%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n006.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 4.17s 1.28s
% Output : Refutation 4.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 23
% Syntax : Number of formulae : 82 ( 21 unt; 9 def)
% Number of atoms : 209 ( 13 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 238 ( 111 ~; 118 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 10 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 44 ( 0 sgn 44 !; 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,
! [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(f812,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(f813,plain,
( ~ c_Relation_Otrans(hAPP(v_P,v_x),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_1 ),
inference(avatar_component_clause,[],[f812]) ).
fof(f815,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(f816,plain,
( ~ c_Relation_Oirrefl(hAPP(v_P,v_x),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_x),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_x),tc_Arrow__Order__Mirabelle_Oalt)
| spl0_3 ),
inference(avatar_component_clause,[],[f818]) ).
fof(f825,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(f826,plain,
( c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f825]) ).
fof(f827,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f782,f825,f818,f815,f812]) ).
fof(f829,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(f830,plain,
( c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f829]) ).
fof(f831,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f781,f829,f818,f815,f812]) ).
fof(f840,plain,
! [X2,X0,X1] :
( 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)
| ~ hBOOL(hAPP(hAPP(X2,v_i),c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(resolution,[],[f784,f774]) ).
fof(f904,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f813,f776]) ).
fof(f905,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f904]) ).
fof(f906,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f816,f777]) ).
fof(f907,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f906]) ).
fof(f915,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f819,f778]) ).
fof(f916,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f915]) ).
fof(f959,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,f766]) ).
fof(f961,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,[],[f959,f830]) ).
fof(f966,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(f969,definition,
( spl0_7
<=> ! [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_7])],[avatar_definition]) ).
fof(f970,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_7 ),
inference(avatar_component_clause,[],[f969]) ).
fof(f972,definition,
( spl0_8
<=> v_a = v_b ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f973,plain,
( v_a = v_b
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f972]) ).
fof(f975,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(f976,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,[],[f975]) ).
fof(f977,plain,
( spl0_7
| spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f966,f975,f972,f969]) ).
fof(f980,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_8 ),
inference(superposition,[],[f779,f973]) ).
fof(f987,plain,
( ~ c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_8 ),
inference(resolution,[],[f980,f767]) ).
fof(f991,plain,
( $false
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f987,f826]) ).
fof(f992,plain,
( ~ spl0_5
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f991]) ).
fof(f996,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,[],[f976,f775]) ).
fof(f1006,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
| ~ 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)
| ~ 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,[],[f961,f840]) ).
fof(f1009,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
| ~ 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)
| ~ 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(forward_subsumption_resolution,[],[f1006,f778]) ).
fof(f1010,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
| ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ 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(forward_subsumption_resolution,[],[f1009,f777]) ).
fof(f1011,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(forward_subsumption_resolution,[],[f1010,f776]) ).
fof(f1012,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,[],[f1011,f767]) ).
fof(f1018,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,[],[f1012,f826]) ).
fof(f1020,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(f1021,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,[],[f1020]) ).
fof(f1022,plain,
( ~ spl0_11
| spl0_8
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f1018,f829,f825,f972,f1020]) ).
fof(f1028,plain,
( $false
| ~ spl0_9
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f1021,f996]) ).
fof(f1029,plain,
( ~ spl0_9
| spl0_11 ),
inference(avatar_contradiction_clause,[],[f1028]) ).
fof(f1031,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_7 ),
inference(resolution,[],[f970,f778]) ).
fof(f1032,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_7 ),
inference(forward_subsumption_resolution,[],[f1031,f771]) ).
fof(f1033,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f1032,f771]) ).
fof(f1034,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f1033]) ).
cnf(s2,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f827]) ).
cnf(s3,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f831]) ).
cnf(s4,plain,
spl0_1,
inference(sat_conversion,[],[f905]) ).
cnf(s5,plain,
spl0_2,
inference(sat_conversion,[],[f907]) ).
cnf(s6,plain,
spl0_3,
inference(sat_conversion,[],[f916]) ).
cnf(s7,plain,
( spl0_7
| spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f977]) ).
cnf(s8,plain,
( ~ spl0_5
| ~ spl0_8 ),
inference(sat_conversion,[],[f992]) ).
cnf(s10,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_8
| ~ spl0_11 ),
inference(sat_conversion,[],[f1022]) ).
cnf(s12,plain,
( ~ spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f1029]) ).
cnf(s13,plain,
~ spl0_7,
inference(sat_conversion,[],[f1034]) ).
cnf(s14,plain,
( spl0_8
| spl0_9 ),
inference(rat,[],[s7,s13]) ).
cnf(s15,plain,
spl0_6,
inference(rat,[],[s3,s6,s5,s4]) ).
cnf(s16,plain,
spl0_5,
inference(rat,[],[s2,s6,s5,s4]) ).
cnf(s17,plain,
~ spl0_8,
inference(rat,[],[s8,s16]) ).
cnf(s18,plain,
spl0_9,
inference(rat,[],[s14,s17]) ).
cnf(s19,plain,
~ spl0_11,
inference(rat,[],[s10,s16,s15,s17]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s12,s19,s18]) ).
fof(f1035,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT021-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 23:29:40 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 4.17/1.28 % (3446560)Input is clausal, will run a generic CNF schedule.
% 4.17/1.28 % (3446567)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=398183597:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.17/1.28 % (3446571)dis-21_1_sil=8000:lcm=predicate:random_seed=1123567714: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)
% 4.17/1.28 % (3446565)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=1578616616:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.17/1.28 % (3446568)lrs+10_1_sil=8000:sp=occurrence:random_seed=1914226441:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.17/1.28 % (3446569)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2694352638:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.17/1.28 % (3446570)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=608665742:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.17/1.28 % (3446566)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2414401334:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.17/1.28 % (3446571)Instruction limit reached!
% 4.17/1.28 % (3446571)------------------------------
% 4.17/1.28 % (3446571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.28 % (3446571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.28 % (3446571)CaDiCaL version: 2.1.3
% 4.17/1.28 % (3446571)Termination reason: Instruction limit
% 4.17/1.28 % (3446571)Termination phase: Saturation
% 4.17/1.28 % (3446571)Time elapsed: 0.047 s
% 4.17/1.28 % (3446571)Peak memory usage: 89 MB
% 4.17/1.28 % (3446571)Instructions burned: 117 (million)
% 4.17/1.28 % (3446568)Instruction limit reached!
% 4.17/1.28 % (3446568)------------------------------
% 4.17/1.28 % (3446568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.28 % (3446568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.28 % (3446568)CaDiCaL version: 2.1.3
% 4.17/1.28 % (3446568)Termination reason: Instruction limit
% 4.17/1.28 % (3446568)Termination phase: Saturation
% 4.17/1.28 % (3446568)Time elapsed: 0.072 s
% 4.17/1.28 % (3446568)Peak memory usage: 89 MB
% 4.17/1.28 % (3446568)Instructions burned: 107 (million)
% 4.17/1.28 % (3446569)Instruction limit reached!
% 4.17/1.28 % (3446569)------------------------------
% 4.17/1.28 % (3446569)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.28 % (3446569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.28 % (3446569)CaDiCaL version: 2.1.3
% 4.17/1.28 % (3446569)Termination reason: Instruction limit
% 4.17/1.28 % (3446569)Termination phase: Saturation
% 4.17/1.28 % (3446569)Time elapsed: 0.073 s
% 4.17/1.28 % (3446569)Peak memory usage: 89 MB
% 4.17/1.28 % (3446569)Instructions burned: 115 (million)
% 4.17/1.28 % (3446570)Instruction limit reached!
% 4.17/1.28 % (3446570)------------------------------
% 4.17/1.28 % (3446570)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.28 % (3446570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.28 % (3446570)CaDiCaL version: 2.1.3
% 4.17/1.28 % (3446570)Termination reason: Instruction limit
% 4.17/1.28 % (3446570)Termination phase: Saturation
% 4.17/1.28 % (3446570)Time elapsed: 0.123 s
% 4.17/1.28 % (3446570)Peak memory usage: 89 MB
% 4.17/1.28 % (3446570)Instructions burned: 180 (million)
% 4.17/1.28 % (3446579)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=412176029:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.17/1.28 % (3446580)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=667148147: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)
% 4.17/1.28 % (3446581)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=27986294:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.17/1.28 % (3446579)First to succeed.
% 4.17/1.28 % (3446579)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3446560"
% 4.17/1.28 % (3446582)lrs+10_64_to=lpo:sil=8000:random_seed=1850124529:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 4.17/1.28 % (3446580)Instruction limit reached!
% 4.17/1.28 % (3446580)------------------------------
% 4.17/1.28 % (3446580)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.28 % (3446580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.28 % (3446580)CaDiCaL version: 2.1.3
% 4.17/1.28 % (3446580)Termination reason: Instruction limit
% 4.17/1.28 % (3446580)Termination phase: Saturation
% 4.17/1.28 % (3446580)Time elapsed: 0.106 s
% 4.17/1.28 % (3446580)Peak memory usage: 91 MB
% 4.17/1.28 % (3446580)Instructions burned: 190 (million)
% 4.17/1.28 % (3446581)Instruction limit reached!
% 4.17/1.28 % (3446581)------------------------------
% 4.17/1.28 % (3446581)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.28 % (3446581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.28 % (3446581)CaDiCaL version: 2.1.3
% 4.17/1.28 % (3446581)Termination reason: Instruction limit
% 4.17/1.28 % (3446581)Termination phase: Saturation
% 4.17/1.28 % (3446581)Time elapsed: 0.121 s
% 4.17/1.28 % (3446581)Peak memory usage: 90 MB
% 4.17/1.28 % (3446581)Instructions burned: 220 (million)
% 4.17/1.28 % (3446582)Instruction limit reached!
% 4.17/1.28 % (3446582)------------------------------
% 4.17/1.28 % (3446582)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.28 % (3446582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.28 % (3446582)CaDiCaL version: 2.1.3
% 4.17/1.28 % (3446582)Termination reason: Instruction limit
% 4.17/1.28 % (3446582)Termination phase: Saturation
% 4.17/1.28 % (3446582)Time elapsed: 0.082 s
% 4.17/1.28 % (3446582)Peak memory usage: 90 MB
% 4.17/1.28 % (3446582)Instructions burned: 127 (million)
% 4.17/1.28 % (3446587)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1810252115:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 4.17/1.28 % (3446579)Refutation found. Thanks to Tanya!
% 4.17/1.28 % SZS status Unsatisfiable for theBenchmark
% 4.17/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 4.94/1.38 % (3446579)------------------------------
% 4.94/1.38 % (3446579)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.94/1.38 % (3446579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.94/1.38 % (3446579)CaDiCaL version: 2.1.3
% 4.94/1.38 % (3446579)Termination reason: Refutation
% 4.94/1.38 % (3446579)Time elapsed: 0.031 s
% 4.94/1.38 % (3446579)Peak memory usage: 90 MB
% 4.94/1.38 % (3446579)Instructions burned: 42 (million)
% 4.94/1.38 % (3446579)------------------------------
% 4.94/1.38 % (3446579)------------------------------
% 4.94/1.38 % (3446560)Success in time 0.675 s
% 4.94/1.38 % Vampire exiting
%------------------------------------------------------------------------------