%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU168+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 12:52:13 PM UTC 2026
% Result : Theorem 0.59s 0.46s
% Output : Refutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 147 ( 8 unt; 7 def)
% Number of atoms : 503 ( 2 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 624 ( 268 ~; 282 |; 52 &)
% ( 11 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 124 ( 0 sgn 105 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f7,conjecture,
! [X0] :
? [X1] :
( in(X0,X1)
& ! [X2,X3] :
( ( in(X2,X1)
& subset(X3,X2) )
=> in(X3,X1) )
& ! [X2] :
( in(X2,X1)
=> in(powerset(X2),X1) )
& ! [X2] :
~ ( subset(X2,X1)
& ~ are_equipotent(X2,X1)
& ~ in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0] :
? [X1] :
( in(X0,X1)
& ! [X2,X3] :
( ( in(X2,X1)
& subset(X3,X2) )
=> in(X3,X1) )
& ! [X2] :
( in(X2,X1)
=> in(powerset(X2),X1) )
& ! [X2] :
~ ( subset(X2,X1)
& ~ are_equipotent(X2,X1)
& ~ in(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [X0] :
? [X1] :
( in(X0,X1)
& ! [X2,X3] :
( ( in(X2,X1)
& subset(X3,X2) )
=> in(X3,X1) )
& ! [X2] :
~ ( in(X2,X1)
& ! [X3] :
~ ( in(X3,X1)
& ! [X4] :
( subset(X4,X2)
=> in(X4,X3) ) ) )
& ! [X2] :
~ ( subset(X2,X1)
& ~ are_equipotent(X2,X1)
& ~ in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
fof(f11,plain,
~ ! [X0] :
? [X1] :
( in(X0,X1)
& ! [X2,X3] :
( ( in(X2,X1)
& subset(X3,X2) )
=> in(X3,X1) )
& ! [X4] :
( in(X4,X1)
=> in(powerset(X4),X1) )
& ! [X5] :
~ ( subset(X5,X1)
& ~ are_equipotent(X5,X1)
& ~ in(X5,X1) ) ),
inference(rectify,[],[f8]) ).
fof(f12,plain,
! [X0] :
? [X1] :
( in(X0,X1)
& ! [X2,X3] :
( ( in(X2,X1)
& subset(X3,X2) )
=> in(X3,X1) )
& ! [X4] :
~ ( in(X4,X1)
& ! [X5] :
~ ( in(X5,X1)
& ! [X6] :
( subset(X6,X4)
=> in(X6,X5) ) ) )
& ! [X7] :
~ ( subset(X7,X1)
& ~ are_equipotent(X7,X1)
& ~ in(X7,X1) ) ),
inference(rectify,[],[f9]) ).
fof(f14,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f15,plain,
? [X0] :
! [X1] :
( ~ in(X0,X1)
| ? [X2,X3] :
( ~ in(X3,X1)
& in(X2,X1)
& subset(X3,X2) )
| ? [X4] :
( ~ in(powerset(X4),X1)
& in(X4,X1) )
| ? [X5] :
( subset(X5,X1)
& ~ are_equipotent(X5,X1)
& ~ in(X5,X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f16,plain,
? [X0] :
! [X1] :
( ~ in(X0,X1)
| ? [X2,X3] :
( ~ in(X3,X1)
& in(X2,X1)
& subset(X3,X2) )
| ? [X4] :
( ~ in(powerset(X4),X1)
& in(X4,X1) )
| ? [X5] :
( subset(X5,X1)
& ~ are_equipotent(X5,X1)
& ~ in(X5,X1) ) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0] :
? [X1] :
( in(X0,X1)
& ! [X2,X3] :
( in(X3,X1)
| ~ in(X2,X1)
| ~ subset(X3,X2) )
& ! [X4] :
( ~ in(X4,X1)
| ? [X5] :
( in(X5,X1)
& ! [X6] :
( in(X6,X5)
| ~ subset(X6,X4) ) ) )
& ! [X7] :
( ~ subset(X7,X1)
| are_equipotent(X7,X1)
| in(X7,X1) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f18,plain,
! [X0] :
? [X1] :
( in(X0,X1)
& ! [X2,X3] :
( in(X3,X1)
| ~ in(X2,X1)
| ~ subset(X3,X2) )
& ! [X4] :
( ~ in(X4,X1)
| ? [X5] :
( in(X5,X1)
& ! [X6] :
( in(X6,X5)
| ~ subset(X6,X4) ) ) )
& ! [X7] :
( ~ subset(X7,X1)
| are_equipotent(X7,X1)
| in(X7,X1) ) ),
inference(flattening,[],[f17]) ).
fof(f21,plain,
! [X2,X0,X1] :
( subset(X2,X0)
| ~ in(X2,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f2]) ).
fof(f25,plain,
! [X0,X1] :
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f26,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f30,plain,
! [X1] :
( ~ in(powerset(sK6(X1)),X1)
| ~ in(sK5(X1),X1)
| subset(sK8(X1),sK7(X1))
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
! [X1] :
( ~ in(powerset(sK6(X1)),X1)
| ~ in(sK5(X1),X1)
| in(sK7(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f32,plain,
! [X1] :
( ~ in(powerset(sK6(X1)),X1)
| ~ in(sK5(X1),X1)
| ~ in(sK8(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f33,plain,
! [X1] :
( subset(sK8(X1),sK7(X1))
| in(sK6(X1),X1)
| ~ in(sK5(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f34,plain,
! [X1] :
( ~ in(sK5(X1),X1)
| in(sK6(X1),X1)
| in(sK7(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f35,plain,
! [X1] :
( ~ in(sK8(X1),X1)
| in(sK6(X1),X1)
| ~ in(sK5(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f36,plain,
! [X1] :
( ~ in(powerset(sK6(X1)),X1)
| ~ are_equipotent(sK5(X1),X1)
| subset(sK8(X1),sK7(X1))
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f37,plain,
! [X1] :
( ~ in(powerset(sK6(X1)),X1)
| ~ are_equipotent(sK5(X1),X1)
| in(sK7(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f38,plain,
! [X1] :
( ~ in(powerset(sK6(X1)),X1)
| ~ are_equipotent(sK5(X1),X1)
| ~ in(sK8(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f39,plain,
! [X1] :
( subset(sK8(X1),sK7(X1))
| in(sK6(X1),X1)
| ~ are_equipotent(sK5(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f40,plain,
! [X1] :
( ~ are_equipotent(sK5(X1),X1)
| in(sK6(X1),X1)
| in(sK7(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f41,plain,
! [X1] :
( ~ are_equipotent(sK5(X1),X1)
| in(sK6(X1),X1)
| ~ in(sK8(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f42,plain,
! [X1] :
( ~ in(powerset(sK6(X1)),X1)
| subset(sK5(X1),X1)
| subset(sK8(X1),sK7(X1))
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f43,plain,
! [X1] :
( ~ in(powerset(sK6(X1)),X1)
| subset(sK5(X1),X1)
| in(sK7(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f44,plain,
! [X1] :
( ~ in(powerset(sK6(X1)),X1)
| subset(sK5(X1),X1)
| ~ in(sK8(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f45,plain,
! [X1] :
( subset(sK8(X1),sK7(X1))
| in(sK6(X1),X1)
| subset(sK5(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f46,plain,
! [X1] :
( subset(sK5(X1),X1)
| in(sK6(X1),X1)
| in(sK7(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f47,plain,
! [X1] :
( ~ in(sK8(X1),X1)
| in(sK6(X1),X1)
| subset(sK5(X1),X1)
| ~ in(sK4,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f48,plain,
! [X0,X6,X4] :
( ~ in(X4,sK9(X0))
| in(X6,sK10(X0,X4))
| ~ subset(X6,X4) ),
inference(cnf_transformation,[],[f18]) ).
fof(f49,plain,
! [X0,X4] :
( in(sK10(X0,X4),sK9(X0))
| ~ in(X4,sK9(X0)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f50,plain,
! [X2,X3,X0] :
( ~ in(X2,sK9(X0))
| ~ subset(X3,X2)
| in(X3,sK9(X0)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f51,plain,
! [X0,X7] :
( are_equipotent(X7,sK9(X0))
| in(X7,sK9(X0))
| ~ subset(X7,sK9(X0)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f52,plain,
! [X0] : in(X0,sK9(X0)),
inference(cnf_transformation,[],[f18]) ).
fof(f53,plain,
! [X2,X0] :
( ~ in(X2,powerset(X0))
| subset(X2,X0) ),
inference(equality_resolution,[],[f21]) ).
fof(f79,plain,
! [X0,X1] :
( subset(sK1(powerset(X0),X1),X0)
| subset(powerset(X0),X1) ),
inference(resolution,[],[f25,f53]) ).
fof(f105,definition,
( spl11_2
<=> in(sK7(sK9(sK4)),sK9(sK4)) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
fof(f107,plain,
( in(sK7(sK9(sK4)),sK9(sK4))
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f109,definition,
( spl11_3
<=> in(sK6(sK9(sK4)),sK9(sK4)) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
fof(f110,plain,
( ~ in(sK6(sK9(sK4)),sK9(sK4))
| spl11_3 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f111,plain,
( in(sK6(sK9(sK4)),sK9(sK4))
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ subset(X0,sK10(X1,X2))
| in(X0,sK9(X1))
| ~ in(X2,sK9(X1)) ),
inference(resolution,[],[f50,f49]) ).
fof(f155,plain,
! [X0] :
( in(sK5(sK9(X0)),sK9(X0))
| ~ subset(sK5(sK9(X0)),sK9(X0))
| in(sK6(sK9(X0)),sK9(X0))
| ~ in(sK8(sK9(X0)),sK9(X0))
| ~ in(sK4,sK9(X0)) ),
inference(resolution,[],[f51,f41]) ).
fof(f156,plain,
! [X0] :
( in(sK5(sK9(X0)),sK9(X0))
| ~ subset(sK5(sK9(X0)),sK9(X0))
| in(sK6(sK9(X0)),sK9(X0))
| in(sK7(sK9(X0)),sK9(X0))
| ~ in(sK4,sK9(X0)) ),
inference(resolution,[],[f51,f40]) ).
fof(f157,plain,
! [X0] :
( in(sK5(sK9(X0)),sK9(X0))
| in(sK6(sK9(X0)),sK9(X0))
| in(sK7(sK9(X0)),sK9(X0))
| ~ in(sK4,sK9(X0)) ),
inference(forward_subsumption_resolution,[],[f156,f46]) ).
fof(f158,plain,
! [X0] :
( in(sK5(sK9(X0)),sK9(X0))
| in(sK6(sK9(X0)),sK9(X0))
| ~ in(sK8(sK9(X0)),sK9(X0))
| ~ in(sK4,sK9(X0)) ),
inference(forward_subsumption_resolution,[],[f155,f47]) ).
fof(f160,plain,
! [X0] :
( ~ in(sK4,sK9(X0))
| in(sK7(sK9(X0)),sK9(X0))
| in(sK6(sK9(X0)),sK9(X0)) ),
inference(forward_subsumption_resolution,[],[f157,f34]) ).
fof(f161,plain,
! [X0] :
( ~ in(sK8(sK9(X0)),sK9(X0))
| in(sK6(sK9(X0)),sK9(X0))
| ~ in(sK4,sK9(X0)) ),
inference(forward_subsumption_resolution,[],[f158,f35]) ).
fof(f163,plain,
( in(sK7(sK9(sK4)),sK9(sK4))
| in(sK6(sK9(sK4)),sK9(sK4)) ),
inference(resolution,[],[f160,f52]) ).
fof(f164,plain,
( spl11_3
| spl11_2 ),
inference(avatar_split_clause,[],[f163,f105,f109]) ).
fof(f166,plain,
( ! [X0] :
( ~ subset(X0,sK7(sK9(sK4)))
| in(X0,sK9(sK4)) )
| ~ spl11_2 ),
inference(resolution,[],[f107,f50]) ).
fof(f171,plain,
( in(sK8(sK9(sK4)),sK9(sK4))
| in(sK6(sK9(sK4)),sK9(sK4))
| ~ are_equipotent(sK5(sK9(sK4)),sK9(sK4))
| ~ in(sK4,sK9(sK4))
| ~ spl11_2 ),
inference(resolution,[],[f166,f39]) ).
fof(f172,plain,
( in(sK8(sK9(sK4)),sK9(sK4))
| in(sK6(sK9(sK4)),sK9(sK4))
| ~ in(sK5(sK9(sK4)),sK9(sK4))
| ~ in(sK4,sK9(sK4))
| ~ spl11_2 ),
inference(resolution,[],[f166,f33]) ).
fof(f173,plain,
( in(sK6(sK9(sK4)),sK9(sK4))
| ~ in(sK5(sK9(sK4)),sK9(sK4))
| ~ in(sK4,sK9(sK4))
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f172,f35]) ).
fof(f174,plain,
( in(sK6(sK9(sK4)),sK9(sK4))
| ~ are_equipotent(sK5(sK9(sK4)),sK9(sK4))
| ~ in(sK4,sK9(sK4))
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f171,f41]) ).
fof(f192,plain,
( in(sK6(sK9(sK4)),sK9(sK4))
| ~ in(sK5(sK9(sK4)),sK9(sK4))
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f173,f52]) ).
fof(f193,plain,
( in(sK6(sK9(sK4)),sK9(sK4))
| ~ are_equipotent(sK5(sK9(sK4)),sK9(sK4))
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f174,f52]) ).
fof(f195,definition,
( spl11_11
<=> in(sK5(sK9(sK4)),sK9(sK4)) ),
introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition]) ).
fof(f197,plain,
( ~ in(sK5(sK9(sK4)),sK9(sK4))
| spl11_11 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f198,plain,
( ~ spl11_11
| spl11_3
| ~ spl11_2 ),
inference(avatar_split_clause,[],[f192,f105,f109,f195]) ).
fof(f200,definition,
( spl11_12
<=> are_equipotent(sK5(sK9(sK4)),sK9(sK4)) ),
introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition]) ).
fof(f202,plain,
( ~ are_equipotent(sK5(sK9(sK4)),sK9(sK4))
| spl11_12 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f203,plain,
( ~ spl11_12
| spl11_3
| ~ spl11_2 ),
inference(avatar_split_clause,[],[f193,f105,f109,f200]) ).
fof(f204,plain,
( ! [X0] :
( ~ subset(X0,sK6(sK9(sK4)))
| in(X0,sK10(sK4,sK6(sK9(sK4)))) )
| ~ spl11_3 ),
inference(resolution,[],[f111,f48]) ).
fof(f440,definition,
( spl11_38
<=> in(sK8(sK9(sK4)),sK9(sK4)) ),
introduced(definition,[new_symbols(definition,[spl11_38])],[avatar_definition]) ).
fof(f442,plain,
( ~ in(sK8(sK9(sK4)),sK9(sK4))
| spl11_38 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f449,definition,
( spl11_40
<=> subset(sK8(sK9(sK4)),sK7(sK9(sK4))) ),
introduced(definition,[new_symbols(definition,[spl11_40])],[avatar_definition]) ).
fof(f451,plain,
( subset(sK8(sK9(sK4)),sK7(sK9(sK4)))
| ~ spl11_40 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f1265,plain,
( ! [X0] :
( in(sK1(powerset(sK6(sK9(sK4))),X0),sK10(sK4,sK6(sK9(sK4))))
| subset(powerset(sK6(sK9(sK4))),X0) )
| ~ spl11_3 ),
inference(resolution,[],[f79,f204]) ).
fof(f2542,plain,
( subset(powerset(sK6(sK9(sK4))),sK10(sK4,sK6(sK9(sK4))))
| subset(powerset(sK6(sK9(sK4))),sK10(sK4,sK6(sK9(sK4))))
| ~ spl11_3 ),
inference(resolution,[],[f1265,f26]) ).
fof(f2544,plain,
( subset(powerset(sK6(sK9(sK4))),sK10(sK4,sK6(sK9(sK4))))
| ~ spl11_3 ),
inference(duplicate_literal_removal,[],[f2542]) ).
fof(f2546,plain,
( in(powerset(sK6(sK9(sK4))),sK9(sK4))
| ~ in(sK6(sK9(sK4)),sK9(sK4))
| ~ spl11_3 ),
inference(resolution,[],[f2544,f139]) ).
fof(f2551,plain,
( in(powerset(sK6(sK9(sK4))),sK9(sK4))
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f2546,f111]) ).
fof(f2555,plain,
( ~ in(sK5(sK9(sK4)),sK9(sK4))
| subset(sK8(sK9(sK4)),sK7(sK9(sK4)))
| ~ in(sK4,sK9(sK4))
| ~ spl11_3 ),
inference(resolution,[],[f2551,f30]) ).
fof(f2556,plain,
( ~ in(sK5(sK9(sK4)),sK9(sK4))
| in(sK7(sK9(sK4)),sK9(sK4))
| ~ in(sK4,sK9(sK4))
| ~ spl11_3 ),
inference(resolution,[],[f2551,f31]) ).
fof(f2557,plain,
( ~ in(sK5(sK9(sK4)),sK9(sK4))
| ~ in(sK8(sK9(sK4)),sK9(sK4))
| ~ in(sK4,sK9(sK4))
| ~ spl11_3 ),
inference(resolution,[],[f2551,f32]) ).
fof(f2558,plain,
( ~ are_equipotent(sK5(sK9(sK4)),sK9(sK4))
| subset(sK8(sK9(sK4)),sK7(sK9(sK4)))
| ~ in(sK4,sK9(sK4))
| ~ spl11_3 ),
inference(resolution,[],[f2551,f36]) ).
fof(f2559,plain,
( ~ are_equipotent(sK5(sK9(sK4)),sK9(sK4))
| in(sK7(sK9(sK4)),sK9(sK4))
| ~ in(sK4,sK9(sK4))
| ~ spl11_3 ),
inference(resolution,[],[f2551,f37]) ).
fof(f2560,plain,
( ~ are_equipotent(sK5(sK9(sK4)),sK9(sK4))
| ~ in(sK8(sK9(sK4)),sK9(sK4))
| ~ in(sK4,sK9(sK4))
| ~ spl11_3 ),
inference(resolution,[],[f2551,f38]) ).
fof(f2561,plain,
( subset(sK5(sK9(sK4)),sK9(sK4))
| subset(sK8(sK9(sK4)),sK7(sK9(sK4)))
| ~ in(sK4,sK9(sK4))
| ~ spl11_3 ),
inference(resolution,[],[f2551,f42]) ).
fof(f2562,plain,
( subset(sK5(sK9(sK4)),sK9(sK4))
| in(sK7(sK9(sK4)),sK9(sK4))
| ~ in(sK4,sK9(sK4))
| ~ spl11_3 ),
inference(resolution,[],[f2551,f43]) ).
fof(f2563,plain,
( subset(sK5(sK9(sK4)),sK9(sK4))
| ~ in(sK8(sK9(sK4)),sK9(sK4))
| ~ in(sK4,sK9(sK4))
| ~ spl11_3 ),
inference(resolution,[],[f2551,f44]) ).
fof(f2566,plain,
( subset(sK5(sK9(sK4)),sK9(sK4))
| ~ in(sK8(sK9(sK4)),sK9(sK4))
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f2563,f52]) ).
fof(f2567,plain,
( subset(sK5(sK9(sK4)),sK9(sK4))
| in(sK7(sK9(sK4)),sK9(sK4))
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f2562,f52]) ).
fof(f2568,plain,
( subset(sK5(sK9(sK4)),sK9(sK4))
| subset(sK8(sK9(sK4)),sK7(sK9(sK4)))
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f2561,f52]) ).
fof(f2569,plain,
( ~ are_equipotent(sK5(sK9(sK4)),sK9(sK4))
| ~ in(sK8(sK9(sK4)),sK9(sK4))
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f2560,f52]) ).
fof(f2570,plain,
( ~ are_equipotent(sK5(sK9(sK4)),sK9(sK4))
| in(sK7(sK9(sK4)),sK9(sK4))
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f2559,f52]) ).
fof(f2571,plain,
( ~ are_equipotent(sK5(sK9(sK4)),sK9(sK4))
| subset(sK8(sK9(sK4)),sK7(sK9(sK4)))
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f2558,f52]) ).
fof(f2572,plain,
( ~ in(sK5(sK9(sK4)),sK9(sK4))
| ~ in(sK8(sK9(sK4)),sK9(sK4))
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f2557,f52]) ).
fof(f2573,plain,
( ~ in(sK5(sK9(sK4)),sK9(sK4))
| in(sK7(sK9(sK4)),sK9(sK4))
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f2556,f52]) ).
fof(f2574,plain,
( ~ in(sK5(sK9(sK4)),sK9(sK4))
| subset(sK8(sK9(sK4)),sK7(sK9(sK4)))
| ~ spl11_3 ),
inference(forward_subsumption_resolution,[],[f2555,f52]) ).
fof(f2576,definition,
( spl11_301
<=> subset(sK5(sK9(sK4)),sK9(sK4)) ),
introduced(definition,[new_symbols(definition,[spl11_301])],[avatar_definition]) ).
fof(f2577,plain,
( ~ subset(sK5(sK9(sK4)),sK9(sK4))
| spl11_301 ),
inference(avatar_component_clause,[],[f2576]) ).
fof(f2578,plain,
( subset(sK5(sK9(sK4)),sK9(sK4))
| ~ spl11_301 ),
inference(avatar_component_clause,[],[f2576]) ).
fof(f2579,plain,
( ~ spl11_38
| spl11_301
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f2566,f109,f2576,f440]) ).
fof(f2580,plain,
( spl11_2
| spl11_301
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f2567,f109,f2576,f105]) ).
fof(f2581,plain,
( spl11_40
| spl11_301
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f2568,f109,f2576,f449]) ).
fof(f2582,plain,
( ~ spl11_38
| ~ spl11_12
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f2569,f109,f200,f440]) ).
fof(f2583,plain,
( spl11_2
| ~ spl11_12
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f2570,f109,f200,f105]) ).
fof(f2584,plain,
( spl11_40
| ~ spl11_12
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f2571,f109,f200,f449]) ).
fof(f2585,plain,
( ~ spl11_38
| ~ spl11_11
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f2572,f109,f195,f440]) ).
fof(f2586,plain,
( spl11_2
| ~ spl11_11
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f2573,f109,f195,f105]) ).
fof(f2587,plain,
( spl11_40
| ~ spl11_11
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f2574,f109,f195,f449]) ).
fof(f2588,plain,
( in(sK5(sK9(sK4)),sK9(sK4))
| ~ subset(sK5(sK9(sK4)),sK9(sK4))
| spl11_12 ),
inference(resolution,[],[f202,f51]) ).
fof(f2589,plain,
( ~ subset(sK5(sK9(sK4)),sK9(sK4))
| spl11_11
| spl11_12 ),
inference(forward_subsumption_resolution,[],[f2588,f197]) ).
fof(f2593,plain,
( $false
| spl11_11
| spl11_12
| ~ spl11_301 ),
inference(forward_subsumption_resolution,[],[f2589,f2578]) ).
fof(f2594,plain,
( spl11_11
| spl11_12
| ~ spl11_301 ),
inference(avatar_contradiction_clause,[],[f2593]) ).
fof(f2596,plain,
( ! [X0] :
( ~ subset(X0,sK7(sK9(sK4)))
| in(X0,sK9(sK4)) )
| ~ spl11_2 ),
inference(resolution,[],[f107,f50]) ).
fof(f2612,plain,
( in(sK8(sK9(sK4)),sK9(sK4))
| in(sK6(sK9(sK4)),sK9(sK4))
| subset(sK5(sK9(sK4)),sK9(sK4))
| ~ in(sK4,sK9(sK4))
| ~ spl11_2 ),
inference(resolution,[],[f2596,f45]) ).
fof(f2615,plain,
( in(sK8(sK9(sK4)),sK9(sK4))
| ~ spl11_2
| ~ spl11_40 ),
inference(resolution,[],[f2596,f451]) ).
fof(f2616,plain,
( $false
| ~ spl11_2
| spl11_38
| ~ spl11_40 ),
inference(forward_subsumption_resolution,[],[f2615,f442]) ).
fof(f2617,plain,
( ~ spl11_2
| spl11_38
| ~ spl11_40 ),
inference(avatar_contradiction_clause,[],[f2616]) ).
fof(f2620,plain,
( in(sK6(sK9(sK4)),sK9(sK4))
| subset(sK5(sK9(sK4)),sK9(sK4))
| ~ in(sK4,sK9(sK4))
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f2612,f161]) ).
fof(f2625,plain,
( in(sK6(sK9(sK4)),sK9(sK4))
| ~ in(sK4,sK9(sK4))
| ~ spl11_2
| spl11_301 ),
inference(forward_subsumption_resolution,[],[f2620,f2577]) ).
fof(f2626,plain,
( in(sK6(sK9(sK4)),sK9(sK4))
| ~ spl11_2
| spl11_301 ),
inference(forward_subsumption_resolution,[],[f2625,f52]) ).
fof(f2633,plain,
( $false
| ~ spl11_2
| spl11_3
| spl11_301 ),
inference(forward_subsumption_resolution,[],[f2626,f110]) ).
fof(f2634,plain,
( ~ spl11_2
| spl11_3
| spl11_301 ),
inference(avatar_contradiction_clause,[],[f2633]) ).
cnf(s3,plain,
( spl11_2
| spl11_3 ),
inference(sat_conversion,[],[f164]) ).
cnf(s5,plain,
( ~ spl11_2
| spl11_3
| ~ spl11_11 ),
inference(sat_conversion,[],[f198]) ).
cnf(s6,plain,
( ~ spl11_2
| spl11_3
| ~ spl11_12 ),
inference(sat_conversion,[],[f203]) ).
cnf(s146,plain,
( ~ spl11_3
| ~ spl11_38
| spl11_301 ),
inference(sat_conversion,[],[f2579]) ).
cnf(s147,plain,
( spl11_2
| ~ spl11_3
| spl11_301 ),
inference(sat_conversion,[],[f2580]) ).
cnf(s148,plain,
( ~ spl11_3
| spl11_40
| spl11_301 ),
inference(sat_conversion,[],[f2581]) ).
cnf(s149,plain,
( ~ spl11_3
| ~ spl11_12
| ~ spl11_38 ),
inference(sat_conversion,[],[f2582]) ).
cnf(s150,plain,
( spl11_2
| ~ spl11_3
| ~ spl11_12 ),
inference(sat_conversion,[],[f2583]) ).
cnf(s151,plain,
( ~ spl11_3
| ~ spl11_12
| spl11_40 ),
inference(sat_conversion,[],[f2584]) ).
cnf(s152,plain,
( ~ spl11_3
| ~ spl11_11
| ~ spl11_38 ),
inference(sat_conversion,[],[f2585]) ).
cnf(s153,plain,
( spl11_2
| ~ spl11_3
| ~ spl11_11 ),
inference(sat_conversion,[],[f2586]) ).
cnf(s154,plain,
( ~ spl11_3
| ~ spl11_11
| spl11_40 ),
inference(sat_conversion,[],[f2587]) ).
cnf(s155,plain,
( spl11_11
| spl11_12
| ~ spl11_301 ),
inference(sat_conversion,[],[f2594]) ).
cnf(s156,plain,
( ~ spl11_2
| spl11_38
| ~ spl11_40 ),
inference(sat_conversion,[],[f2617]) ).
cnf(s160,plain,
( ~ spl11_2
| spl11_3
| spl11_301 ),
inference(sat_conversion,[],[f2634]) ).
cnf(s163,plain,
( spl11_2
| ~ spl11_3 ),
inference(rat,[],[s155,s150,s153,s147]) ).
cnf(s164,plain,
spl11_2,
inference(rat,[],[s163,s3]) ).
cnf(s165,plain,
( spl11_301
| ~ spl11_3 ),
inference(rat,[],[s156,s146,s148,s164]) ).
cnf(s166,plain,
( ~ spl11_12
| ~ spl11_3 ),
inference(rat,[],[s156,s149,s151,s164]) ).
cnf(s167,plain,
( ~ spl11_11
| ~ spl11_3 ),
inference(rat,[],[s156,s152,s154,s164]) ).
cnf(s168,plain,
~ spl11_3,
inference(rat,[],[s167,s155,s166,s165]) ).
cnf(s169,plain,
spl11_301,
inference(rat,[],[s160,s164,s168]) ).
cnf(s171,plain,
~ spl11_12,
inference(rat,[],[s6,s164,s168]) ).
cnf(s172,plain,
~ spl11_11,
inference(rat,[],[s5,s164,s168]) ).
cnf(s173,plain,
$false,
inference(rat,[],[s155,s169,s172,s171]) ).
fof(f2635,plain,
$false,
inference(avatar_sat_refutation,[],[s173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU168+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Mon Sep 28 03:51:34 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.33 Running first-order model finding
% 0.07/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.59/0.46 % (2999762)Will run a generic schedule for satisfiability detection.
% 0.59/0.46 % (2999768)% WARNING: option uhcvi not known.
% 0.59/0.46 % (2999770)dis+10_1_sil=32000:sp=arity:random_seed=2048037578:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.59/0.46 % (2999771)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1704336070:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.59/0.46 % (2999773)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2622023193:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.59/0.46 % (2999767)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=988088005_2999 on theBenchmark for (2999ds/0Mi)
% 0.59/0.46 % (2999768)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3877140633:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.59/0.46 % (2999769)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=690550406:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.59/0.46 % (2999772)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2193077151:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.59/0.46 % TRYING [1]
% 0.59/0.46 % TRYING [2]
% 0.59/0.46 % TRYING [3]
% 0.59/0.46 % TRYING [4]
% 0.59/0.46 % TRYING [5]
% 0.59/0.46 % TRYING [6]
% 0.59/0.46 % TRYING [7]
% 0.59/0.46 % (2999770)Instruction limit reached!
% 0.59/0.46 % (2999770)------------------------------
% 0.59/0.46 % (2999770)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.46 % (2999770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.46 % (2999770)CaDiCaL version: 2.1.3
% 0.59/0.46 % (2999770)Termination reason: Instruction limit
% 0.59/0.46 % (2999770)Termination phase: Saturation
% 0.59/0.46 % (2999770)Time elapsed: 0.034 s
% 0.59/0.46 % (2999770)Peak memory usage: 12 MB
% 0.59/0.46 % (2999770)Instructions burned: 104 (million)
% 0.59/0.46 % (2999771)Instruction limit reached!
% 0.59/0.46 % (2999771)------------------------------
% 0.59/0.46 % (2999771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.46 % (2999771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.46 % (2999771)CaDiCaL version: 2.1.3
% 0.59/0.46 % (2999771)Termination reason: Instruction limit
% 0.59/0.46 % (2999771)Termination phase: Saturation
% 0.59/0.46 % (2999771)Time elapsed: 0.035 s
% 0.59/0.46 % (2999771)Peak memory usage: 12 MB
% 0.59/0.46 % (2999771)Instructions burned: 119 (million)
% 0.59/0.46 % TRYING [8]
% 0.59/0.46 % (2999781)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2984768740:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.59/0.46 % (2999782)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1323336911:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.59/0.46 % TRYING [1]
% 0.59/0.46 % TRYING [2]
% 0.59/0.46 % (2999772)Instruction limit reached!
% 0.59/0.46 % (2999772)------------------------------
% 0.59/0.46 % (2999772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.46 % (2999772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.46 % TRYING [3]
% 0.59/0.46 % (2999772)CaDiCaL version: 2.1.3
% 0.59/0.46 % (2999772)Termination reason: Instruction limit
% 0.59/0.46 % (2999772)Termination phase: Saturation
% 0.59/0.46 % (2999772)Time elapsed: 0.046 s
% 0.59/0.46 % (2999772)Peak memory usage: 13 MB
% 0.59/0.46 % (2999772)Instructions burned: 133 (million)
% 0.59/0.46 % TRYING [4]
% 0.59/0.46 % TRYING [5]
% 0.59/0.46 % TRYING [6]
% 0.59/0.46 % (2999785)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=1601480237:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.59/0.46 % (2999773)Instruction limit reached!
% 0.59/0.46 % (2999773)------------------------------
% 0.59/0.46 % (2999773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.46 % (2999773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.46 % (2999773)CaDiCaL version: 2.1.3
% 0.59/0.46 % (2999773)Termination reason: Instruction limit
% 0.59/0.46 % (2999773)Termination phase: Saturation
% 0.59/0.46 % (2999773)Time elapsed: 0.060 s
% 0.59/0.46 % (2999773)Peak memory usage: 14 MB
% 0.59/0.46 % (2999773)Instructions burned: 159 (million)
% 0.59/0.46 % (2999787)ott-21_1_sil=16000:fs=off:random_seed=356292861:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.59/0.46 % (2999782)Instruction limit reached!
% 0.59/0.46 % (2999782)------------------------------
% 0.59/0.46 % (2999782)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.46 % (2999782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.46 % (2999782)CaDiCaL version: 2.1.3
% 0.59/0.46 % (2999782)Termination reason: Instruction limit
% 0.59/0.46 % (2999782)Termination phase: Saturation
% 0.59/0.46 % (2999782)Time elapsed: 0.046 s
% 0.59/0.46 % (2999782)Peak memory usage: 13 MB
% 0.59/0.46 % (2999782)Instructions burned: 134 (million)
% 0.59/0.46 % (2999785) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2999762-2999785"...
% 0.59/0.46 % TRYING [7]
% 0.59/0.46 % (2999785)...printing done.
% 0.59/0.46 % (2999785)Refutation found. Thanks to Tanya!
% 0.59/0.46 % SZS status Theorem for theBenchmark
% 0.59/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.59/0.46 % (2999785)------------------------------
% 0.59/0.46 % (2999785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.46 % (2999785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.46 % (2999785)CaDiCaL version: 2.1.3
% 0.59/0.46 % (2999785)Termination reason: Refutation
% 0.59/0.46 % (2999785)Time elapsed: 0.038 s
% 0.59/0.46 % (2999785)Peak memory usage: 14 MB
% 0.59/0.46 % (2999785)Instructions burned: 105 (million)
% 0.59/0.46 % (2999762)Success in time 0.123 s
% 0.59/0.46 % Vampire exiting
%------------------------------------------------------------------------------