%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT020-1 : 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 : n004.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 4.11s 1.54s
% Output : Refutation 5.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 66 ( 18 unt; 6 def)
% Number of atoms : 163 ( 10 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 186 ( 89 ~; 91 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 34 ( 0 sgn 34 !; 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] :
( 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(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,
! [X0] :
( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X0,hAPP(v_x,X0)),tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Otrans(v_F(X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X0,hAPP(v_x,X0)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(X0,hAPP(v_x,X0)),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f782,negated_conjecture,
! [X0] :
( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X0,hAPP(v_x,X0)),tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Oirrefl(v_F(X0),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X0,hAPP(v_x,X0)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(X0,hAPP(v_x,X0)),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(f893,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,[],[f779,f765]) ).
fof(f897,definition,
( spl0_1
<=> c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f898,plain,
( ~ c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_1 ),
inference(avatar_component_clause,[],[f897]) ).
fof(f900,definition,
( spl0_2
<=> ! [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))) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f901,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_2 ),
inference(avatar_component_clause,[],[f900]) ).
fof(f903,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f893,f900,f897]) ).
fof(f904,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(f907,definition,
( spl0_3
<=> ! [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_3])],[avatar_definition]) ).
fof(f908,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_3 ),
inference(avatar_component_clause,[],[f907]) ).
fof(f910,definition,
( spl0_4
<=> v_a = v_b ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f911,plain,
( v_a = v_b
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f910]) ).
fof(f913,definition,
( spl0_5
<=> 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_5])],[avatar_definition]) ).
fof(f914,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_5 ),
inference(avatar_component_clause,[],[f913]) ).
fof(f915,plain,
( spl0_3
| spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f904,f913,f910,f907]) ).
fof(f951,plain,
( c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[],[f781,f778]) ).
fof(f971,plain,
( ~ c_Relation_Oirrefl(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f951,f898]) ).
fof(f972,plain,
( ~ c_Relation_Otrans(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f971,f777]) ).
fof(f973,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f972,f776]) ).
fof(f974,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f973]) ).
fof(f978,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_3 ),
inference(resolution,[],[f908,f778]) ).
fof(f979,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_3 ),
inference(forward_subsumption_resolution,[],[f978,f771]) ).
fof(f980,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f979,f771]) ).
fof(f981,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f980]) ).
fof(f992,definition,
( spl0_6
<=> hBOOL(c_in(c_Pair(v_b,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))) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f993,plain,
( hBOOL(c_in(c_Pair(v_b,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_6 ),
inference(avatar_component_clause,[],[f992]) ).
fof(f995,plain,
( c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(resolution,[],[f782,f778]) ).
fof(f1015,plain,
( c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(forward_subsumption_resolution,[],[f995,f777]) ).
fof(f1016,plain,
c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
inference(forward_subsumption_resolution,[],[f1015,f776]) ).
fof(f1021,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_4 ),
inference(superposition,[],[f779,f911]) ).
fof(f1058,plain,
( ~ c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_4 ),
inference(resolution,[],[f1021,f767]) ).
fof(f1062,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f1058,f1016]) ).
fof(f1063,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f1062]) ).
fof(f1089,plain,
( hBOOL(c_in(c_Pair(v_b,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)))
| v_a = v_b
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_Pa(v_P)),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)
| ~ spl0_5 ),
inference(resolution,[],[f914,f784]) ).
fof(f1095,plain,
( hBOOL(c_in(c_Pair(v_b,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)))
| v_a = v_b
| ~ 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)
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f1089,f778]) ).
fof(f1096,plain,
( hBOOL(c_in(c_Pair(v_b,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)))
| v_a = v_b
| ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f1095,f777]) ).
fof(f1097,plain,
( hBOOL(c_in(c_Pair(v_b,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)))
| v_a = v_b
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f1096,f776]) ).
fof(f1098,plain,
( spl0_4
| spl0_6
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f1097,f913,f992,f910]) ).
fof(f1125,plain,
( hBOOL(c_in(c_Pair(v_b,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_2
| ~ spl0_6 ),
inference(resolution,[],[f993,f901]) ).
fof(f1135,plain,
( ~ c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_2
| ~ spl0_6 ),
inference(resolution,[],[f1125,f767]) ).
fof(f1139,plain,
( $false
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f1135,f1016]) ).
fof(f1140,plain,
( ~ spl0_2
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f1139]) ).
cnf(s2,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f903]) ).
cnf(s3,plain,
( spl0_3
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f915]) ).
cnf(s4,plain,
spl0_1,
inference(sat_conversion,[],[f974]) ).
cnf(s5,plain,
~ spl0_3,
inference(sat_conversion,[],[f981]) ).
cnf(s8,plain,
~ spl0_4,
inference(sat_conversion,[],[f1063]) ).
cnf(s10,plain,
( spl0_4
| ~ spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f1098]) ).
cnf(s12,plain,
( ~ spl0_2
| ~ spl0_6 ),
inference(sat_conversion,[],[f1140]) ).
cnf(s14,plain,
spl0_5,
inference(rat,[],[s3,s8,s5]) ).
cnf(s16,plain,
spl0_6,
inference(rat,[],[s10,s8,s14]) ).
cnf(s17,plain,
~ spl0_2,
inference(rat,[],[s12,s16]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s2,s17,s4]) ).
fof(f1141,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT020-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n004.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 23:29:52 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 4.11/1.54 % (4001844)Input is clausal, will run a generic CNF schedule.
% 4.11/1.54 % (4001849)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=1584081115:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.11/1.54 % (4001851)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1189119863:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.11/1.54 % (4001853)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3805524206:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.11/1.54 % (4001850)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=279512211:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.11/1.54 % (4001852)lrs+10_1_sil=8000:sp=occurrence:random_seed=735573725:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.11/1.54 % (4001855)dis-21_1_sil=8000:lcm=predicate:random_seed=2505066203: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)
% 4.11/1.54 % (4001854)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4065984432:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.11/1.54 % (4001855)Instruction limit reached!
% 4.11/1.54 % (4001855)------------------------------
% 4.11/1.54 % (4001855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.54 % (4001855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.54 % (4001855)CaDiCaL version: 2.1.3
% 4.11/1.54 % (4001855)Termination reason: Instruction limit
% 4.11/1.54 % (4001855)Termination phase: Saturation
% 4.11/1.54 % (4001855)Time elapsed: 0.047 s
% 4.11/1.54 % (4001855)Peak memory usage: 89 MB
% 4.11/1.54 % (4001855)Instructions burned: 119 (million)
% 4.11/1.54 % (4001852)Instruction limit reached!
% 4.11/1.54 % (4001852)------------------------------
% 4.11/1.54 % (4001852)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.54 % (4001852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.54 % (4001852)CaDiCaL version: 2.1.3
% 4.11/1.54 % (4001852)Termination reason: Instruction limit
% 4.11/1.54 % (4001852)Termination phase: Saturation
% 4.11/1.54 % (4001852)Time elapsed: 0.072 s
% 4.11/1.54 % (4001852)Peak memory usage: 89 MB
% 4.11/1.54 % (4001852)Instructions burned: 107 (million)
% 4.11/1.54 % (4001853)Instruction limit reached!
% 4.11/1.54 % (4001853)------------------------------
% 4.11/1.54 % (4001853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.54 % (4001853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.54 % (4001853)CaDiCaL version: 2.1.3
% 4.11/1.54 % (4001853)Termination reason: Instruction limit
% 4.11/1.54 % (4001853)Termination phase: Saturation
% 4.11/1.54 % (4001853)Time elapsed: 0.074 s
% 4.11/1.54 % (4001853)Peak memory usage: 89 MB
% 4.11/1.54 % (4001853)Instructions burned: 115 (million)
% 4.11/1.54 % (4001854)Instruction limit reached!
% 4.11/1.54 % (4001854)------------------------------
% 4.11/1.54 % (4001854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.54 % (4001854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.54 % (4001854)CaDiCaL version: 2.1.3
% 4.11/1.54 % (4001854)Termination reason: Instruction limit
% 4.11/1.54 % (4001854)Termination phase: Saturation
% 4.11/1.54 % (4001854)Time elapsed: 0.115 s
% 4.11/1.54 % (4001854)Peak memory usage: 89 MB
% 4.11/1.54 % (4001854)Instructions burned: 180 (million)
% 4.11/1.54 % (4001863)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=3362279429:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.11/1.54 % (4001865)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3234219668:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.11/1.54 % (4001864)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=539471165: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)
% 4.11/1.54 % (4001863)First to succeed.
% 4.11/1.54 % (4001863)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4001844"
% 4.11/1.54 % (4001866)lrs+10_64_to=lpo:sil=8000:random_seed=1916402867:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 4.11/1.54 % (4001864)Instruction limit reached!
% 4.11/1.54 % (4001864)------------------------------
% 4.11/1.54 % (4001864)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.54 % (4001864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.54 % (4001864)CaDiCaL version: 2.1.3
% 4.11/1.54 % (4001864)Termination reason: Instruction limit
% 4.11/1.54 % (4001864)Termination phase: Saturation
% 4.11/1.54 % (4001864)Time elapsed: 0.104 s
% 4.11/1.54 % (4001864)Peak memory usage: 91 MB
% 4.11/1.54 % (4001864)Instructions burned: 191 (million)
% 4.11/1.54 % (4001866)Instruction limit reached!
% 4.11/1.54 % (4001866)------------------------------
% 4.11/1.54 % (4001866)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.54 % (4001866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.54 % (4001866)CaDiCaL version: 2.1.3
% 4.11/1.54 % (4001866)Termination reason: Instruction limit
% 4.11/1.54 % (4001866)Termination phase: Saturation
% 4.11/1.54 % (4001866)Time elapsed: 0.069 s
% 4.11/1.54 % (4001866)Peak memory usage: 90 MB
% 4.11/1.54 % (4001866)Instructions burned: 126 (million)
% 4.11/1.54 % (4001865)Instruction limit reached!
% 4.11/1.54 % (4001865)------------------------------
% 4.11/1.54 % (4001865)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.54 % (4001865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.54 % (4001865)CaDiCaL version: 2.1.3
% 4.11/1.54 % (4001865)Termination reason: Instruction limit
% 4.11/1.54 % (4001865)Termination phase: Saturation
% 4.11/1.54 % (4001865)Time elapsed: 0.129 s
% 4.11/1.54 % (4001865)Peak memory usage: 91 MB
% 4.11/1.54 % (4001865)Instructions burned: 220 (million)
% 4.11/1.54 % (4001863)Refutation found. Thanks to Tanya!
% 4.11/1.54 % SZS status Unsatisfiable for theBenchmark
% 4.11/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 5.26/1.74 % (4001863)------------------------------
% 5.26/1.74 % (4001863)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.26/1.74 % (4001863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.26/1.74 % (4001863)CaDiCaL version: 2.1.3
% 5.26/1.74 % (4001863)Termination reason: Refutation
% 5.26/1.74 % (4001863)Time elapsed: 0.034 s
% 5.26/1.74 % (4001863)Peak memory usage: 90 MB
% 5.26/1.74 % (4001863)Instructions burned: 52 (million)
% 5.26/1.74 % (4001863)------------------------------
% 5.26/1.74 % (4001863)------------------------------
% 5.26/1.74 % (4001844)Success in time 0.686 s
% 5.26/1.74 % Vampire exiting
%------------------------------------------------------------------------------