%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SCT021-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 12:37:23 PM UTC 2026
% Result : Unsatisfiable 0.98s 0.64s
% Output : Refutation 0.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 22
% Syntax : Number of formulae : 79 ( 20 unt; 8 def)
% Number of atoms : 194 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 207 ( 92 ~; 107 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 9 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 56 ( 0 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f765,axiom,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(c_in(c_Pair(X4,X1,X2,X2),X3,tc_prod(X2,X2)))
| hBOOL(c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)))
| ~ hBOOL(c_in(c_Pair(X0,X4,X2,X2),X3,tc_prod(X2,X2)))
| ~ c_Relation_Otrans(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_0) ).
fof(f767,axiom,
! [X2,X0,X1] :
( ~ hBOOL(c_in(c_Pair(X0,X0,X1,X1),X2,tc_prod(X1,X1)))
| ~ c_Relation_Oirrefl(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
fof(f771,axiom,
! [X0,X1] : hBOOL(c_in(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
fof(f772,axiom,
! [X2,X3,X0,X1,X4] :
( hBOOL(c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)))
| hBOOL(c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2)))
| X1 = X0
| ~ hBOOL(c_in(X0,X4,X2))
| ~ hBOOL(c_in(X1,X4,X2))
| ~ c_Relation_Ototal__on(X4,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).
fof(f773,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Relation_Ototal__on(X4,X3,X2)
| hBOOL(c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2)))
| X0 = X1
| ~ hBOOL(c_in(X0,X4,X2))
| ~ hBOOL(c_in(X1,X4,X2))
| hBOOL(c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2))) ),
inference(reorient_equations,[],[f772]) ).
fof(f774,axiom,
! [X2,X0,X1] :
( hBOOL(c_in(X0,X1,X2))
| ~ hBOOL(hAPP(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f775,axiom,
! [X2,X0,X1] :
( ~ hBOOL(c_in(X1,X0,X2))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f776,negated_conjecture,
! [X0] : c_Relation_Otrans(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f777,negated_conjecture,
! [X0] : c_Relation_Oirrefl(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f778,negated_conjecture,
! [X0] : c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f779,negated_conjecture,
hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f780,negated_conjecture,
~ hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f781,negated_conjecture,
( c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f782,negated_conjecture,
( c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f784,negated_conjecture,
! [X2,X0,X1] :
( ~ hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X0 = X1
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(X2,v_Pa(X2)),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_8) ).
fof(f877,definition,
( spl0_1
<=> c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f879,plain,
( ~ c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_1 ),
inference(avatar_component_clause,[],[f877]) ).
fof(f881,definition,
( spl0_2
<=> c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f883,plain,
( ~ c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_2 ),
inference(avatar_component_clause,[],[f881]) ).
fof(f885,definition,
( spl0_3
<=> c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f887,plain,
( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_3 ),
inference(avatar_component_clause,[],[f885]) ).
fof(f894,definition,
( spl0_5
<=> c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f896,plain,
( c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f894]) ).
fof(f897,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f782,f894,f885,f881,f877]) ).
fof(f899,definition,
( spl0_6
<=> c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f901,plain,
( c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f899]) ).
fof(f902,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f781,f899,f885,f881,f877]) ).
fof(f903,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f879,f776]) ).
fof(f904,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f903]) ).
fof(f905,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f883,f777]) ).
fof(f906,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f905]) ).
fof(f907,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f887,f778]) ).
fof(f908,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f907]) ).
fof(f911,plain,
! [X2,X0,X1] :
( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X0,v_Pa(X0)),tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X0),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(X0,v_i),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Oirrefl(hAPP(X0,v_Pa(X0)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(X0,v_Pa(X0)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[],[f774,f784]) ).
fof(f912,plain,
! [X0,X1] :
( hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X0 = X1
| ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[],[f911,f778]) ).
fof(f913,plain,
! [X0,X1] :
( hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X0 = X1
| ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(forward_subsumption_resolution,[],[f912,f777]) ).
fof(f914,plain,
! [X0,X1] :
( hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X0 = X1
| ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(forward_subsumption_resolution,[],[f913,f776]) ).
fof(f915,plain,
hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(resolution,[],[f775,f779]) ).
fof(f946,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,c_Pair(X2,X2,X1,X1)))
| ~ c_Relation_Oirrefl(X0,X1) ),
inference(resolution,[],[f767,f774]) ).
fof(f1005,plain,
! [X0] :
( hBOOL(c_in(c_Pair(X0,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(X0,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[],[f765,f779]) ).
fof(f1012,plain,
( ! [X0] :
( ~ hBOOL(c_in(c_Pair(X0,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X0,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f1005,f901]) ).
fof(f1013,plain,
( ! [X0] :
( hBOOL(c_in(c_Pair(X0,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| v_a = X0
| ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(X0,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_6 ),
inference(resolution,[],[f1012,f914]) ).
fof(f1024,plain,
( v_a = v_b
| ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_6 ),
inference(resolution,[],[f1013,f767]) ).
fof(f1028,plain,
( v_a = v_b
| ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f1024,f896]) ).
fof(f1030,definition,
( spl0_7
<=> hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f1032,plain,
( ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| spl0_7 ),
inference(avatar_component_clause,[],[f1030]) ).
fof(f1034,definition,
( spl0_8
<=> v_a = v_b ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f1036,plain,
( v_a = v_b
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f1034]) ).
fof(f1037,plain,
( ~ spl0_7
| spl0_8
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f1028,f899,f894,f1034,f1030]) ).
fof(f1104,plain,
! [X2,X0,X1] :
( hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X0 = X1
| ~ hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))
| ~ hBOOL(c_in(X0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))
| hBOOL(c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[],[f773,f778]) ).
fof(f1110,plain,
! [X2,X0,X1] :
( hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X0 = X1
| ~ hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))
| hBOOL(c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(forward_subsumption_resolution,[],[f1104,f771]) ).
fof(f1112,plain,
! [X2,X0,X1] :
( hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f1110,f771]) ).
fof(f1126,plain,
( hBOOL(c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| v_a = v_b ),
inference(resolution,[],[f1112,f780]) ).
fof(f1142,definition,
( spl0_9
<=> hBOOL(c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f1144,plain,
( hBOOL(c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f1142]) ).
fof(f1148,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f1126,f1142,f1034]) ).
fof(f1156,plain,
( hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_8 ),
inference(superposition,[],[f915,f1036]) ).
fof(f1162,plain,
( ~ c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_8 ),
inference(resolution,[],[f1156,f946]) ).
fof(f1163,plain,
( $false
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f1162,f896]) ).
fof(f1164,plain,
( ~ spl0_5
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f1163]) ).
fof(f1167,plain,
( hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_9 ),
inference(resolution,[],[f1144,f775]) ).
fof(f1168,plain,
( $false
| spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f1167,f1032]) ).
fof(f1169,plain,
( spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f1168]) ).
cnf(s2,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f897]) ).
cnf(s3,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f902]) ).
cnf(s4,plain,
spl0_1,
inference(sat_conversion,[],[f904]) ).
cnf(s5,plain,
spl0_2,
inference(sat_conversion,[],[f906]) ).
cnf(s6,plain,
spl0_3,
inference(sat_conversion,[],[f908]) ).
cnf(s7,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f1037]) ).
cnf(s9,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f1148]) ).
cnf(s10,plain,
( ~ spl0_5
| ~ spl0_8 ),
inference(sat_conversion,[],[f1164]) ).
cnf(s11,plain,
( spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f1169]) ).
cnf(s12,plain,
spl0_6,
inference(rat,[],[s3,s6,s5,s4]) ).
cnf(s13,plain,
spl0_5,
inference(rat,[],[s2,s6,s5,s4]) ).
cnf(s14,plain,
~ spl0_8,
inference(rat,[],[s10,s13]) ).
cnf(s15,plain,
~ spl0_7,
inference(rat,[],[s7,s14,s12,s13]) ).
cnf(s16,plain,
spl0_9,
inference(rat,[],[s9,s14]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s11,s16,s15]) ).
fof(f1175,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT021-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 % Computer : n018.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 23:32:09 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 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
% 0.98/0.64 % (2852087)Will run a generic schedule for satisfiability detection.
% 0.98/0.64 % (2852097)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=521130773:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.98/0.64 % (2852093)% WARNING: option uhcvi not known.
% 0.98/0.64 % (2852092)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4010879750_2999 on theBenchmark for (2999ds/0Mi)
% 0.98/0.64 % (2852096)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=123445588:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.98/0.64 % (2852093)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2685997308:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.98/0.64 % (2852094)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1570107186:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.98/0.64 % (2852095)dis+10_1_sil=32000:sp=arity:random_seed=2490669632:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.98/0.64 % (2852098)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=610460074:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.98/0.64 % (2852097)Instruction limit reached!
% 0.98/0.64 % (2852097)------------------------------
% 0.98/0.64 % (2852097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.64 % (2852097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.64 % (2852097)CaDiCaL version: 2.1.3
% 0.98/0.64 % (2852097)Termination reason: Instruction limit
% 0.98/0.64 % (2852097)Termination phase: Saturation
% 0.98/0.64 % (2852097)Time elapsed: 0.049 s
% 0.98/0.64 % (2852097)Peak memory usage: 14 MB
% 0.98/0.64 % (2852097)Instructions burned: 134 (million)
% 0.98/0.64 % (2852106)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3668300892:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 0.98/0.64 % (2852095)Instruction limit reached!
% 0.98/0.64 % (2852095)------------------------------
% 0.98/0.64 % (2852095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.64 % (2852095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.64 % (2852095)CaDiCaL version: 2.1.3
% 0.98/0.64 % (2852095)Termination reason: Instruction limit
% 0.98/0.64 % (2852095)Termination phase: Saturation
% 0.98/0.64 % (2852095)Time elapsed: 0.066 s
% 0.98/0.64 % (2852095)Peak memory usage: 13 MB
% 0.98/0.64 % (2852095)Instructions burned: 104 (million)
% 0.98/0.64 % (2852096)Instruction limit reached!
% 0.98/0.64 % (2852096)------------------------------
% 0.98/0.64 % (2852096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.64 % (2852096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.64 % (2852096)CaDiCaL version: 2.1.3
% 0.98/0.64 % (2852096)Termination reason: Instruction limit
% 0.98/0.64 % (2852096)Termination phase: Saturation
% 0.98/0.64 % (2852096)Time elapsed: 0.071 s
% 0.98/0.64 % (2852096)Peak memory usage: 13 MB
% 0.98/0.64 % (2852096)Instructions burned: 116 (million)
% 0.98/0.64 % (2852108)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2458901717:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.98/0.64 % (2852109)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=311729961:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.98/0.64 % (2852098)Instruction limit reached!
% 0.98/0.64 % (2852098)------------------------------
% 0.98/0.64 % (2852098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.64 % (2852098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.64 % (2852098)CaDiCaL version: 2.1.3
% 0.98/0.64 % (2852098)Termination reason: Instruction limit
% 0.98/0.64 % (2852098)Termination phase: Saturation
% 0.98/0.64 % (2852098)Time elapsed: 0.105 s
% 0.98/0.64 % (2852098)Peak memory usage: 14 MB
% 0.98/0.64 % (2852098)Instructions burned: 159 (million)
% 0.98/0.64 % (2852112)ott-21_1_sil=16000:fs=off:random_seed=7560492:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.98/0.64 % (2852109) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2852087-2852109"...
% 0.98/0.64 % (2852109)...printing done.
% 0.98/0.64 % (2852109)Refutation found. Thanks to Tanya!
% 0.98/0.64 % SZS status Unsatisfiable for theBenchmark
% 0.98/0.64 % SZS output start Proof for theBenchmark
% See solution above
% 0.98/0.65 % (2852109)------------------------------
% 0.98/0.65 % (2852109)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.65 % (2852109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.65 % (2852109)CaDiCaL version: 2.1.3
% 0.98/0.65 % (2852109)Termination reason: Refutation
% 0.98/0.65 % (2852109)Time elapsed: 0.039 s
% 0.98/0.65 % (2852109)Peak memory usage: 13 MB
% 0.98/0.65 % (2852109)Instructions burned: 66 (million)
% 0.98/0.65 % (2852087)Success in time 0.205 s
% 0.98/0.65 % Vampire exiting
%------------------------------------------------------------------------------