%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SCT105+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 : Tue Sep 29 12:37:32 PM UTC 2026
% Result : Theorem 0.28s 0.59s
% Output : Refutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 91 ( 13 unt; 11 def)
% Number of atoms : 312 ( 24 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 373 ( 152 ~; 179 |; 20 &)
% ( 14 <=>; 6 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 12 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-4 aty)
% Number of variables : 42 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f523,conjecture,
( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [X0] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X0),v_L)
& ! [X0,X1] :
( X0 != X1
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L) ) ) )
<=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [X0] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X0),v_L)
& ! [X0,X1] :
( X0 != X1
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f524,negated_conjecture,
~ ( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [X0] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X0),v_L)
& ! [X0,X1] :
( X0 != X1
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L) ) ) )
<=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [X0] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X0),v_L)
& ! [X0,X1] :
( X0 != X1
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f523]) ).
fof(f528,plain,
~ ( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [X0] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X0),v_L)
& ! [X1,X2] :
( X1 != X2
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X1),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L) ) ) )
<=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [X3] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X3),v_L)
& ! [X4,X5] :
( X4 != X5
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X5),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),v_L) ) ) ) ),
inference(rectify,[],[f524]) ).
fof(f1036,plain,
( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [X0] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X0),v_L)
& ! [X1,X2] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X1),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L)
| X1 = X2 ) )
<~> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [X3] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X3),v_L)
& ! [X4,X5] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X5),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),v_L)
| X4 = X5 ) ) ),
inference(ennf_transformation,[],[f528]) ).
fof(f1037,plain,
( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [X0] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X0),v_L)
& ! [X1,X2] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X1),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L)
| X1 = X2 ) )
<~> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
& ! [X3] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X3),v_L)
& ! [X4,X5] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X5),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),v_L)
| X4 = X5 ) ) ),
inference(flattening,[],[f1036]) ).
fof(f1783,plain,
! [X2,X1,X4,X5] :
( X4 = X5
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X5),v_L)
| X1 = X2
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X1),v_L) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f1784,plain,
( sK89 != sK90
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK91,sK91),v_L)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK87,sK86),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK88,sK88),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f1785,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK90,sK89),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK91,sK91),v_L)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK87,sK86),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK88,sK88),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f1786,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK89,sK90),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK91,sK91),v_L)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK87,sK86),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK88,sK88),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f1787,plain,
( sK89 != sK90
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK91,sK91),v_L)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK86,sK87),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK88,sK88),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f1788,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK90,sK89),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK91,sK91),v_L)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK86,sK87),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK88,sK88),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f1789,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK89,sK90),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK91,sK91),v_L)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK86,sK87),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK88,sK88),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f1790,plain,
( sK89 != sK90
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK91,sK91),v_L)
| sK86 != sK87
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK88,sK88),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f1791,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK90,sK89),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK91,sK91),v_L)
| sK86 != sK87
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK88,sK88),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f1792,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK89,sK90),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK91,sK91),v_L)
| sK86 != sK87
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK88,sK88),v_L)
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f1796,plain,
c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L),
inference(cnf_transformation,[],[f1037]) ).
fof(f1797,plain,
! [X3,X0] :
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X3),v_L)
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X0),v_L) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f2418,definition,
( spl92_1
<=> ! [X0] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X0),v_L) ),
introduced(definition,[new_symbols(definition,[spl92_1])],[avatar_definition]) ).
fof(f2419,plain,
( ! [X0] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X0),v_L)
| ~ spl92_1 ),
inference(avatar_component_clause,[],[f2418]) ).
fof(f2421,definition,
( spl92_2
<=> ! [X4,X5] :
( X4 = X5
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X5),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),v_L) ) ),
introduced(definition,[new_symbols(definition,[spl92_2])],[avatar_definition]) ).
fof(f2422,plain,
( ! [X4,X5] :
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X5,X4),v_L)
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X5),v_L)
| X4 = X5 )
| ~ spl92_2 ),
inference(avatar_component_clause,[],[f2421]) ).
fof(f2425,definition,
( spl92_3
<=> c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
introduced(definition,[new_symbols(definition,[spl92_3])],[avatar_definition]) ).
fof(f2429,plain,
( spl92_2
| spl92_2 ),
inference(avatar_split_clause,[],[f1783,f2421,f2421]) ).
fof(f2431,definition,
( spl92_4
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK88,sK88),v_L) ),
introduced(definition,[new_symbols(definition,[spl92_4])],[avatar_definition]) ).
fof(f2433,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK88,sK88),v_L)
| ~ spl92_4 ),
inference(avatar_component_clause,[],[f2431]) ).
fof(f2435,definition,
( spl92_5
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK87,sK86),v_L) ),
introduced(definition,[new_symbols(definition,[spl92_5])],[avatar_definition]) ).
fof(f2437,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK87,sK86),v_L)
| spl92_5 ),
inference(avatar_component_clause,[],[f2435]) ).
fof(f2439,definition,
( spl92_6
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK91,sK91),v_L) ),
introduced(definition,[new_symbols(definition,[spl92_6])],[avatar_definition]) ).
fof(f2441,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK91,sK91),v_L)
| ~ spl92_6 ),
inference(avatar_component_clause,[],[f2439]) ).
fof(f2443,definition,
( spl92_7
<=> sK89 = sK90 ),
introduced(definition,[new_symbols(definition,[spl92_7])],[avatar_definition]) ).
fof(f2446,plain,
( ~ spl92_3
| spl92_4
| ~ spl92_5
| spl92_6
| ~ spl92_7 ),
inference(avatar_split_clause,[],[f1784,f2443,f2439,f2435,f2431,f2425]) ).
fof(f2448,definition,
( spl92_8
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK90,sK89),v_L) ),
introduced(definition,[new_symbols(definition,[spl92_8])],[avatar_definition]) ).
fof(f2450,plain,
( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK90,sK89),v_L)
| spl92_8 ),
inference(avatar_component_clause,[],[f2448]) ).
fof(f2451,plain,
( ~ spl92_3
| spl92_4
| ~ spl92_5
| spl92_6
| ~ spl92_8 ),
inference(avatar_split_clause,[],[f1785,f2448,f2439,f2435,f2431,f2425]) ).
fof(f2453,definition,
( spl92_9
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK89,sK90),v_L) ),
introduced(definition,[new_symbols(definition,[spl92_9])],[avatar_definition]) ).
fof(f2456,plain,
( ~ spl92_3
| spl92_4
| ~ spl92_5
| spl92_6
| ~ spl92_9 ),
inference(avatar_split_clause,[],[f1786,f2453,f2439,f2435,f2431,f2425]) ).
fof(f2458,definition,
( spl92_10
<=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK86,sK87),v_L) ),
introduced(definition,[new_symbols(definition,[spl92_10])],[avatar_definition]) ).
fof(f2461,plain,
( ~ spl92_3
| spl92_4
| ~ spl92_10
| spl92_6
| ~ spl92_7 ),
inference(avatar_split_clause,[],[f1787,f2443,f2439,f2458,f2431,f2425]) ).
fof(f2462,plain,
( ~ spl92_3
| spl92_4
| ~ spl92_10
| spl92_6
| ~ spl92_8 ),
inference(avatar_split_clause,[],[f1788,f2448,f2439,f2458,f2431,f2425]) ).
fof(f2463,plain,
( ~ spl92_3
| spl92_4
| ~ spl92_10
| spl92_6
| ~ spl92_9 ),
inference(avatar_split_clause,[],[f1789,f2453,f2439,f2458,f2431,f2425]) ).
fof(f2465,definition,
( spl92_11
<=> sK86 = sK87 ),
introduced(definition,[new_symbols(definition,[spl92_11])],[avatar_definition]) ).
fof(f2468,plain,
( ~ spl92_3
| spl92_4
| ~ spl92_11
| spl92_6
| ~ spl92_7 ),
inference(avatar_split_clause,[],[f1790,f2443,f2439,f2465,f2431,f2425]) ).
fof(f2469,plain,
( ~ spl92_3
| spl92_4
| ~ spl92_11
| spl92_6
| ~ spl92_8 ),
inference(avatar_split_clause,[],[f1791,f2448,f2439,f2465,f2431,f2425]) ).
fof(f2470,plain,
( ~ spl92_3
| spl92_4
| ~ spl92_11
| spl92_6
| ~ spl92_9 ),
inference(avatar_split_clause,[],[f1792,f2453,f2439,f2465,f2431,f2425]) ).
fof(f2474,plain,
spl92_3,
inference(avatar_split_clause,[],[f1796,f2425]) ).
fof(f2475,plain,
( spl92_1
| spl92_1 ),
inference(avatar_split_clause,[],[f1797,f2418,f2418]) ).
fof(f2477,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK86,sK87),v_L)
| sK86 = sK87
| ~ spl92_2
| spl92_5 ),
inference(resolution,[],[f2422,f2437]) ).
fof(f2489,plain,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK89,sK90),v_L)
| sK89 = sK90
| ~ spl92_2
| spl92_8 ),
inference(resolution,[],[f2450,f2422]) ).
fof(f2494,plain,
( $false
| ~ spl92_1
| ~ spl92_4 ),
inference(forward_subsumption_resolution,[],[f2433,f2419]) ).
fof(f2495,plain,
( ~ spl92_1
| ~ spl92_4 ),
inference(avatar_contradiction_clause,[],[f2494]) ).
fof(f2497,plain,
( spl92_11
| spl92_10
| ~ spl92_2
| spl92_5 ),
inference(avatar_split_clause,[],[f2477,f2435,f2421,f2458,f2465]) ).
fof(f2499,plain,
( spl92_7
| spl92_9
| ~ spl92_2
| spl92_8 ),
inference(avatar_split_clause,[],[f2489,f2448,f2421,f2453,f2443]) ).
fof(f2500,plain,
( $false
| ~ spl92_1
| ~ spl92_6 ),
inference(forward_subsumption_resolution,[],[f2441,f2419]) ).
fof(f2501,plain,
( ~ spl92_1
| ~ spl92_6 ),
inference(avatar_contradiction_clause,[],[f2500]) ).
cnf(s3,plain,
( spl92_2
| spl92_2 ),
inference(sat_conversion,[],[f2429]) ).
cnf(s4,plain,
spl92_2,
inference(rat,[],[s3]) ).
cnf(s5,plain,
( ~ spl92_3
| spl92_4
| ~ spl92_5
| spl92_6
| ~ spl92_7 ),
inference(sat_conversion,[],[f2446]) ).
cnf(s6,plain,
( ~ spl92_3
| spl92_4
| ~ spl92_5
| spl92_6
| ~ spl92_8 ),
inference(sat_conversion,[],[f2451]) ).
cnf(s7,plain,
( ~ spl92_3
| spl92_4
| ~ spl92_5
| spl92_6
| ~ spl92_9 ),
inference(sat_conversion,[],[f2456]) ).
cnf(s8,plain,
( ~ spl92_3
| spl92_4
| spl92_6
| ~ spl92_7
| ~ spl92_10 ),
inference(sat_conversion,[],[f2461]) ).
cnf(s9,plain,
( ~ spl92_3
| spl92_4
| spl92_6
| ~ spl92_8
| ~ spl92_10 ),
inference(sat_conversion,[],[f2462]) ).
cnf(s10,plain,
( ~ spl92_3
| spl92_4
| spl92_6
| ~ spl92_9
| ~ spl92_10 ),
inference(sat_conversion,[],[f2463]) ).
cnf(s11,plain,
( ~ spl92_3
| spl92_4
| spl92_6
| ~ spl92_7
| ~ spl92_11 ),
inference(sat_conversion,[],[f2468]) ).
cnf(s12,plain,
( ~ spl92_3
| spl92_4
| spl92_6
| ~ spl92_8
| ~ spl92_11 ),
inference(sat_conversion,[],[f2469]) ).
cnf(s13,plain,
( ~ spl92_3
| spl92_4
| spl92_6
| ~ spl92_9
| ~ spl92_11 ),
inference(sat_conversion,[],[f2470]) ).
cnf(s17,plain,
spl92_3,
inference(sat_conversion,[],[f2474]) ).
cnf(s18,plain,
( spl92_1
| spl92_1 ),
inference(sat_conversion,[],[f2475]) ).
cnf(s19,plain,
spl92_1,
inference(rat,[],[s18]) ).
cnf(s27,plain,
( ~ spl92_1
| ~ spl92_4 ),
inference(sat_conversion,[],[f2495]) ).
cnf(s29,plain,
( ~ spl92_2
| spl92_5
| spl92_10
| spl92_11 ),
inference(sat_conversion,[],[f2497]) ).
cnf(s31,plain,
( ~ spl92_2
| spl92_7
| spl92_8
| spl92_9 ),
inference(sat_conversion,[],[f2499]) ).
cnf(s32,plain,
( ~ spl92_1
| ~ spl92_6 ),
inference(sat_conversion,[],[f2501]) ).
cnf(s33,plain,
~ spl92_6,
inference(rat,[],[s32,s19]) ).
cnf(s34,plain,
~ spl92_4,
inference(rat,[],[s27,s19]) ).
cnf(s35,plain,
( ~ spl92_9
| ~ spl92_11 ),
inference(rat,[],[s13,s33,s34,s17]) ).
cnf(s36,plain,
( ~ spl92_8
| ~ spl92_11 ),
inference(rat,[],[s12,s33,s34,s17]) ).
cnf(s37,plain,
( ~ spl92_7
| ~ spl92_11 ),
inference(rat,[],[s11,s33,s34,s17]) ).
cnf(s38,plain,
( ~ spl92_9
| ~ spl92_10 ),
inference(rat,[],[s10,s33,s34,s17]) ).
cnf(s39,plain,
( ~ spl92_8
| ~ spl92_10 ),
inference(rat,[],[s9,s33,s34,s17]) ).
cnf(s40,plain,
( ~ spl92_7
| ~ spl92_10 ),
inference(rat,[],[s8,s33,s34,s17]) ).
cnf(s41,plain,
( ~ spl92_5
| ~ spl92_9 ),
inference(rat,[],[s7,s33,s34,s17]) ).
cnf(s42,plain,
( ~ spl92_5
| ~ spl92_8 ),
inference(rat,[],[s6,s33,s34,s17]) ).
cnf(s43,plain,
( ~ spl92_5
| ~ spl92_7 ),
inference(rat,[],[s5,s33,s34,s17]) ).
cnf(s44,plain,
( ~ spl92_9
| spl92_5 ),
inference(rat,[],[s29,s38,s35,s4]) ).
cnf(s45,plain,
( ~ spl92_8
| spl92_5 ),
inference(rat,[],[s29,s39,s36,s4]) ).
cnf(s46,plain,
spl92_5,
inference(rat,[],[s29,s40,s37,s31,s45,s44,s4]) ).
cnf(s47,plain,
~ spl92_9,
inference(rat,[],[s41,s46]) ).
cnf(s48,plain,
~ spl92_8,
inference(rat,[],[s42,s46]) ).
cnf(s49,plain,
~ spl92_7,
inference(rat,[],[s43,s46]) ).
cnf(s50,plain,
$false,
inference(rat,[],[s31,s47,s4,s49,s48]) ).
fof(f2502,plain,
$false,
inference(avatar_sat_refutation,[],[s50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SCT105+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.18/0.43 % Computer : n017.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sun Sep 27 23:38:05 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.22/0.48 Running first-order model finding
% 0.22/0.49 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.28/0.59 % (3072524)Will run a generic schedule for satisfiability detection.
% 0.28/0.59 % (3072530)% WARNING: option uhcvi not known.
% 0.28/0.59 % (3072530)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2822831579:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.28/0.59 % (3072529)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1200348883_2999 on theBenchmark for (2999ds/0Mi)
% 0.28/0.59 % (3072531)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2264333200:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.28/0.59 % (3072533)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3924240190:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.28/0.59 % (3072532)dis+10_1_sil=32000:sp=arity:random_seed=4142642614:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.28/0.59 % (3072534)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1963210327:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.28/0.59 % (3072535)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1034328418:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.28/0.59 % (3072530) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3072524-3072530"...
% 0.28/0.59 % (3072530)...printing done.
% 0.28/0.59 % (3072530)Refutation found. Thanks to Tanya!
% 0.28/0.59 % SZS status Theorem for theBenchmark
% 0.28/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 0.28/0.59 % (3072530)------------------------------
% 0.28/0.59 % (3072530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.59 % (3072530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.59 % (3072530)CaDiCaL version: 2.1.3
% 0.28/0.59 % (3072530)Termination reason: Refutation
% 0.28/0.59 % (3072530)Time elapsed: 0.024 s
% 0.28/0.59 % (3072530)Peak memory usage: 13 MB
% 0.28/0.59 % (3072530)Instructions burned: 50 (million)
% 0.28/0.59 % (3072524)Success in time 0.087 s
% 0.28/0.59 % Vampire exiting
%------------------------------------------------------------------------------