%------------------------------------------------------------------------------
% File : Vampire---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 THM
% 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 12:36:45 PM UTC 2026
% Result : Unsatisfiable 4.20s 1.51s
% Output : Refutation 5.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 27
% Syntax : Number of formulae : 99 ( 28 unt; 13 def)
% Number of atoms : 241 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 260 ( 118 ~; 129 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 14 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-4 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f766,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_transD_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] :
( hBOOL(c_in(c_Pair(X1,X0,X2,X2),X3,tc_prod(X2,X2)))
| hBOOL(c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)))
| X0 = X1
| ~ hBOOL(c_in(X0,X4,X2))
| ~ hBOOL(c_in(X1,X4,X2))
| ~ c_Relation_Ototal__on(X4,X3,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(f812,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(f813,plain,
( ~ c_Relation_Otrans(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_1 ),
inference(avatar_component_clause,[],[f812]) ).
fof(f815,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(f816,plain,
( ~ c_Relation_Oirrefl(hAPP(v_P,v_xa),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_2 ),
inference(avatar_component_clause,[],[f815]) ).
fof(f818,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(f819,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,[],[f818]) ).
fof(f821,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(f822,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,[],[f821]) ).
fof(f823,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f784,f821,f818,f815,f812]) ).
fof(f825,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(f826,plain,
( ~ c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_5 ),
inference(avatar_component_clause,[],[f825]) ).
fof(f828,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(f829,plain,
( ~ c_Relation_Oirrefl(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_6 ),
inference(avatar_component_clause,[],[f828]) ).
fof(f831,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(f832,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,[],[f831]) ).
fof(f838,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(f839,plain,
( c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f838]) ).
fof(f840,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| spl0_9 ),
inference(avatar_split_clause,[],[f782,f838,f831,f828,f825]) ).
fof(f842,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(f843,plain,
( c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f842]) ).
fof(f844,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| spl0_10 ),
inference(avatar_split_clause,[],[f781,f842,f831,f828,f825]) ).
fof(f845,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f826,f776]) ).
fof(f846,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f845]) ).
fof(f847,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f829,f777]) ).
fof(f848,plain,
spl0_6,
inference(avatar_contradiction_clause,[],[f847]) ).
fof(f852,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f819,f778]) ).
fof(f853,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f852]) ).
fof(f854,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f813,f776]) ).
fof(f855,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f854]) ).
fof(f856,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f816,f777]) ).
fof(f857,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f856]) ).
fof(f860,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,[],[f822,f774]) ).
fof(f862,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f832,f778]) ).
fof(f863,plain,
spl0_7,
inference(avatar_contradiction_clause,[],[f862]) ).
fof(f869,plain,
( ! [X2,X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X2,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(X2,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)))
| ~ c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_4 ),
inference(resolution,[],[f860,f766]) ).
fof(f871,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(c_in(c_Pair(X2,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)))
| ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X2,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 )
| ~ spl0_4
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f869,f843]) ).
fof(f884,plain,
! [X0] :
( 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
| ~ hBOOL(c_in(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Ototal__on(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[],[f780,f773]) ).
fof(f887,definition,
( spl0_11
<=> ! [X0] :
( ~ hBOOL(c_in(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Relation_Ototal__on(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f888,plain,
( ! [X0] :
( ~ c_Relation_Ototal__on(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt))
| ~ hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt)) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f887]) ).
fof(f890,definition,
( spl0_12
<=> v_a = v_b ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f891,plain,
( v_a = v_b
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f890]) ).
fof(f893,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(f894,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,[],[f893]) ).
fof(f895,plain,
( spl0_11
| spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f884,f893,f890,f887]) ).
fof(f898,plain,
( hBOOL(c_in(c_Pair(v_a,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)))
| ~ spl0_12 ),
inference(superposition,[],[f779,f891]) ).
fof(f902,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)))
| ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| v_b = X0 )
| ~ spl0_4
| ~ spl0_10 ),
inference(resolution,[],[f871,f779]) ).
fof(f907,plain,
( ~ c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_12 ),
inference(resolution,[],[f898,f767]) ).
fof(f912,plain,
( $false
| ~ spl0_9
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f907,f839]) ).
fof(f913,plain,
( ~ spl0_9
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f912]) ).
fof(f914,plain,
( ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| v_a = v_b
| ~ c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_4
| ~ spl0_10 ),
inference(resolution,[],[f902,f767]) ).
fof(f921,plain,
( ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| v_a = v_b
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f914,f839]) ).
fof(f923,definition,
( spl0_14
<=> 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_14])],[avatar_definition]) ).
fof(f924,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_14 ),
inference(avatar_component_clause,[],[f923]) ).
fof(f925,plain,
( spl0_12
| ~ spl0_14
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f921,f842,f838,f821,f923,f890]) ).
fof(f929,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,[],[f894,f775]) ).
fof(f930,plain,
( $false
| ~ spl0_13
| spl0_14 ),
inference(forward_subsumption_resolution,[],[f929,f924]) ).
fof(f931,plain,
( ~ spl0_13
| spl0_14 ),
inference(avatar_contradiction_clause,[],[f930]) ).
fof(f939,plain,
( ~ hBOOL(c_in(v_b,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))
| ~ hBOOL(c_in(v_a,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_11 ),
inference(resolution,[],[f888,f778]) ).
fof(f940,plain,
( ~ hBOOL(c_in(v_b,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f939,f771]) ).
fof(f941,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f940,f771]) ).
fof(f942,plain,
~ spl0_11,
inference(avatar_contradiction_clause,[],[f941]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f823]) ).
cnf(s3,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f840]) ).
cnf(s4,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f844]) ).
cnf(s5,plain,
spl0_5,
inference(sat_conversion,[],[f846]) ).
cnf(s6,plain,
spl0_6,
inference(sat_conversion,[],[f848]) ).
cnf(s7,plain,
spl0_3,
inference(sat_conversion,[],[f853]) ).
cnf(s8,plain,
spl0_1,
inference(sat_conversion,[],[f855]) ).
cnf(s9,plain,
spl0_2,
inference(sat_conversion,[],[f857]) ).
cnf(s10,plain,
spl0_7,
inference(sat_conversion,[],[f863]) ).
cnf(s11,plain,
( spl0_11
| spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f895]) ).
cnf(s12,plain,
( ~ spl0_9
| ~ spl0_12 ),
inference(sat_conversion,[],[f913]) ).
cnf(s13,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| spl0_12
| ~ spl0_14 ),
inference(sat_conversion,[],[f925]) ).
cnf(s14,plain,
( ~ spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f931]) ).
cnf(s16,plain,
~ spl0_11,
inference(sat_conversion,[],[f942]) ).
cnf(s17,plain,
( spl0_12
| spl0_13 ),
inference(rat,[],[s11,s16]) ).
cnf(s18,plain,
spl0_10,
inference(rat,[],[s4,s10,s6,s5]) ).
cnf(s19,plain,
spl0_9,
inference(rat,[],[s3,s10,s6,s5]) ).
cnf(s20,plain,
~ spl0_12,
inference(rat,[],[s12,s19]) ).
cnf(s21,plain,
spl0_13,
inference(rat,[],[s17,s20]) ).
cnf(s22,plain,
spl0_14,
inference(rat,[],[s14,s21]) ).
cnf(s23,plain,
~ spl0_4,
inference(rat,[],[s13,s20,s19,s18,s22]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s1,s23,s7,s9,s8]) ).
fof(f943,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT022-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n018.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 23:32:39 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 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
% 4.20/1.51 % (2852899)Input is clausal, will run a generic CNF schedule.
% 4.20/1.51 % (2852906)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2293002939:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.20/1.51 % (2852909)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2793818804:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.20/1.51 % (2852907)lrs+10_1_sil=8000:sp=occurrence:random_seed=453256504:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.20/1.51 % (2852910)dis-21_1_sil=8000:lcm=predicate:random_seed=2710540850:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 4.20/1.51 % (2852904)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=2929081655:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.20/1.51 % (2852905)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1684138788:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.20/1.51 % (2852908)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=529201813:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.20/1.51 % (2852910)Instruction limit reached!
% 4.20/1.51 % (2852910)------------------------------
% 4.20/1.51 % (2852910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.20/1.51 % (2852910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.51 % (2852910)CaDiCaL version: 2.1.3
% 4.20/1.51 % (2852910)Termination reason: Instruction limit
% 4.20/1.51 % (2852910)Termination phase: Saturation
% 4.20/1.51 % (2852910)Time elapsed: 0.047 s
% 4.20/1.51 % (2852910)Peak memory usage: 89 MB
% 4.20/1.51 % (2852910)Instructions burned: 119 (million)
% 4.20/1.51 % (2852909)Instruction limit reached!
% 4.20/1.51 % (2852909)------------------------------
% 4.20/1.51 % (2852909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.20/1.51 % (2852909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.51 % (2852909)CaDiCaL version: 2.1.3
% 4.20/1.51 % (2852909)Termination reason: Instruction limit
% 4.20/1.51 % (2852909)Termination phase: Saturation
% 4.20/1.51 % (2852909)Time elapsed: 0.061 s
% 4.20/1.51 % (2852909)Peak memory usage: 90 MB
% 4.20/1.51 % (2852909)Instructions burned: 182 (million)
% 4.20/1.51 % (2852908)Instruction limit reached!
% 4.20/1.51 % (2852908)------------------------------
% 4.20/1.51 % (2852908)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.20/1.51 % (2852908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.51 % (2852908)CaDiCaL version: 2.1.3
% 4.20/1.51 % (2852908)Termination reason: Instruction limit
% 4.20/1.51 % (2852908)Termination phase: Saturation
% 4.20/1.51 % (2852908)Time elapsed: 0.071 s
% 4.20/1.51 % (2852908)Peak memory usage: 89 MB
% 4.20/1.51 % (2852908)Instructions burned: 115 (million)
% 4.20/1.51 % (2852907)Instruction limit reached!
% 4.20/1.51 % (2852907)------------------------------
% 4.20/1.51 % (2852907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.20/1.51 % (2852907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.51 % (2852907)CaDiCaL version: 2.1.3
% 4.20/1.51 % (2852907)Termination reason: Instruction limit
% 4.20/1.51 % (2852907)Termination phase: Saturation
% 4.20/1.51 % (2852907)Time elapsed: 0.074 s
% 4.20/1.51 % (2852907)Peak memory usage: 90 MB
% 4.20/1.51 % (2852907)Instructions burned: 108 (million)
% 4.20/1.51 % (2852919)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2709277158:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 4.20/1.51 % (2852918)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1368400595:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.20/1.51 % (2852918)First to succeed.
% 4.20/1.51 % (2852918)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2852899"
% 4.20/1.51 % (2852919)Instruction limit reached!
% 4.20/1.51 % (2852919)------------------------------
% 4.20/1.51 % (2852919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.20/1.51 % (2852919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.51 % (2852919)CaDiCaL version: 2.1.3
% 4.20/1.51 % (2852919)Termination reason: Instruction limit
% 4.20/1.51 % (2852919)Termination phase: Saturation
% 4.20/1.51 % (2852919)Time elapsed: 0.059 s
% 4.20/1.51 % (2852919)Peak memory usage: 91 MB
% 4.20/1.51 % (2852919)Instructions burned: 190 (million)
% 4.20/1.51 % (2852920)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2899343108:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.20/1.51 % (2852921)lrs+10_64_to=lpo:sil=8000:random_seed=1000348020:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 4.20/1.51 % (2852921)Instruction limit reached!
% 4.20/1.51 % (2852921)------------------------------
% 4.20/1.51 % (2852921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.20/1.51 % (2852921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.51 % (2852921)CaDiCaL version: 2.1.3
% 4.20/1.51 % (2852921)Termination reason: Instruction limit
% 4.20/1.51 % (2852921)Termination phase: Saturation
% 4.20/1.51 % (2852921)Time elapsed: 0.085 s
% 4.20/1.51 % (2852921)Peak memory usage: 90 MB
% 4.20/1.51 % (2852921)Instructions burned: 127 (million)
% 4.20/1.51 % (2852925)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3704648711:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 4.20/1.51 % (2852920)Instruction limit reached!
% 4.20/1.51 % (2852920)------------------------------
% 4.20/1.51 % (2852920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.20/1.51 % (2852920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.51 % (2852920)CaDiCaL version: 2.1.3
% 4.20/1.51 % (2852920)Termination reason: Instruction limit
% 4.20/1.51 % (2852920)Termination phase: Saturation
% 4.20/1.51 % (2852920)Time elapsed: 0.134 s
% 4.20/1.51 % (2852920)Peak memory usage: 91 MB
% 4.20/1.51 % (2852920)Instructions burned: 220 (million)
% 4.20/1.51 % (2852925)Instruction limit reached!
% 4.20/1.51 % (2852925)------------------------------
% 4.20/1.51 % (2852925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.20/1.51 % (2852925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.51 % (2852925)CaDiCaL version: 2.1.3
% 4.20/1.51 % (2852925)Termination reason: Instruction limit
% 4.20/1.51 % (2852925)Termination phase: Saturation
% 4.20/1.51 % (2852925)Time elapsed: 0.066 s
% 4.20/1.51 % (2852925)Peak memory usage: 91 MB
% 4.20/1.51 % (2852925)Instructions burned: 197 (million)
% 4.20/1.51 % (2852918)Refutation found. Thanks to Tanya!
% 4.20/1.51 % SZS status Unsatisfiable for theBenchmark
% 4.20/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 5.02/1.61 % (2852918)------------------------------
% 5.02/1.61 % (2852918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.02/1.61 % (2852918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.02/1.61 % (2852918)CaDiCaL version: 2.1.3
% 5.02/1.61 % (2852918)Termination reason: Refutation
% 5.02/1.61 % (2852918)Time elapsed: 0.020 s
% 5.02/1.61 % (2852918)Peak memory usage: 90 MB
% 5.02/1.61 % (2852918)Instructions burned: 29 (million)
% 5.02/1.61 % (2852918)------------------------------
% 5.02/1.61 % (2852918)------------------------------
% 5.02/1.61 % (2852899)Success in time 0.663 s
% 5.02/1.61 % Vampire exiting
%------------------------------------------------------------------------------