%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SCT022-1 : 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 : n013.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 1.07s 0.65s
% Output : Refutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 26
% Syntax : Number of formulae : 96 ( 27 unt; 12 def)
% Number of atoms : 232 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 241 ( 105 ~; 124 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 8 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,
! [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)))
| ~ hBOOL(c_in(c_Pair(X0,X1,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)))
| X0 = X1
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(v_P,v_xa),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_xa),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f879,plain,
( ~ c_Relation_Otrans(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_1 ),
inference(avatar_component_clause,[],[f877]) ).
fof(f881,definition,
( spl0_2
<=> c_Relation_Oirrefl(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f883,plain,
( ~ c_Relation_Oirrefl(hAPP(v_P,v_xa),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_xa),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_xa),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_3 ),
inference(avatar_component_clause,[],[f885]) ).
fof(f889,definition,
( spl0_4
<=> ! [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(c_in(c_Pair(X0,X1,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_4])],[avatar_definition]) ).
fof(f890,plain,
( ! [X0,X1] :
( ~ hBOOL(c_in(c_Pair(X0,X1,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)))
| 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))) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f889]) ).
fof(f891,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f784,f889,f885,f881,f877]) ).
fof(f893,definition,
( spl0_5
<=> c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f895,plain,
( ~ c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_5 ),
inference(avatar_component_clause,[],[f893]) ).
fof(f897,definition,
( spl0_6
<=> c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f899,plain,
( ~ c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_6 ),
inference(avatar_component_clause,[],[f897]) ).
fof(f901,definition,
( spl0_7
<=> 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_7])],[avatar_definition]) ).
fof(f903,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_7 ),
inference(avatar_component_clause,[],[f901]) ).
fof(f910,definition,
( spl0_9
<=> c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f912,plain,
( c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f910]) ).
fof(f913,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| spl0_9 ),
inference(avatar_split_clause,[],[f782,f910,f901,f897,f893]) ).
fof(f915,definition,
( spl0_10
<=> c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f917,plain,
( c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f915]) ).
fof(f918,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| spl0_10 ),
inference(avatar_split_clause,[],[f781,f915,f901,f897,f893]) ).
fof(f919,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f895,f776]) ).
fof(f920,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f919]) ).
fof(f921,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f899,f777]) ).
fof(f922,plain,
spl0_6,
inference(avatar_contradiction_clause,[],[f921]) ).
fof(f923,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f887,f778]) ).
fof(f924,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f923]) ).
fof(f925,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f879,f776]) ).
fof(f926,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f925]) ).
fof(f927,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f883,f777]) ).
fof(f928,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f927]) ).
fof(f929,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f903,f778]) ).
fof(f930,plain,
spl0_7,
inference(avatar_contradiction_clause,[],[f929]) ).
fof(f933,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))) )
| ~ spl0_4 ),
inference(resolution,[],[f774,f890]) ).
fof(f934,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(f956,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,c_Pair(X2,X2,X1,X1)))
| ~ c_Relation_Oirrefl(X0,X1) ),
inference(resolution,[],[f767,f774]) ).
fof(f997,plain,
( ! [X2,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)))
| ~ hBOOL(c_in(c_Pair(X0,X2,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)
| X1 = X2
| ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_4 ),
inference(resolution,[],[f765,f933]) ).
fof(f1000,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(c_Pair(X0,X2,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,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)))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_4
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f997,f917]) ).
fof(f1015,definition,
( spl0_11
<=> 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_11])],[avatar_definition]) ).
fof(f1017,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_11 ),
inference(avatar_component_clause,[],[f1015]) ).
fof(f1019,definition,
( spl0_12
<=> v_a = v_b ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f1021,plain,
( v_a = v_b
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f1019]) ).
fof(f1030,plain,
( ! [X0] :
( hBOOL(c_in(c_Pair(v_a,X0,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_b = X0
| ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
| ~ spl0_4
| ~ spl0_10 ),
inference(resolution,[],[f1000,f779]) ).
fof(f1038,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_4
| ~ spl0_10 ),
inference(resolution,[],[f1030,f767]) ).
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)))
| 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(f1118,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,[],[f1112,f771]) ).
fof(f1120,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,[],[f1118,f771]) ).
fof(f1188,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,[],[f1120,f780]) ).
fof(f1203,definition,
( spl0_13
<=> 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_13])],[avatar_definition]) ).
fof(f1205,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_13 ),
inference(avatar_component_clause,[],[f1203]) ).
fof(f1208,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f1188,f1203,f1019]) ).
fof(f1209,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_4
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f1038,f912]) ).
fof(f1210,plain,
( ~ spl0_11
| spl0_12
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f1209,f915,f910,f889,f1019,f1015]) ).
fof(f1214,plain,
( hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ spl0_12 ),
inference(superposition,[],[f934,f1021]) ).
fof(f1227,plain,
( ~ c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_12 ),
inference(resolution,[],[f1214,f956]) ).
fof(f1228,plain,
( $false
| ~ spl0_9
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f1227,f912]) ).
fof(f1229,plain,
( ~ spl0_9
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f1228]) ).
fof(f1239,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_13 ),
inference(resolution,[],[f1205,f775]) ).
fof(f1240,plain,
( $false
| spl0_11
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1239,f1017]) ).
fof(f1241,plain,
( spl0_11
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f1240]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f891]) ).
cnf(s3,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f913]) ).
cnf(s4,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f918]) ).
cnf(s5,plain,
spl0_5,
inference(sat_conversion,[],[f920]) ).
cnf(s6,plain,
spl0_6,
inference(sat_conversion,[],[f922]) ).
cnf(s7,plain,
spl0_3,
inference(sat_conversion,[],[f924]) ).
cnf(s8,plain,
spl0_1,
inference(sat_conversion,[],[f926]) ).
cnf(s9,plain,
spl0_2,
inference(sat_conversion,[],[f928]) ).
cnf(s10,plain,
spl0_7,
inference(sat_conversion,[],[f930]) ).
cnf(s13,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f1208]) ).
cnf(s14,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f1210]) ).
cnf(s15,plain,
( ~ spl0_9
| ~ spl0_12 ),
inference(sat_conversion,[],[f1229]) ).
cnf(s16,plain,
( spl0_11
| ~ spl0_13 ),
inference(sat_conversion,[],[f1241]) ).
cnf(s17,plain,
spl0_10,
inference(rat,[],[s4,s10,s6,s5]) ).
cnf(s18,plain,
spl0_9,
inference(rat,[],[s3,s10,s6,s5]) ).
cnf(s19,plain,
~ spl0_12,
inference(rat,[],[s15,s18]) ).
cnf(s20,plain,
spl0_13,
inference(rat,[],[s13,s19]) ).
cnf(s21,plain,
spl0_11,
inference(rat,[],[s16,s20]) ).
cnf(s22,plain,
~ spl0_4,
inference(rat,[],[s14,s19,s18,s17,s21]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s1,s22,s7,s9,s8]) ).
fof(f1244,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT022-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 23:29:52 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 1.07/0.65 % (663915)Will run a generic schedule for satisfiability detection.
% 1.07/0.65 % (663920)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3007363776_2999 on theBenchmark for (2999ds/0Mi)
% 1.07/0.65 % (663921)% WARNING: option uhcvi not known.
% 1.07/0.65 % (663921)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2347440584:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.07/0.65 % (663922)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1611227654:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.07/0.65 % (663923)dis+10_1_sil=32000:sp=arity:random_seed=3807135332:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.07/0.65 % (663924)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3136373523:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.07/0.65 % (663925)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2362848044:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.07/0.65 % (663926)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2364031006:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.07/0.65 % (663923)Instruction limit reached!
% 1.07/0.65 % (663923)------------------------------
% 1.07/0.65 % (663923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.65 % (663923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.65 % (663923)CaDiCaL version: 2.1.3
% 1.07/0.65 % (663923)Termination reason: Instruction limit
% 1.07/0.65 % (663923)Termination phase: Saturation
% 1.07/0.65 % (663923)Time elapsed: 0.066 s
% 1.07/0.65 % (663923)Peak memory usage: 12 MB
% 1.07/0.65 % (663923)Instructions burned: 104 (million)
% 1.07/0.65 % (663924)Instruction limit reached!
% 1.07/0.65 % (663924)------------------------------
% 1.07/0.65 % (663924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.65 % (663924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.65 % (663924)CaDiCaL version: 2.1.3
% 1.07/0.65 % (663924)Termination reason: Instruction limit
% 1.07/0.65 % (663924)Termination phase: Saturation
% 1.07/0.65 % (663924)Time elapsed: 0.071 s
% 1.07/0.65 % (663924)Peak memory usage: 13 MB
% 1.07/0.65 % (663924)Instructions burned: 116 (million)
% 1.07/0.65 % (663934)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2614741819:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 1.07/0.65 % (663935)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3042768798:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.07/0.65 % (663925)Instruction limit reached!
% 1.07/0.65 % (663925)------------------------------
% 1.07/0.65 % (663925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.65 % (663925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.65 % (663925)CaDiCaL version: 2.1.3
% 1.07/0.65 % (663925)Termination reason: Instruction limit
% 1.07/0.65 % (663925)Termination phase: Saturation
% 1.07/0.65 % (663925)Time elapsed: 0.091 s
% 1.07/0.65 % (663925)Peak memory usage: 14 MB
% 1.07/0.65 % (663925)Instructions burned: 132 (million)
% 1.07/0.65 % (663926)Instruction limit reached!
% 1.07/0.65 % (663926)------------------------------
% 1.07/0.65 % (663926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.65 % (663926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.65 % (663926)CaDiCaL version: 2.1.3
% 1.07/0.65 % (663926)Termination reason: Instruction limit
% 1.07/0.65 % (663926)Termination phase: Saturation
% 1.07/0.65 % (663926)Time elapsed: 0.102 s
% 1.07/0.65 % (663926)Peak memory usage: 13 MB
% 1.07/0.65 % (663926)Instructions burned: 160 (million)
% 1.07/0.65 % TRYING [1]
% 1.07/0.65 % (663938)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=200644228:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.07/0.65 % TRYING [2]
% 1.07/0.65 % (663939)ott-21_1_sil=16000:fs=off:random_seed=4286298004:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.07/0.65 % (663938) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-663915-663938"...
% 1.07/0.65 % (663938)...printing done.
% 1.07/0.65 % (663938)Refutation found. Thanks to Tanya!
% 1.07/0.65 % SZS status Unsatisfiable for theBenchmark
% 1.07/0.65 % SZS output start Proof for theBenchmark
% See solution above
% 1.07/0.65 % (663938)------------------------------
% 1.07/0.65 % (663938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.65 % (663938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.65 % (663938)CaDiCaL version: 2.1.3
% 1.07/0.65 % (663938)Termination reason: Refutation
% 1.07/0.65 % (663938)Time elapsed: 0.041 s
% 1.07/0.65 % (663938)Peak memory usage: 13 MB
% 1.07/0.65 % (663938)Instructions burned: 70 (million)
% 1.07/0.65 % (663915)Success in time 0.221 s
% 1.07/0.65 % Vampire exiting
%------------------------------------------------------------------------------