%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:36:56 PM UTC 2026
% Result : Theorem 1.40s 1.20s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 96 ( 10 unt; 14 def)
% Number of atoms : 376 ( 33 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 440 ( 160 ~; 190 |; 64 &)
% ( 17 <=>; 6 =>; 0 <=; 3 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 14 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-4 aty)
% Number of variables : 96 ( 0 sgn 78 !; 18 ?)
% 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(f1040,definition,
( sP1
<=> ( 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 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f1041,plain,
( sP1
<~> ( 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(definition_folding,[],[f1037,f1040]) ).
fof(f1246,plain,
( ( sP1
| ~ 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)
& ! [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 ) )
| ~ sP1 ) ),
inference(nnf_transformation,[],[f1040]) ).
fof(f1247,plain,
( ( sP1
| ~ 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)
& ! [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 ) )
| ~ sP1 ) ),
inference(flattening,[],[f1246]) ).
fof(f1248,plain,
( ( sP1
| ~ 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,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 ) )
| ~ sP1 ) ),
inference(rectify,[],[f1247]) ).
fof(f1249,plain,
( ( sP1
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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_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,sK89,sK90),v_L)
& sK89 != sK90 ) )
& ( ( 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,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 ) )
| ~ sP1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88,sK89,sK90]),skolemize(X0,sK88),skolemize(X1,sK89),skolemize(X2,sK90)],[f1248]) ).
fof(f1250,plain,
( ( ~ 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 )
| ~ sP1 )
& ( ( 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 ) )
| sP1 ) ),
inference(nnf_transformation,[],[f1041]) ).
fof(f1251,plain,
( ( ~ 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 )
| ~ sP1 )
& ( ( 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 ) )
| sP1 ) ),
inference(flattening,[],[f1250]) ).
fof(f1252,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,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)
& X1 != X2 )
| ~ sP1 )
& ( ( 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 ) )
| sP1 ) ),
inference(rectify,[],[f1251]) ).
fof(f1253,plain,
( ( ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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,sK92,sK93),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,sK93,sK92),v_L)
& sK92 != sK93 )
| ~ sP1 )
& ( ( 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 ) )
| sP1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91,sK92,sK93]),skolemize(X0,sK91),skolemize(X1,sK92),skolemize(X2,sK93)],[f1252]) ).
fof(f2010,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
| ~ sP1 ),
inference(cnf_transformation,[],[f1249]) ).
fof(f2011,plain,
! [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)
| ~ sP1 ),
inference(cnf_transformation,[],[f1249]) ).
fof(f2012,plain,
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| ~ sP1 ),
inference(cnf_transformation,[],[f1249]) ).
fof(f2013,plain,
( sP1
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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)
| sK89 != sK90 ),
inference(cnf_transformation,[],[f1249]) ).
fof(f2014,plain,
( sP1
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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_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) ),
inference(cnf_transformation,[],[f1249]) ).
fof(f2015,plain,
( sP1
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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_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) ),
inference(cnf_transformation,[],[f1249]) ).
fof(f2016,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,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
| sP1 ),
inference(cnf_transformation,[],[f1253]) ).
fof(f2017,plain,
! [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)
| sP1 ),
inference(cnf_transformation,[],[f1253]) ).
fof(f2018,plain,
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L)
| sP1 ),
inference(cnf_transformation,[],[f1253]) ).
fof(f2019,plain,
( ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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)
| sK92 != sK93
| ~ sP1 ),
inference(cnf_transformation,[],[f1253]) ).
fof(f2020,plain,
( ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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,sK93,sK92),v_L)
| ~ sP1 ),
inference(cnf_transformation,[],[f1253]) ).
fof(f2021,plain,
( ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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,sK92,sK93),v_L)
| ~ sP1 ),
inference(cnf_transformation,[],[f1253]) ).
fof(f2207,definition,
! [X0,X1] :
( sQ94_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ94_eqProxy])],[equality_proxy_definition]) ).
fof(f2440,plain,
( sP1
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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)
| ~ sQ94_eqProxy(sK89,sK90) ),
inference(equality_proxy_replacement,[],[f2013,f2207]) ).
fof(f2441,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)
| sQ94_eqProxy(X4,X5)
| ~ sP1 ),
inference(equality_proxy_replacement,[],[f2010,f2207]) ).
fof(f2442,plain,
( ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,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)
| ~ sQ94_eqProxy(sK92,sK93)
| ~ sP1 ),
inference(equality_proxy_replacement,[],[f2019,f2207]) ).
fof(f2443,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,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)
| sQ94_eqProxy(X4,X5)
| sP1 ),
inference(equality_proxy_replacement,[],[f2016,f2207]) ).
fof(f2455,definition,
( spl95_1
<=> sP1 ),
introduced(definition,[new_symbols(definition,[spl95_1])],[avatar_definition]) ).
fof(f2458,definition,
( spl95_2
<=> ! [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)
| sQ94_eqProxy(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) ) ),
introduced(definition,[new_symbols(definition,[spl95_2])],[avatar_definition]) ).
fof(f2459,plain,
( ! [X4,X5] :
( sQ94_eqProxy(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) )
| ~ spl95_2 ),
inference(avatar_component_clause,[],[f2458]) ).
fof(f2460,plain,
( spl95_1
| spl95_2 ),
inference(avatar_split_clause,[],[f2443,f2458,f2455]) ).
fof(f2462,definition,
( spl95_3
<=> ! [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) ),
introduced(definition,[new_symbols(definition,[spl95_3])],[avatar_definition]) ).
fof(f2463,plain,
( ! [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)
| ~ spl95_3 ),
inference(avatar_component_clause,[],[f2462]) ).
fof(f2464,plain,
( spl95_1
| spl95_3 ),
inference(avatar_split_clause,[],[f2017,f2462,f2455]) ).
fof(f2466,definition,
( spl95_4
<=> c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_L) ),
introduced(definition,[new_symbols(definition,[spl95_4])],[avatar_definition]) ).
fof(f2468,plain,
( spl95_1
| spl95_4 ),
inference(avatar_split_clause,[],[f2018,f2466,f2455]) ).
fof(f2471,definition,
( spl95_5
<=> sQ94_eqProxy(sK92,sK93) ),
introduced(definition,[new_symbols(definition,[spl95_5])],[avatar_definition]) ).
fof(f2472,plain,
( ~ sQ94_eqProxy(sK92,sK93)
| spl95_5 ),
inference(avatar_component_clause,[],[f2471]) ).
fof(f2474,definition,
( spl95_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,[spl95_6])],[avatar_definition]) ).
fof(f2475,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)
| ~ spl95_6 ),
inference(avatar_component_clause,[],[f2474]) ).
fof(f2477,plain,
( ~ spl95_1
| ~ spl95_5
| spl95_6
| ~ spl95_4 ),
inference(avatar_split_clause,[],[f2442,f2466,f2474,f2471,f2455]) ).
fof(f2479,definition,
( spl95_7
<=> 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,sK93,sK92),v_L) ),
introduced(definition,[new_symbols(definition,[spl95_7])],[avatar_definition]) ).
fof(f2481,plain,
( ~ spl95_1
| ~ spl95_7
| spl95_6
| ~ spl95_4 ),
inference(avatar_split_clause,[],[f2020,f2466,f2474,f2479,f2455]) ).
fof(f2483,definition,
( spl95_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,sK92,sK93),v_L) ),
introduced(definition,[new_symbols(definition,[spl95_8])],[avatar_definition]) ).
fof(f2485,plain,
( ~ spl95_1
| ~ spl95_8
| spl95_6
| ~ spl95_4 ),
inference(avatar_split_clause,[],[f2021,f2466,f2474,f2483,f2455]) ).
fof(f2486,plain,
( ~ spl95_1
| spl95_2 ),
inference(avatar_split_clause,[],[f2441,f2458,f2455]) ).
fof(f2487,plain,
( ~ spl95_1
| spl95_3 ),
inference(avatar_split_clause,[],[f2011,f2462,f2455]) ).
fof(f2488,plain,
( ~ spl95_1
| spl95_4 ),
inference(avatar_split_clause,[],[f2012,f2466,f2455]) ).
fof(f2490,definition,
( spl95_9
<=> sQ94_eqProxy(sK89,sK90) ),
introduced(definition,[new_symbols(definition,[spl95_9])],[avatar_definition]) ).
fof(f2491,plain,
( ~ sQ94_eqProxy(sK89,sK90)
| spl95_9 ),
inference(avatar_component_clause,[],[f2490]) ).
fof(f2493,definition,
( spl95_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,sK88,sK88),v_L) ),
introduced(definition,[new_symbols(definition,[spl95_10])],[avatar_definition]) ).
fof(f2494,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)
| ~ spl95_10 ),
inference(avatar_component_clause,[],[f2493]) ).
fof(f2495,plain,
( ~ spl95_9
| spl95_10
| ~ spl95_4
| spl95_1 ),
inference(avatar_split_clause,[],[f2440,f2455,f2466,f2493,f2490]) ).
fof(f2497,definition,
( spl95_11
<=> 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,[spl95_11])],[avatar_definition]) ).
fof(f2499,plain,
( ~ spl95_11
| spl95_10
| ~ spl95_4
| spl95_1 ),
inference(avatar_split_clause,[],[f2014,f2455,f2466,f2493,f2497]) ).
fof(f2501,definition,
( spl95_12
<=> 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,[spl95_12])],[avatar_definition]) ).
fof(f2503,plain,
( ~ spl95_12
| spl95_10
| ~ spl95_4
| spl95_1 ),
inference(avatar_split_clause,[],[f2015,f2455,f2466,f2493,f2501]) ).
fof(f2504,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,sK90,sK89),v_L)
| ~ spl95_2
| spl95_9 ),
inference(resolution,[],[f2491,f2459]) ).
fof(f2507,plain,
( spl95_12
| spl95_11
| ~ spl95_2
| spl95_9 ),
inference(avatar_split_clause,[],[f2504,f2490,f2458,f2497,f2501]) ).
fof(f2508,plain,
( $false
| ~ spl95_3
| ~ spl95_10 ),
inference(resolution,[],[f2494,f2463]) ).
fof(f2509,plain,
( ~ spl95_3
| ~ spl95_10 ),
inference(avatar_contradiction_clause,[],[f2508]) ).
fof(f2510,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,sK92,sK93),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,sK93,sK92),v_L)
| ~ spl95_2
| spl95_5 ),
inference(resolution,[],[f2472,f2459]) ).
fof(f2513,plain,
( spl95_7
| spl95_8
| ~ spl95_2
| spl95_5 ),
inference(avatar_split_clause,[],[f2510,f2471,f2458,f2483,f2479]) ).
fof(f2514,plain,
( $false
| ~ spl95_3
| ~ spl95_6 ),
inference(resolution,[],[f2475,f2463]) ).
fof(f2515,plain,
( ~ spl95_3
| ~ spl95_6 ),
inference(avatar_contradiction_clause,[],[f2514]) ).
cnf(s1,plain,
( spl95_1
| spl95_2 ),
inference(sat_conversion,[],[f2460]) ).
cnf(s2,plain,
( spl95_1
| spl95_3 ),
inference(sat_conversion,[],[f2464]) ).
cnf(s3,plain,
( spl95_1
| spl95_4 ),
inference(sat_conversion,[],[f2468]) ).
cnf(s4,plain,
( ~ spl95_1
| ~ spl95_4
| ~ spl95_5
| spl95_6 ),
inference(sat_conversion,[],[f2477]) ).
cnf(s5,plain,
( ~ spl95_1
| ~ spl95_4
| spl95_6
| ~ spl95_7 ),
inference(sat_conversion,[],[f2481]) ).
cnf(s6,plain,
( ~ spl95_1
| ~ spl95_4
| spl95_6
| ~ spl95_8 ),
inference(sat_conversion,[],[f2485]) ).
cnf(s7,plain,
( ~ spl95_1
| spl95_2 ),
inference(sat_conversion,[],[f2486]) ).
cnf(s8,plain,
( ~ spl95_1
| spl95_3 ),
inference(sat_conversion,[],[f2487]) ).
cnf(s9,plain,
( ~ spl95_1
| spl95_4 ),
inference(sat_conversion,[],[f2488]) ).
cnf(s10,plain,
( spl95_1
| ~ spl95_4
| ~ spl95_9
| spl95_10 ),
inference(sat_conversion,[],[f2495]) ).
cnf(s11,plain,
( spl95_1
| ~ spl95_4
| spl95_10
| ~ spl95_11 ),
inference(sat_conversion,[],[f2499]) ).
cnf(s12,plain,
( spl95_1
| ~ spl95_4
| spl95_10
| ~ spl95_12 ),
inference(sat_conversion,[],[f2503]) ).
cnf(s13,plain,
( ~ spl95_2
| spl95_9
| spl95_11
| spl95_12 ),
inference(sat_conversion,[],[f2507]) ).
cnf(s14,plain,
( ~ spl95_3
| ~ spl95_10 ),
inference(sat_conversion,[],[f2509]) ).
cnf(s15,plain,
( ~ spl95_2
| spl95_5
| spl95_7
| spl95_8 ),
inference(sat_conversion,[],[f2513]) ).
cnf(s16,plain,
( ~ spl95_3
| ~ spl95_6 ),
inference(sat_conversion,[],[f2515]) ).
cnf(s17,plain,
spl95_1,
inference(rat,[],[s13,s10,s11,s12,s14,s1,s2,s3]) ).
cnf(s18,plain,
spl95_4,
inference(rat,[],[s9,s17]) ).
cnf(s19,plain,
spl95_3,
inference(rat,[],[s8,s17]) ).
cnf(s20,plain,
spl95_2,
inference(rat,[],[s7,s17]) ).
cnf(s21,plain,
~ spl95_6,
inference(rat,[],[s16,s19]) ).
cnf(s23,plain,
~ spl95_8,
inference(rat,[],[s6,s18,s17,s21]) ).
cnf(s24,plain,
~ spl95_7,
inference(rat,[],[s5,s18,s17,s21]) ).
cnf(s25,plain,
~ spl95_5,
inference(rat,[],[s4,s18,s17,s21]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s15,s23,s20,s24,s25]) ).
fof(f2516,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT105+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 23:42:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.40/1.20 % (297255)Detected formulas, will run a generic FOF schedule.
% 1.40/1.20 % (297266)dis-21_1_sil=8000:lcm=predicate:random_seed=581344988:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 1.40/1.20 % (297266)First to succeed.
% 1.40/1.20 % (297266)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-297255"
% 1.40/1.20 % (297260)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=668196699:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.40/1.20 % (297263)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3119315681:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.40/1.20 % (297262)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1382528145:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.40/1.20 % (297264)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1554507733:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.40/1.20 % (297261)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=281984641:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.40/1.20 % (297263)Also succeeded, but the first one will report.
% 1.40/1.20 % (297265)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=214388273:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.40/1.20 % (297264)Instruction limit reached!
% 1.40/1.20 % (297264)------------------------------
% 1.40/1.20 % (297264)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.40/1.20 % (297264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.40/1.20 % (297264)CaDiCaL version: 2.1.3
% 1.40/1.20 % (297264)Termination reason: Instruction limit
% 1.40/1.20 % (297264)Termination phase: Saturation
% 1.40/1.20 % (297264)Time elapsed: 0.076 s
% 1.40/1.20 % (297264)Peak memory usage: 89 MB
% 1.40/1.20 % (297264)Instructions burned: 120 (million)
% 1.40/1.20 % (297265)Instruction limit reached!
% 1.40/1.20 % (297265)------------------------------
% 1.40/1.20 % (297265)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.40/1.20 % (297265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.40/1.20 % (297265)CaDiCaL version: 2.1.3
% 1.40/1.20 % (297265)Termination reason: Instruction limit
% 1.40/1.20 % (297265)Termination phase: Saturation
% 1.40/1.20 % (297265)Time elapsed: 0.079 s
% 1.40/1.20 % (297265)Peak memory usage: 90 MB
% 1.40/1.20 % (297265)Instructions burned: 140 (million)
% 1.40/1.20 % (297266)Refutation found. Thanks to Tanya!
% 1.40/1.20 % SZS status Theorem for theBenchmark
% 1.40/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.41 % (297266)------------------------------
% 0.16/1.41 % (297266)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.41 % (297266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.41 % (297266)CaDiCaL version: 2.1.3
% 0.16/1.41 % (297266)Termination reason: Refutation
% 0.16/1.41 % (297266)Time elapsed: 0.016 s
% 0.16/1.41 % (297266)Peak memory usage: 90 MB
% 0.16/1.41 % (297266)Instructions burned: 57 (million)
% 0.16/1.41 % (297266)------------------------------
% 0.16/1.41 % (297266)------------------------------
% 0.16/1.41 % (297255)Success in time 0.348 s
% 0.16/1.41 % Vampire exiting
%------------------------------------------------------------------------------