%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG045+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 : n009.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 12:53:16 PM UTC 2026
% Result : Unsatisfiable 1.13s 1.29s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 200 ( 75 unt; 3 def)
% Number of atoms : 690 ( 627 equ)
% Maximal formula atoms : 128 ( 3 avg)
% Number of connectives : 700 ( 210 ~; 349 |; 141 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 8 !; 0 ?; 8 :)
% 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,
( ( 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/sandbox/benchmark/theBenchmark.p',ax2) ).
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/sandbox/benchmark/theBenchmark.p',ax3) ).
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/sandbox/benchmark/theBenchmark.p',ax4) ).
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/sandbox/benchmark/theBenchmark.p',ax6) ).
fof(f8,axiom,
~ ( e3 = op(e2,e1)
& e0 = op(e1,e1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
fof(f14,axiom,
~ ( e3 = op(e2,e0)
& e1 = op(e0,e0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14) ).
fof(f16,axiom,
~ ( e3 = op(e0,e2)
& e1 = op(e2,e2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f20,axiom,
~ ( e3 = op(e1,e0)
& e2 = op(e0,e0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
fof(f22,axiom,
~ ( e3 = op(e0,e1)
& e2 = op(e1,e1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
fof(f25,axiom,
~ ( e1 = op(e2,e0)
& e3 = op(e0,e0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
fof(f26,axiom,
~ ( e2 = op(e1,e0)
& e3 = op(e0,e0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f32,plain,
( e3 != op(e2,e1)
| e0 != op(e1,e1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f38,plain,
( e3 != op(e2,e0)
| op(e0,e0) != e1 ),
inference(ennf_transformation,[],[f14]) ).
fof(f40,plain,
( e3 != op(e0,e2)
| e1 != op(e2,e2) ),
inference(ennf_transformation,[],[f16]) ).
fof(f44,plain,
( e3 != op(e1,e0)
| op(e0,e0) != e2 ),
inference(ennf_transformation,[],[f20]) ).
fof(f46,plain,
( e3 != op(e0,e1)
| e2 != op(e1,e1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f49,plain,
( e1 != op(e2,e0)
| op(e0,e0) != e3 ),
inference(ennf_transformation,[],[f25]) ).
fof(f50,plain,
( e2 != op(e1,e0)
| op(e0,e0) != e3 ),
inference(ennf_transformation,[],[f26]) ).
fof(f59,plain,
( ~ sP2
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f60,plain,
( ~ sP1
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f68,plain,
( e3 = op(e2,e1)
| e2 = op(e2,e1)
| e1 = op(e2,e1)
| e0 = op(e2,e1) ),
inference(cnf_transformation,[],[f1]) ).
fof(f69,plain,
( e3 = op(e2,e0)
| e2 = op(e2,e0)
| e1 = op(e2,e0)
| e0 = op(e2,e0) ),
inference(cnf_transformation,[],[f1]) ).
fof(f73,plain,
( e3 = op(e1,e0)
| e2 = op(e1,e0)
| e1 = op(e1,e0)
| e0 = op(e1,e0) ),
inference(cnf_transformation,[],[f1]) ).
fof(f78,plain,
( e3 = unit
| e2 = unit
| e1 = unit
| e0 = unit ),
inference(cnf_transformation,[],[f2]) ).
fof(f79,plain,
e3 = op(e3,unit),
inference(cnf_transformation,[],[f2]) ).
fof(f80,plain,
e3 = op(unit,e3),
inference(cnf_transformation,[],[f2]) ).
fof(f81,plain,
e2 = op(e2,unit),
inference(cnf_transformation,[],[f2]) ).
fof(f82,plain,
e2 = op(unit,e2),
inference(cnf_transformation,[],[f2]) ).
fof(f83,plain,
e1 = op(e1,unit),
inference(cnf_transformation,[],[f2]) ).
fof(f84,plain,
e1 = op(unit,e1),
inference(cnf_transformation,[],[f2]) ).
fof(f86,plain,
e0 = op(unit,e0),
inference(cnf_transformation,[],[f2]) ).
fof(f112,plain,
( e3 = op(e0,e3)
| e3 = op(e0,e2)
| e3 = op(e0,e1)
| op(e0,e0) = e3 ),
inference(cnf_transformation,[],[f3]) ).
fof(f122,plain,
op(e3,e0) != op(e3,e3),
inference(cnf_transformation,[],[f4]) ).
fof(f125,plain,
op(e2,e2) != op(e2,e3),
inference(cnf_transformation,[],[f4]) ).
fof(f129,plain,
op(e2,e0) != op(e2,e2),
inference(cnf_transformation,[],[f4]) ).
fof(f130,plain,
op(e2,e0) != op(e2,e1),
inference(cnf_transformation,[],[f4]) ).
fof(f132,plain,
op(e1,e1) != op(e1,e3),
inference(cnf_transformation,[],[f4]) ).
fof(f133,plain,
op(e1,e1) != op(e1,e2),
inference(cnf_transformation,[],[f4]) ).
fof(f134,plain,
op(e1,e0) != op(e1,e3),
inference(cnf_transformation,[],[f4]) ).
fof(f135,plain,
op(e1,e0) != op(e1,e2),
inference(cnf_transformation,[],[f4]) ).
fof(f136,plain,
op(e1,e0) != op(e1,e1),
inference(cnf_transformation,[],[f4]) ).
fof(f147,plain,
op(e0,e3) != op(e2,e3),
inference(cnf_transformation,[],[f4]) ).
fof(f148,plain,
op(e0,e3) != op(e1,e3),
inference(cnf_transformation,[],[f4]) ).
fof(f149,plain,
op(e2,e2) != op(e3,e2),
inference(cnf_transformation,[],[f4]) ).
fof(f152,plain,
op(e0,e2) != op(e3,e2),
inference(cnf_transformation,[],[f4]) ).
fof(f156,plain,
op(e1,e1) != op(e3,e1),
inference(cnf_transformation,[],[f4]) ).
fof(f157,plain,
op(e1,e1) != op(e2,e1),
inference(cnf_transformation,[],[f4]) ).
fof(f158,plain,
op(e0,e1) != op(e3,e1),
inference(cnf_transformation,[],[f4]) ).
fof(f159,plain,
op(e0,e1) != op(e2,e1),
inference(cnf_transformation,[],[f4]) ).
fof(f162,plain,
op(e1,e0) != op(e3,e0),
inference(cnf_transformation,[],[f4]) ).
fof(f163,plain,
op(e1,e0) != op(e2,e0),
inference(cnf_transformation,[],[f4]) ).
fof(f164,plain,
op(e0,e0) != op(e3,e0),
inference(cnf_transformation,[],[f4]) ).
fof(f165,plain,
op(e0,e0) != op(e2,e0),
inference(cnf_transformation,[],[f4]) ).
fof(f166,plain,
op(e0,e0) != op(e1,e0),
inference(cnf_transformation,[],[f4]) ).
fof(f174,plain,
( ~ sP2
| e1 = op(e2,e2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f175,plain,
( ~ sP2
| e1 = op(e1,e1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f176,plain,
( ~ sP2
| op(e0,e0) = e1 ),
inference(cnf_transformation,[],[f59]) ).
fof(f178,plain,
( ~ sP1
| e2 = op(e2,e2) ),
inference(cnf_transformation,[],[f60]) ).
fof(f179,plain,
( ~ sP1
| e2 = op(e1,e1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f180,plain,
( ~ sP1
| op(e0,e0) = e2 ),
inference(cnf_transformation,[],[f60]) ).
fof(f185,plain,
( sP0
| sP1
| sP2
| e0 = op(e3,e3) ),
inference(cnf_transformation,[],[f58]) ).
fof(f186,plain,
( sP0
| sP1
| sP2
| e0 = op(e2,e2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f187,plain,
( sP0
| sP1
| sP2
| e0 = op(e1,e1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f190,plain,
( e3 != op(e2,e1)
| e0 != op(e1,e1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f196,plain,
( e3 != op(e2,e0)
| op(e0,e0) != e1 ),
inference(cnf_transformation,[],[f38]) ).
fof(f198,plain,
( e3 != op(e0,e2)
| e1 != op(e2,e2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f202,plain,
( e3 != op(e1,e0)
| op(e0,e0) != e2 ),
inference(cnf_transformation,[],[f44]) ).
fof(f204,plain,
( e3 != op(e0,e1)
| e2 != op(e1,e1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f207,plain,
( e1 != op(e2,e0)
| op(e0,e0) != e3 ),
inference(cnf_transformation,[],[f49]) ).
fof(f208,plain,
( e2 != op(e1,e0)
| op(e0,e0) != e3 ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_53,plain,
( ( op(e1,e0) = e3 )
| ( op(e1,e0) = e2 )
| ( op(e1,e0) = e1 )
| ( op(e1,e0) = e0 ) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_57,plain,
( ( op(e2,e0) = e3 )
| ( op(e2,e0) = e2 )
| ( op(e2,e0) = e1 )
| ( op(e2,e0) = e0 ) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_58,plain,
( ( op(e2,e1) = e3 )
| ( op(e2,e1) = e2 )
| ( op(e2,e1) = e1 )
| ( op(e2,e1) = e0 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_65,plain,
op(unit,e0) = e0,
inference(cnf_transformation,[],[f86]) ).
tcf(c_67,plain,
op(unit,e1) = e1,
inference(cnf_transformation,[],[f84]) ).
tcf(c_68,plain,
op(e1,unit) = e1,
inference(cnf_transformation,[],[f83]) ).
tcf(c_69,plain,
op(unit,e2) = e2,
inference(cnf_transformation,[],[f82]) ).
tcf(c_70,plain,
op(e2,unit) = e2,
inference(cnf_transformation,[],[f81]) ).
tcf(c_71,plain,
op(unit,e3) = e3,
inference(cnf_transformation,[],[f80]) ).
tcf(c_72,plain,
op(e3,unit) = e3,
inference(cnf_transformation,[],[f79]) ).
tcf(c_73,plain,
( ( e3 = unit )
| ( e2 = unit )
| ( e1 = unit )
| ( e0 = unit ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_80,plain,
( ( op(e0,e3) = e3 )
| ( op(e0,e2) = e3 )
| ( op(e0,e1) = e3 )
| ( op(e0,e0) = e3 ) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_106,plain,
op(e0,e0) != op(e1,e0),
inference(cnf_transformation,[],[f166]) ).
tcf(c_107,plain,
op(e0,e0) != op(e2,e0),
inference(cnf_transformation,[],[f165]) ).
tcf(c_108,plain,
op(e0,e0) != op(e3,e0),
inference(cnf_transformation,[],[f164]) ).
tcf(c_109,plain,
op(e1,e0) != op(e2,e0),
inference(cnf_transformation,[],[f163]) ).
tcf(c_110,plain,
op(e1,e0) != op(e3,e0),
inference(cnf_transformation,[],[f162]) ).
tcf(c_113,plain,
op(e0,e1) != op(e2,e1),
inference(cnf_transformation,[],[f159]) ).
tcf(c_114,plain,
op(e0,e1) != op(e3,e1),
inference(cnf_transformation,[],[f158]) ).
tcf(c_115,plain,
op(e1,e1) != op(e2,e1),
inference(cnf_transformation,[],[f157]) ).
tcf(c_116,plain,
op(e1,e1) != op(e3,e1),
inference(cnf_transformation,[],[f156]) ).
tcf(c_120,plain,
op(e0,e2) != op(e3,e2),
inference(cnf_transformation,[],[f152]) ).
tcf(c_123,plain,
op(e2,e2) != op(e3,e2),
inference(cnf_transformation,[],[f149]) ).
tcf(c_124,plain,
op(e0,e3) != op(e1,e3),
inference(cnf_transformation,[],[f148]) ).
tcf(c_125,plain,
op(e0,e3) != op(e2,e3),
inference(cnf_transformation,[],[f147]) ).
tcf(c_136,plain,
op(e1,e0) != op(e1,e1),
inference(cnf_transformation,[],[f136]) ).
tcf(c_137,plain,
op(e1,e0) != op(e1,e2),
inference(cnf_transformation,[],[f135]) ).
tcf(c_138,plain,
op(e1,e0) != op(e1,e3),
inference(cnf_transformation,[],[f134]) ).
tcf(c_139,plain,
op(e1,e1) != op(e1,e2),
inference(cnf_transformation,[],[f133]) ).
tcf(c_140,plain,
op(e1,e1) != op(e1,e3),
inference(cnf_transformation,[],[f132]) ).
tcf(c_142,plain,
op(e2,e0) != op(e2,e1),
inference(cnf_transformation,[],[f130]) ).
tcf(c_143,plain,
op(e2,e0) != op(e2,e2),
inference(cnf_transformation,[],[f129]) ).
tcf(c_147,plain,
op(e2,e2) != op(e2,e3),
inference(cnf_transformation,[],[f125]) ).
tcf(c_150,plain,
op(e3,e0) != op(e3,e3),
inference(cnf_transformation,[],[f122]) ).
tcf(c_160,plain,
( ( op(e0,e0) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_161,plain,
( ( op(e1,e1) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_162,plain,
( ( op(e2,e2) = e1 )
| ~ sP2 ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_164,plain,
( ( op(e0,e0) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_165,plain,
( ( op(e1,e1) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_166,plain,
( ( op(e2,e2) = e2 )
| ~ sP1 ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_173,plain,
( sP0
| sP1
| sP2
| ( op(e1,e1) = e0 ) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_174,plain,
( sP0
| sP1
| sP2
| ( op(e2,e2) = e0 ) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_175,plain,
( sP0
| sP1
| sP2
| ( op(e3,e3) = e0 ) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_177,plain,
( ( op(e2,e1) != e3 )
| ( op(e1,e1) != e0 ) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_183,plain,
( ( op(e2,e0) != e3 )
| ( op(e0,e0) != e1 ) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_185,plain,
( ( op(e2,e2) != e1 )
| ( op(e0,e2) != e3 ) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_189,plain,
( ( op(e1,e0) != e3 )
| ( op(e0,e0) != e2 ) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_191,plain,
( ( op(e1,e1) != e2 )
| ( op(e0,e1) != e3 ) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_194,plain,
( ( op(e2,e0) != e1 )
| ( op(e0,e0) != e3 ) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_195,plain,
( ( op(e1,e0) != e2 )
| ( op(e0,e0) != e3 ) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_1578,plain,
( sP0
| sP1
| ( op(e2,e2) = e1 )
| ( op(e1,e1) = e0 ) ),
inference(resolution,[status(thm)],[c_173,c_162]) ).
tcf(c_1604,plain,
( sP0
| sP1
| ( op(e1,e1) = e0 )
| ( op(e0,e0) = e1 ) ),
inference(resolution,[status(thm)],[c_173,c_160]) ).
tcf(c_1811,plain,
( sP0
| sP2
| ( op(e2,e2) = e0 )
| ( op(e1,e1) = e2 ) ),
inference(resolution,[status(thm)],[c_174,c_165]) ).
tcf(c_1824,plain,
( sP0
| sP2
| ( op(e2,e2) = e0 )
| ( op(e0,e0) = e2 ) ),
inference(resolution,[status(thm)],[c_174,c_164]) ).
tcf(c_2278,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3102,plain,
( ( op(e1,e0) = e2 )
| ( op(e1,e0) = e1 )
| ( op(e1,e0) = e0 )
| ( op(e0,e0) != e3 ) ),
inference(superposition,[status(thm)],[c_53,c_106]) ).
tcf(c_3445,plain,
( ( e2 = unit )
| ( e1 = unit )
| ( e0 = unit )
| ( op(e2,e3) = e2 ) ),
inference(superposition,[status(thm)],[c_73,c_70]) ).
tcf(c_3447,plain,
( ( e2 = unit )
| ( e1 = unit )
| ( e0 = unit )
| ( op(e1,e3) = e1 ) ),
inference(superposition,[status(thm)],[c_73,c_68]) ).
tcf(c_3448,plain,
( ( e2 = unit )
| ( e1 = unit )
| ( e0 = unit )
| ( op(e3,e1) = e1 ) ),
inference(superposition,[status(thm)],[c_73,c_67]) ).
tcf(c_3450,plain,
( ( e2 = unit )
| ( e1 = unit )
| ( e0 = unit )
| ( op(e3,e0) = e0 ) ),
inference(superposition,[status(thm)],[c_73,c_65]) ).
tcf(c_4014,plain,
! [X0: $i] :
( ( op(e1,e0) = op(e2,e0) )
| ( op(e2,e0) != X0 )
| ( op(e1,e0) != X0 ) ),
inference(instantiation,[status(thm)],[c_2278]) ).
tcf(c_4015,plain,
( ( op(e1,e0) = op(e2,e0) )
| ( op(e2,e0) != e0 )
| ( op(e1,e0) != e0 ) ),
inference(instantiation,[status(thm)],[c_4014]) ).
tcf(c_4016,plain,
! [X0: $i] :
( ( op(e1,e0) = op(e3,e0) )
| ( op(e3,e0) != X0 )
| ( op(e1,e0) != X0 ) ),
inference(instantiation,[status(thm)],[c_2278]) ).
tcf(c_4017,plain,
( ( op(e1,e0) = op(e3,e0) )
| ( op(e3,e0) != e0 )
| ( op(e1,e0) != e0 ) ),
inference(instantiation,[status(thm)],[c_4016]) ).
tcf(c_4068,plain,
! [X0: $i] :
( ( op(e1,e0) = op(e1,e1) )
| ( op(e1,e1) != X0 )
| ( op(e1,e0) != X0 ) ),
inference(instantiation,[status(thm)],[c_2278]) ).
tcf(c_4069,plain,
( ( op(e1,e0) = op(e1,e1) )
| ( op(e1,e1) != e0 )
| ( op(e1,e0) != e0 ) ),
inference(instantiation,[status(thm)],[c_4068]) ).
tcf(c_4082,plain,
! [X0: $i] :
( ( op(e2,e0) = op(e2,e2) )
| ( op(e2,e2) != X0 )
| ( op(e2,e0) != X0 ) ),
inference(instantiation,[status(thm)],[c_2278]) ).
tcf(c_4083,plain,
( ( op(e2,e0) = op(e2,e2) )
| ( op(e2,e2) != e0 )
| ( op(e2,e0) != e0 ) ),
inference(instantiation,[status(thm)],[c_4082]) ).
tcf(c_4096,plain,
! [X0: $i] :
( ( op(e3,e0) = op(e3,e3) )
| ( op(e3,e3) != X0 )
| ( op(e3,e0) != X0 ) ),
inference(instantiation,[status(thm)],[c_2278]) ).
tcf(c_4097,plain,
( ( op(e3,e0) = op(e3,e3) )
| ( op(e3,e3) != e0 )
| ( op(e3,e0) != e0 ) ),
inference(instantiation,[status(thm)],[c_4096]) ).
tcf(c_4289,plain,
( ( e2 = unit )
| ( e1 = unit )
| ( e0 = unit )
| ( op(e2,e2) != e2 ) ),
inference(superposition,[status(thm)],[c_3445,c_147]) ).
tcf(c_4360,plain,
( ( e2 = unit )
| ( e1 = unit )
| ( e0 = unit )
| ( op(e1,e1) != e1 ) ),
inference(superposition,[status(thm)],[c_3447,c_140]) ).
tcf(c_4361,plain,
( ( e2 = unit )
| ( e1 = unit )
| ( e0 = unit )
| ( op(e1,e0) != e1 ) ),
inference(superposition,[status(thm)],[c_3447,c_138]) ).
fof(f55,definition,
( ~ sP0
| ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f56,definition,
( ~ sP1
| ( op(e3,e3) = e2
& op(e2,e2) = e2
& op(e1,e1) = e2
& op(e0,e0) = e2 ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f57,definition,
( ~ sP2
| ( op(e3,e3) = e1
& op(e2,e2) = e1
& op(e1,e1) = e1
& op(e0,e0) = e1 ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f58,plain,
( sP0
| sP1
| sP2
| ( op(e3,e3) = e0
& op(e2,e2) = e0
& op(e1,e1) = e0
& op(e0,e0) = e0 ) ),
inference(definition_folding,[],[f6,f57,f56,f55]) ).
fof(f61,plain,
( ~ sP0
| ( op(e3,e3) = e3
& op(e2,e2) = e3
& op(e1,e1) = e3
& op(e0,e0) = e3 ) ),
inference(nnf_transformation,[],[f55]) ).
fof(f182,plain,
( ~ sP0
| e3 = op(e2,e2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f183,plain,
( ~ sP0
| e3 = op(e1,e1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f184,plain,
( ~ sP0
| op(e0,e0) = e3 ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_168,plain,
( ( op(e0,e0) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_169,plain,
( ( op(e1,e1) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_170,plain,
( ( op(e2,e2) = e3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_2044,plain,
( sP1
| sP2
| ( op(e3,e3) = e0 )
| ( op(e0,e0) = e3 ) ),
inference(resolution,[status(thm)],[c_175,c_168]) ).
tcf(c_3146,plain,
( sP1
| sP2
| ( op(e1,e1) = e0 )
| ( op(e0,e0) = e3 ) ),
inference(superposition,[status(thm)],[c_173,c_168]) ).
tcf(c_4386,plain,
( ( e2 = unit )
| ( e1 = unit )
| ( e0 = unit ) ),
inference(global_subsumption_just,[status(thm)],[c_3448,c_166,c_161,c_150,c_110,c_195,c_2044,c_3102,c_3450,c_4017,c_4097,c_4289,c_4361,c_4360]) ).
tcf(c_4394,plain,
( ( e1 = unit )
| ( e0 = unit )
| ( op(e3,e2) = e3 ) ),
inference(superposition,[status(thm)],[c_4386,c_72]) ).
tcf(c_4395,plain,
( ( e1 = unit )
| ( e0 = unit )
| ( op(e2,e3) = e3 ) ),
inference(superposition,[status(thm)],[c_4386,c_71]) ).
tcf(c_4398,plain,
( ( e1 = unit )
| ( e0 = unit )
| ( op(e1,e2) = e1 ) ),
inference(superposition,[status(thm)],[c_4386,c_68]) ).
tcf(c_4399,plain,
( ( e1 = unit )
| ( e0 = unit )
| ( op(e2,e1) = e1 ) ),
inference(superposition,[status(thm)],[c_4386,c_67]) ).
tcf(c_4401,plain,
( ( e1 = unit )
| ( e0 = unit )
| ( op(e2,e0) = e0 ) ),
inference(superposition,[status(thm)],[c_4386,c_65]) ).
tcf(c_4432,plain,
( ( e1 = unit )
| ( e0 = unit )
| ( op(e2,e2) != e3 ) ),
inference(superposition,[status(thm)],[c_4394,c_123]) ).
tcf(c_4434,plain,
( ( e1 = unit )
| ( e0 = unit )
| ( op(e0,e2) != e3 ) ),
inference(superposition,[status(thm)],[c_4394,c_120]) ).
tcf(c_4461,plain,
( ( e1 = unit )
| ( e0 = unit )
| ( op(e0,e3) != e3 ) ),
inference(superposition,[status(thm)],[c_4395,c_125]) ).
tcf(c_4511,plain,
( ( e1 = unit )
| ( e0 = unit )
| ( op(e1,e1) != e1 ) ),
inference(superposition,[status(thm)],[c_4398,c_139]) ).
tcf(c_4512,plain,
( ( e1 = unit )
| ( e0 = unit )
| ( op(e1,e0) != e1 ) ),
inference(superposition,[status(thm)],[c_4398,c_137]) ).
tcf(c_4529,plain,
( ( e1 = unit )
| ( e0 = unit ) ),
inference(global_subsumption_just,[status(thm)],[c_4399,c_170,c_161,c_143,c_109,c_195,c_191,c_189,c_80,c_53,c_1811,c_1824,c_4015,c_4083,c_4401,c_4434,c_4432,c_4461,c_4512,c_4511]) ).
tcf(c_4535,plain,
( ( e0 = unit )
| ( op(e3,e1) = e3 ) ),
inference(superposition,[status(thm)],[c_4529,c_72]) ).
tcf(c_4536,plain,
( ( e0 = unit )
| ( op(e1,e3) = e3 ) ),
inference(superposition,[status(thm)],[c_4529,c_71]) ).
tcf(c_4537,plain,
( ( e0 = unit )
| ( op(e2,e1) = e2 ) ),
inference(superposition,[status(thm)],[c_4529,c_70]) ).
tcf(c_4538,plain,
( ( e0 = unit )
| ( op(e1,e2) = e2 ) ),
inference(superposition,[status(thm)],[c_4529,c_69]) ).
tcf(c_4542,plain,
( ( e0 = unit )
| ( op(e1,e0) = e0 ) ),
inference(superposition,[status(thm)],[c_4529,c_65]) ).
tcf(c_4690,plain,
( ( e0 = unit )
| ( op(e1,e1) != e3 ) ),
inference(superposition,[status(thm)],[c_4535,c_116]) ).
tcf(c_4691,plain,
( ( e0 = unit )
| ( op(e0,e1) != e3 ) ),
inference(superposition,[status(thm)],[c_4535,c_114]) ).
tcf(c_4708,plain,
( ( e0 = unit )
| ( op(e0,e3) != e3 ) ),
inference(superposition,[status(thm)],[c_4536,c_124]) ).
tcf(c_4722,plain,
( ( e0 = unit )
| ( op(e2,e0) != e2 ) ),
inference(superposition,[status(thm)],[c_4537,c_142]) ).
tcf(c_4723,plain,
( ( e0 = unit )
| ( op(e1,e1) != e2 ) ),
inference(superposition,[status(thm)],[c_4537,c_115]) ).
tcf(c_4731,plain,
e0 = unit,
inference(global_subsumption_just,[status(thm)],[c_4538,c_169,c_165,c_136,c_109,c_194,c_185,c_183,c_80,c_57,c_1578,c_1604,c_4015,c_4069,c_4542,c_4691,c_4690,c_4708,c_4723,c_4722]) ).
tcf(c_4736,plain,
op(e3,e0) = e3,
inference(demodulation,[status(thm)],[c_72,c_4731]) ).
tcf(c_4738,plain,
op(e2,e0) = e2,
inference(demodulation,[status(thm)],[c_70,c_4731]) ).
tcf(c_4740,plain,
op(e1,e0) = e1,
inference(demodulation,[status(thm)],[c_68,c_4731]) ).
tcf(c_4741,plain,
op(e0,e1) = e1,
inference(demodulation,[status(thm)],[c_67,c_4731]) ).
tcf(c_4753,plain,
op(e0,e0) != e3,
inference(demodulation,[status(thm)],[c_108,c_4736]) ).
tcf(c_4755,plain,
( sP1
| sP2
| ( op(e1,e1) = e0 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3146,c_4753]) ).
tcf(c_4810,plain,
op(e2,e1) != e2,
inference(demodulation,[status(thm)],[c_142,c_4738]) ).
tcf(c_4812,plain,
op(e0,e0) != e2,
inference(demodulation,[status(thm)],[c_107,c_4738]) ).
tcf(c_4813,plain,
~ sP1,
inference(backward_subsumption_resolution,[status(thm)],[c_164,c_4812]) ).
tcf(c_4816,plain,
( sP2
| ( op(e1,e1) = e0 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4755,c_4813]) ).
tcf(c_4840,plain,
( ( op(e2,e1) = e3 )
| ( op(e2,e1) = e1 )
| ( op(e2,e1) = e0 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_58,c_4810]) ).
tcf(c_4867,plain,
op(e0,e0) != e1,
inference(demodulation,[status(thm)],[c_106,c_4740]) ).
tcf(c_4868,plain,
~ sP2,
inference(backward_subsumption_resolution,[status(thm)],[c_160,c_4867]) ).
tcf(c_4872,plain,
op(e1,e1) = e0,
inference(backward_subsumption_resolution,[status(thm)],[c_4816,c_4868]) ).
tcf(c_4881,plain,
op(e2,e1) != e3,
inference(backward_subsumption_resolution,[status(thm)],[c_177,c_4872]) ).
tcf(c_4888,plain,
op(e2,e1) != e0,
inference(demodulation,[status(thm)],[c_115,c_4872]) ).
tcf(c_4891,plain,
( ( op(e2,e1) = e1 )
| ( op(e2,e1) = e0 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4840,c_4881]) ).
tcf(c_4897,plain,
op(e2,e1) = e1,
inference(backward_subsumption_resolution,[status(thm)],[c_4891,c_4888]) ).
tcf(c_4901,plain,
op(e0,e1) != e1,
inference(demodulation,[status(thm)],[c_113,c_4897]) ).
tcf(c_4902,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4901,c_4741]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG045+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 04:37:14 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 1.13/1.29 % SZS status Started for theBenchmark.p
% 1.13/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.13/1.29
% 1.13/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.13/1.29
% 1.13/1.29 % ------ iProver source info
% 1.13/1.29
% 1.13/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.13/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.13/1.29 % git: non_committed_changes: false
% 1.13/1.29
% 1.13/1.29 % ------ Parsing...
% 1.13/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.13/1.29
% 1.13/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.13/1.29
% 1.13/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.13/1.29
% 1.13/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.13/1.29 % ------ Proving...
% 1.13/1.29 % ------ Problem Properties
% 1.13/1.29
% 1.13/1.29 %
% 1.13/1.29 % clauses 151
% 1.13/1.29 % conjectures 0
% 1.13/1.29 % EPR 7
% 1.13/1.29 % Horn 98
% 1.13/1.29 % unary 62
% 1.13/1.29 % binary 36
% 1.13/1.29 % lits 346
% 1.13/1.29 % lits eq 322
% 1.13/1.29 % fd_pure 0
% 1.13/1.29 % fd_pseudo 0
% 1.13/1.29 % fd_cond 0
% 1.13/1.29 % fd_pseudo_cond 0
% 1.13/1.29 % AC symbols 0
% 1.13/1.29
% 1.13/1.29 % ------ Schedule dynamic 5 is on
% 1.13/1.29
% 1.13/1.29 % ------ no conjectures: strip conj schedule
% 1.13/1.29
% 1.13/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.13/1.29
% 1.13/1.29
% 1.13/1.29 % ------
% 1.13/1.29 % Current options:
% 1.13/1.29 % ------
% 1.13/1.29
% 1.13/1.29
% 1.13/1.29 %
% 1.13/1.29
% 1.13/1.29 % ------ Proving...
% 1.13/1.29 %
% 1.13/1.29
% 1.13/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.13/1.29
% 1.13/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.13/1.29
% 1.13/1.29
%------------------------------------------------------------------------------