,e3),
inference(cnf_transformation,[],[f124]) ).
tcf(c_134,plain,
op(e2,e0) != op(e2,e2),
inference(cnf_transformation,[],[f121]) ).
tcf(c_136,plain,
op(e2,e1) != op(e2,e2),
inference(cnf_transformation,[],[f119]) ).
tcf(c_138,plain,
op(e2,e2) != op(e2,e3),
inference(cnf_transformation,[],[f117]) ).
tcf(c_139,plain,
op(e3,e0) != op(e3,e1),
inference(cnf_transformation,[],[f116]) ).
tcf(c_140,plain,
op(e3,e0) != op(e3,e2),
inference(cnf_transformation,[],[f115]) ).
tcf(c_141,plain,
op(e3,e0) != op(e3,e3),
inference(cnf_transformation,[],[f114]) ).
tcf(c_145,plain,
e0 != e1,
inference(cnf_transformation,[],[f164]) ).
tcf(c_146,plain,
e0 != e2,
inference(cnf_transformation,[],[f163]) ).
tcf(c_147,plain,
e0 != e3,
inference(cnf_transformation,[],[f162]) ).
tcf(c_148,plain,
e1 != e2,
inference(cnf_transformation,[],[f161]) ).
tcf(c_149,plain,
e1 != e3,
inference(cnf_transformation,[],[f160]) ).
tcf(c_150,plain,
e2 != e3,
inference(cnf_transformation,[],[f159]) ).
tcf(c_151,plain,
( ( op(e3,e3) = e0 )
| ~ sP3 ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_152,plain,
( ~ sP3
| ( op(e0,e0) != e3 ) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_153,plain,
( ( op(e3,e3) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_155,plain,
( ( op(e3,e3) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_156,plain,
( ~ sP1
| ( op(e2,e2) != e3 ) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_159,plain,
( sP3
| ( op(e2,e2) = e0 )
| ( op(e1,e1) = e0 )
| ( op(e0,e0) = e0 ) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_161,plain,
( sP3
| ( op(e2,e2) = e0 )
| ( op(e0,e0) = e0 )
| ( op(e0,e0) != e1 ) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_163,plain,
( sP3
| ( op(e2,e2) = e0 )
| ( op(e1,e1) = e0 )
| ( op(e0,e0) != e0 ) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_165,plain,
( sP3
| ( op(e2,e2) = e0 )
| ( op(e0,e0) != e1 )
| ( op(e0,e0) != e0 ) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_167,plain,
( sP2
| ( op(e2,e2) = e1 )
| ( op(e1,e1) = e1 )
| ( op(e0,e0) = e1 ) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_169,plain,
( sP2
| ( op(e2,e2) = e1 )
| ( op(e0,e0) = e1 )
| ( op(e1,e1) != e1 ) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_175,plain,
( sP1
| ( op(e2,e2) = e2 )
| ( op(e1,e1) = e2 )
| ( op(e0,e0) = e2 ) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_176,plain,
( sP1
| ( op(e1,e1) = e2 )
| ( op(e0,e0) = e2 )
| ( op(e2,e2) != e2 ) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_183,plain,
( sP0
| ( op(e2,e2) = e3 )
| ( op(e1,e1) = e3 )
| ( op(e0,e0) = e3 ) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_184,plain,
( sP0
| ( op(e1,e1) = e3 )
| ( op(e0,e0) = e3 )
| ( op(e3,e3) != e2 ) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_185,plain,
( sP0
| ( op(e2,e2) = e3 )
| ( op(e0,e0) = e3 )
| ( op(e3,e3) != e1 ) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_187,plain,
( sP0
| ( op(e2,e2) = e3 )
| ( op(e1,e1) = e3 )
| ( op(e3,e3) != e0 ) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_188,plain,
( sP0
| ( op(e1,e1) = e3 )
| ( op(e3,e3) != e2 )
| ( op(e3,e3) != e0 ) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_194,plain,
( ( op(e3,e3) != e1 )
| ( op(op(e3,e3),e3) != e0 )
| ( op(op(e3,e3),op(e3,e3)) != e2 ) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_199,plain,
( ( op(e0,e0) != e3 )
| ( op(op(e0,e0),e0) != e1 )
| ( op(op(e0,e0),op(e0,e0)) != e2 ) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_200,plain,
( ( op(e3,e3) != e0 )
| ( op(op(e3,e3),e3) != e1 )
| ( op(op(e3,e3),op(e3,e3)) != e2 ) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_201,plain,
( ( op(e0,e0) != e2 )
| ( op(op(e0,e0),e0) != e1 )
| ( op(op(e0,e0),op(e0,e0)) != e3 ) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_206,plain,
( ( op(e3,e3) != e0 )
| ( op(op(e3,e3),e3) != e2 )
| ( op(op(e3,e3),op(e3,e3)) != e1 ) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_207,plain,
( ( op(e0,e0) != e1 )
| ( op(op(e0,e0),e0) != e2 )
| ( op(op(e0,e0),op(e0,e0)) != e3 ) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_208,plain,
( ( op(e1,e1) != e0 )
| ( op(op(e1,e1),e1) != e2 )
| ( op(op(e1,e1),op(e1,e1)) != e3 ) ),
inference(cnf_transformation,[],[f222]) ).
tcf(c_209,plain,
( ( op(e1,e1) != e2 )
| ( op(op(e1,e1),e1) != e3 )
| ( op(op(e1,e1),op(e1,e1)) != e0 ) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_211,plain,
( ( op(e0,e0) != e2 )
| ( op(op(e0,e0),e0) != e3 )
| ( op(op(e0,e0),op(e0,e0)) != e1 ) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_212,plain,
( ( op(e2,e2) != e0 )
| ( op(op(e2,e2),e2) != e3 )
| ( op(op(e2,e2),op(e2,e2)) != e1 ) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_213,plain,
( ( op(e0,e0) != e1 )
| ( op(op(e0,e0),e0) != e3 )
| ( op(op(e0,e0),op(e0,e0)) != e2 ) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_214,plain,
( ( op(e1,e1) != e0 )
| ( op(op(e1,e1),e1) != e3 )
| ( op(op(e1,e1),op(e1,e1)) != e2 ) ),
inference(cnf_transformation,[],[f228]) ).
tcf(c_221,plain,
( sP1
| ( op(e0,e0) = e2 )
| ( op(e1,e1) = e2 ) ),
inference(global_subsumption_just,[status(thm)],[c_175,c_175,c_176]) ).
tcf(c_222,plain,
( sP1
| ( op(e1,e1) = e2 )
| ( op(e0,e0) = e2 ) ),
inference(renaming,[status(thm)],[c_221]) ).
tcf(c_223,plain,
( sP2
| ( op(e2,e2) = e1 )
| ( op(e0,e0) = e1 ) ),
inference(global_subsumption_just,[status(thm)],[c_167,c_167,c_169]) ).
tcf(c_225,plain,
( sP3
| ( op(e2,e2) = e0 )
| ( op(e1,e1) = e0 ) ),
inference(global_subsumption_just,[status(thm)],[c_159,c_159,c_163]) ).
tcf(c_237,plain,
( sP1
| ( op(e1,e1) = e2 )
| ( op(e0,e0) = e2 ) ),
inference(global_subsumption_just,[status(thm)],[c_176,c_222]) ).
tcf(c_241,plain,
( sP2
| ( op(e2,e2) = e1 )
| ( op(e0,e0) = e1 ) ),
inference(global_subsumption_just,[status(thm)],[c_169,c_223]) ).
tcf(c_245,plain,
( sP3
| ( op(e2,e2) = e0 )
| ( op(e1,e1) = e0 ) ),
inference(global_subsumption_just,[status(thm)],[c_163,c_225]) ).
tcf(c_247,plain,
( sP3
| ( op(e2,e2) = e0 )
| ( op(e0,e0) != e1 ) ),
inference(global_subsumption_just,[status(thm)],[c_161,c_161,c_165]) ).
tcf(c_269,plain,
( sP3
| ( op(e2,e2) = e0 )
| ( op(e0,e0) != e1 ) ),
inference(global_subsumption_just,[status(thm)],[c_165,c_247]) ).
tcf(c_4709,plain,
( ( op(e3,e3) = e2 )
| ( op(e1,e1) = e2 )
| ( op(e0,e0) = e2 ) ),
inference(superposition,[status(thm)],[c_237,c_155]) ).
tcf(c_4719,plain,
( ( op(e3,e3) = e1 )
| ( op(e2,e2) = e1 )
| ( op(e0,e0) = e1 ) ),
inference(superposition,[status(thm)],[c_241,c_153]) ).
tcf(c_4729,plain,
( ( op(e3,e3) = e0 )
| ( op(e2,e2) = e0 )
| ( op(e1,e1) = e0 ) ),
inference(superposition,[status(thm)],[c_245,c_151]) ).
tcf(c_4946,plain,
( ( op(e1,e1) = e2 )
| ( op(e0,e0) = e2 )
| ( op(e3,e0) != e2 ) ),
inference(superposition,[status(thm)],[c_4709,c_141]) ).
tcf(c_4948,plain,
( ( op(e1,e1) = e2 )
| ( op(e0,e0) = e2 )
| ( op(e1,e3) != e2 ) ),
inference(superposition,[status(thm)],[c_4709,c_119]) ).
tcf(c_4949,plain,
( ( op(e1,e1) = e2 )
| ( op(e0,e0) = e2 )
| ( op(e0,e3) != e2 ) ),
inference(superposition,[status(thm)],[c_4709,c_117]) ).
tcf(c_4974,plain,
( ( e1 = e2 )
| ( op(e2,e2) = e1 )
| ( op(e1,e1) = e2 )
| ( op(e0,e0) = e2 )
| ( op(e0,e0) = e1 ) ),
inference(superposition,[status(thm)],[c_4709,c_4719]) ).
tcf(c_4978,plain,
( ( op(e2,e2) = e1 )
| ( op(e0,e0) = e1 )
| ( op(e3,e0) != e1 ) ),
inference(superposition,[status(thm)],[c_4719,c_141]) ).
tcf(c_4980,plain,
( ( op(e2,e2) = e1 )
| ( op(e0,e0) = e1 )
| ( op(e1,e3) != e1 ) ),
inference(superposition,[status(thm)],[c_4719,c_119]) ).
tcf(c_5000,plain,
( ( op(e2,e2) = e1 )
| ( op(e1,e1) = e2 )
| ( op(e0,e0) = e2 )
| ( op(e0,e0) = e1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4974,c_148]) ).
tcf(c_5013,plain,
( ( e0 = e1 )
| ( op(e2,e2) = e1 )
| ( op(e2,e2) = e0 )
| ( op(e1,e1) = e0 )
| ( op(e0,e0) = e1 ) ),
inference(superposition,[status(thm)],[c_4729,c_4719]) ).
tcf(c_5014,plain,
( ( e0 = e2 )
| ( op(e2,e2) = e0 )
| ( op(e1,e1) = e2 )
| ( op(e1,e1) = e0 )
| ( op(e0,e0) = e2 ) ),
inference(superposition,[status(thm)],[c_4729,c_4709]) ).
tcf(c_5020,plain,
( ( op(e2,e2) = e0 )
| ( op(e1,e1) = e0 )
| ( op(e0,e3) != e0 ) ),
inference(superposition,[status(thm)],[c_4729,c_117]) ).
tcf(c_5039,plain,
( ( op(e2,e2) = e0 )
| ( op(e1,e1) = e2 )
| ( op(e1,e1) = e0 )
| ( op(e0,e0) = e2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5014,c_146]) ).
tcf(c_5044,plain,
( ( op(e2,e2) = e1 )
| ( op(e2,e2) = e0 )
| ( op(e1,e1) = e0 )
| ( op(e0,e0) = e1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5013,c_145]) ).
tcf(c_5234,plain,
( ( op(e3,e0) = e2 )
| ( op(e3,e0) = e1 )
| ( op(e3,e0) = e0 )
| ( op(e0,e0) != e3 ) ),
inference(superposition,[status(thm)],[c_61,c_99]) ).
tcf(c_5667,plain,
( ( op(e2,e2) = e1 )
| ( op(e2,e0) = e1 )
| ( op(e1,e0) = e1 )
| ( op(e0,e0) = e1 ) ),
inference(superposition,[status(thm)],[c_68,c_4978]) ).
tcf(c_6163,plain,
( ( op(e1,e2) = e2 )
| ( op(e1,e1) = e2 )
| ( op(e1,e0) = e2 )
| ( op(e0,e0) = e2 ) ),
inference(superposition,[status(thm)],[c_77,c_4948]) ).
tcf(c_6268,plain,
( ( op(e1,e2) = e3 )
| ( op(e1,e1) = e3 )
| ( op(e1,e0) = e3 )
| ( op(e0,e3) != e3 ) ),
inference(superposition,[status(thm)],[c_79,c_115]) ).
tcf(c_6311,plain,
( ( op(e2,e1) = e3 )
| ( op(e1,e1) = e3 )
| ( op(e0,e1) = e3 )
| ( op(e3,e0) != e3 ) ),
inference(superposition,[status(thm)],[c_80,c_139]) ).
tcf(c_6384,plain,
( ( op(e2,e2) = e0 )
| ( op(e1,e2) = e0 )
| ( op(e0,e2) = e0 )
| ( op(e3,e0) != e0 ) ),
inference(superposition,[status(thm)],[c_82,c_140]) ).
tcf(c_6624,plain,
( ( op(e2,e2) = e3 )
| ( op(e2,e1) = e3 )
| ( op(e2,e0) = e3 )
| ( op(e1,e3) != e3 ) ),
inference(superposition,[status(thm)],[c_87,c_118]) ).
tcf(c_6625,plain,
( ( op(e2,e2) = e3 )
| ( op(e2,e1) = e3 )
| ( op(e2,e0) = e3 )
| ( op(e0,e3) != e3 ) ),
inference(superposition,[status(thm)],[c_87,c_116]) ).
tcf(c_7988,plain,
( ( op(e2,e2) = e0 )
| ( op(e1,e1) = e0 )
| ( op(e0,e0) = e1 )
| ( op(e2,e0) != e1 ) ),
inference(superposition,[status(thm)],[c_5044,c_134]) ).
fof(f54,definition,
( ~ sP0
| ( op(e3,e3) != e3
& op(e3,e3) = e3 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f55,definition,
( ~ sP1
| ( op(e2,e2) != e3
& op(e3,e3) = e2 ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f56,definition,
( ~ sP2
| ( op(e1,e1) != e3
& op(e3,e3) = e1 ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f57,definition,
( ~ sP3
| ( op(e0,e0) != e3
& op(e3,e3) = e0 ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f58,plain,
( ( sP0
| ( op(e3,e3) != e2
& op(e2,e2) = e3 )
| ( op(e3,e3) != e1
& op(e1,e1) = e3 )
| ( op(e3,e3) != e0
& op(e0,e0) = e3 ) )
& ( sP1
| ( op(e2,e2) != e2
& op(e2,e2) = e2 )
| ( op(e2,e2) != e1
& op(e1,e1) = e2 )
| ( op(e2,e2) != e0
& op(e0,e0) = e2 ) )
& ( sP2
| ( op(e1,e1) != e2
& op(e2,e2) = e1 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1 )
| ( op(e1,e1) != e0
& op(e0,e0) = e1 ) )
& ( sP3
| ( op(e0,e0) != e2
& op(e2,e2) = e0 )
| ( op(e0,e0) != e1
& op(e1,e1) = e0 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0 ) ) ),
inference(definition_folding,[],[f5,f57,f56,f55,f54]) ).
fof(f62,plain,
( ~ sP0
| ( op(e3,e3) != e3
& op(e3,e3) = e3 ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f171,plain,
( ~ sP0
| e3 != op(e3,e3) ),
inference(cnf_transformation,[],[f62]) ).
fof(f172,plain,
( ~ sP0
| e3 = op(e3,e3) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_157,plain,
( ( op(e3,e3) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_158,plain,
( ~ sP0
| ( op(e3,e3) != e3 ) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_215,plain,
~ sP0,
inference(global_subsumption_just,[status(thm)],[c_157,c_157,c_158]) ).
tcf(c_219,plain,
( ( op(e0,e0) = e3 )
| ( op(e1,e1) = e3 )
| ( op(e2,e2) = e3 ) ),
inference(global_subsumption_just,[status(thm)],[c_183,c_183,c_215]) ).
tcf(c_220,plain,
( ( op(e2,e2) = e3 )
| ( op(e1,e1) = e3 )
| ( op(e0,e0) = e3 ) ),
inference(renaming,[status(thm)],[c_219]) ).
tcf(c_227,plain,
( ( op(e3,e3) != e0 )
| ( op(e1,e1) = e3 )
| ( op(e2,e2) = e3 ) ),
inference(global_subsumption_just,[status(thm)],[c_187,c_157,c_158,c_187]) ).
tcf(c_228,plain,
( ( op(e2,e2) = e3 )
| ( op(e1,e1) = e3 )
| ( op(e3,e3) != e0 ) ),
inference(renaming,[status(thm)],[c_227]) ).
tcf(c_229,plain,
( ( op(e3,e3) != e1 )
| ( op(e0,e0) = e3 )
| ( op(e2,e2) = e3 ) ),
inference(global_subsumption_just,[status(thm)],[c_185,c_157,c_158,c_185]) ).
tcf(c_230,plain,
( ( op(e2,e2) = e3 )
| ( op(e0,e0) = e3 )
| ( op(e3,e3) != e1 ) ),
inference(renaming,[status(thm)],[c_229]) ).
tcf(c_231,plain,
( ( op(e3,e3) != e2 )
| ( op(e0,e0) = e3 )
| ( op(e1,e1) = e3 ) ),
inference(global_subsumption_just,[status(thm)],[c_184,c_157,c_158,c_184]) ).
tcf(c_232,plain,
( ( op(e1,e1) = e3 )
| ( op(e0,e0) = e3 )
| ( op(e3,e3) != e2 ) ),
inference(renaming,[status(thm)],[c_231]) ).
tcf(c_253,plain,
( ( op(e3,e3) != e0 )
| ( op(e3,e3) != e2 )
| ( op(e1,e1) = e3 ) ),
inference(global_subsumption_just,[status(thm)],[c_188,c_157,c_158,c_188]) ).
tcf(c_254,plain,
( ( op(e1,e1) = e3 )
| ( op(e3,e3) != e2 )
| ( op(e3,e3) != e0 ) ),
inference(renaming,[status(thm)],[c_253]) ).
tcf(c_4907,plain,
( ( op(e1,e1) = e3 )
| ( op(e0,e0) = e3 )
| ~ sP1 ),
inference(superposition,[status(thm)],[c_220,c_156]) ).
tcf(c_4908,plain,
( ( op(e1,e1) = e3 )
| ( op(e0,e0) = e3 )
| ( op(e2,e1) != e3 ) ),
inference(superposition,[status(thm)],[c_220,c_136]) ).
tcf(c_4909,plain,
( ( op(e1,e1) = e3 )
| ( op(e0,e0) = e3 )
| ( op(e2,e0) != e3 ) ),
inference(superposition,[status(thm)],[c_220,c_134]) ).
tcf(c_4910,plain,
( ( op(e1,e1) = e3 )
| ( op(e0,e0) = e3 )
| ( op(e1,e2) != e3 ) ),
inference(superposition,[status(thm)],[c_220,c_112]) ).
tcf(c_4911,plain,
( ( op(e1,e1) = e3 )
| ( op(e0,e0) = e3 )
| ( op(e0,e2) != e3 ) ),
inference(superposition,[status(thm)],[c_220,c_110]) ).
tcf(c_4933,plain,
( ( op(e1,e1) = e3 )
| ( op(e1,e1) = e2 )
| ( op(e0,e0) = e3 )
| ( op(e0,e0) = e2 ) ),
inference(superposition,[status(thm)],[c_237,c_4907]) ).
tcf(c_5055,plain,
( ( op(e2,e2) = e3 )
| ( op(e2,e2) = e0 )
| ( op(e1,e1) = e3 )
| ( op(e1,e1) = e0 ) ),
inference(superposition,[status(thm)],[c_4729,c_228]) ).
tcf(c_5069,plain,
( ( op(e2,e2) = e3 )
| ( op(e2,e2) = e1 )
| ( op(e0,e0) = e3 )
| ( op(e0,e0) = e1 ) ),
inference(superposition,[status(thm)],[c_4719,c_230]) ).
tcf(c_5096,plain,
( ( op(e2,e0) = e2 )
| ( op(e2,e0) = e1 )
| ( op(e2,e0) = e0 )
| ( op(e1,e1) = e3 )
| ( op(e0,e0) = e3 ) ),
inference(superposition,[status(thm)],[c_57,c_4909]) ).
tcf(c_5594,plain,
( ( op(e1,e1) = e3 )
| ( op(e1,e1) = e2 )
| ( op(e0,e0) = e2 )
| ( op(e3,e3) != e0 ) ),
inference(superposition,[status(thm)],[c_4709,c_254]) ).
tcf(c_7982,plain,
( ( e1 = e3 )
| ( op(e2,e2) = e0 )
| ( op(e1,e1) = e3 )
| ( op(e1,e1) = e0 )
| ( op(e0,e0) = e3 )
| ( op(e0,e0) = e1 ) ),
inference(superposition,[status(thm)],[c_5044,c_220]) ).
tcf(c_8012,plain,
( ( op(e2,e2) = e0 )
| ( op(e1,e1) = e3 )
| ( op(e1,e1) = e0 )
| ( op(e0,e0) = e3 )
| ( op(e0,e0) = e1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7982,c_149]) ).
tcf(c_8041,plain,
( ( e1 = e3 )
| ( op(e2,e2) = e0 )
| ( op(e1,e1) = e3 )
| ( op(e1,e1) = e0 )
| ( op(e0,e0) = e1 ) ),
inference(superposition,[status(thm)],[c_5055,c_5044]) ).
tcf(c_8073,plain,
( ( op(e2,e2) = e0 )
| ( op(e1,e1) = e3 )
| ( op(e1,e1) = e0 )
| ( op(e0,e0) = e1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8041,c_149]) ).
tcf(c_8125,plain,
( ( e1 = e3 )
| ( op(e2,e2) = e1 )
| ( op(e2,e2) = e0 )
| ( op(e1,e1) = e0 )
| ( op(e0,e0) = e3 )
| ( op(e0,e0) = e1 ) ),
inference(superposition,[status(thm)],[c_5069,c_5044]) ).
tcf(c_8157,plain,
( ( op(e2,e2) = e1 )
| ( op(e2,e2) = e0 )
| ( op(e1,e1) = e0 )
| ( op(e0,e0) = e3 )
| ( op(e0,e0) = e1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8125,c_149]) ).
tcf(c_8312,plain,
( ( e1 = e3 )
| ( op(e2,e0) = e1 )
| ( op(e1,e1) = e3 )
| ( op(e1,e0) = e1 )
| ( op(e0,e0) = e3 )
| ( op(e0,e0) = e1 ) ),
inference(superposition,[status(thm)],[c_5667,c_220]) ).
tcf(c_8343,plain,
( ( op(e2,e0) = e1 )
| ( op(e1,e1) = e3 )
| ( op(e1,e0) = e1 )
| ( op(e0,e0) = e3 )
| ( op(e0,e0) = e1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8312,c_149]) ).
tcf(c_8601,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_8343,c_8157,c_8073,c_8012,c_7988,c_6625,c_6624,c_6384,c_6311,c_6268,c_6163,c_5594,c_5234,c_5096,c_5069,c_5039,c_5020,c_5000,c_4980,c_4949,c_4946,c_4933,c_4911,c_4910,c_4908,c_4709,c_4719,c_4729,c_269,c_232,c_245,c_220,c_214,c_213,c_212,c_211,c_209,c_208,c_207,c_206,c_201,c_200,c_199,c_194,c_152,c_151,c_150,c_149,c_148,c_147,c_146,c_145,c_138,c_131,c_130,c_123,c_122,c_110,c_109,c_106,c_102,c_101,c_99,c_98,c_71,c_69,c_64,c_61,c_56,c_52,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG139+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 04:55:26 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 2.07/1.28 % SZS status Started for theBenchmark.p
% 2.07/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.07/1.28
% 2.07/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.07/1.28
% 2.07/1.28 % ------ iProver source info
% 2.07/1.28
% 2.07/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.07/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.07/1.28 % git: non_committed_changes: false
% 2.07/1.28
% 2.07/1.28 % ------ Parsing...
% 2.07/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.07/1.28
% 2.07/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.07/1.28
% 2.07/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.07/1.28
% 2.07/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.07/1.28 % ------ Proving...
% 2.07/1.28 % ------ Problem Properties
% 2.07/1.28
% 2.07/1.28 %
% 2.07/1.28 % clauses 152
% 2.07/1.28 % conjectures 0
% 2.07/1.28 % EPR 6
% 2.07/1.28 % Horn 91
% 2.07/1.28 % unary 54
% 2.07/1.28 % binary 6
% 2.07/1.28 % lits 390
% 2.07/1.28 % lits eq 372
% 2.07/1.28 % fd_pure 0
% 2.07/1.28 % fd_pseudo 0
% 2.07/1.28 % fd_cond 0
% 2.07/1.28 % fd_pseudo_cond 0
% 2.07/1.28 % AC symbols 0
% 2.07/1.28
% 2.07/1.28 % ------ Schedule dynamic 5 is on
% 2.07/1.28
% 2.07/1.28 % ------ no conjectures: strip conj schedule
% 2.07/1.28
% 2.07/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.07/1.28
% 2.07/1.28
% 2.07/1.28 % ------
% 2.07/1.28 % Current options:
% 2.07/1.28 % ------
% 2.07/1.28
% 2.07/1.28
% 2.07/1.28 %
% 2.07/1.28
% 2.07/1.28 % ------ Proving...
% 2.07/1.28 %
% 2.07/1.28
% 2.07/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.07/1.28
% 2.07/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.07/1.28
% 2.07/1.28
%------------------------------------------------------------------------------