%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM537+2 : TPTP v9.3.1. Released v4.0.0.
% 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 12:24:43 PM UTC 2026
% Result : Theorem 0.07s 0.36s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 147 ( 21 unt; 10 def)
% Number of atoms : 516 ( 47 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 541 ( 172 ~; 235 |; 77 &)
% ( 36 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 11 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 121 ( 0 sgn 117 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f15,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElement0(X1) )
=> ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& ( aElementOf0(X3,X0)
| X3 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefCons) ).
fof(f18,axiom,
( aElement0(xx)
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__679) ).
fof(f19,axiom,
~ aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__679_02) ).
fof(f20,conjecture,
( ( ( aSet0(sdtpldt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xS)
| X0 = xx ) ) ) )
=> ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X0)
& aElementOf0(X0,sdtpldt0(xS,xx))
& X0 != xx ) ) )
=> ( ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) )
& ( ( aSet0(sdtpldt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xS)
| X0 = xx ) ) ) )
=> ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X0)
& aElementOf0(X0,sdtpldt0(xS,xx))
& X0 != xx ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
=> aElementOf0(X0,xS) )
| aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f21,negated_conjecture,
~ ( ( ( aSet0(sdtpldt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xS)
| X0 = xx ) ) ) )
=> ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X0)
& aElementOf0(X0,sdtpldt0(xS,xx))
& X0 != xx ) ) )
=> ( ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) )
& ( ( aSet0(sdtpldt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xS)
| X0 = xx ) ) ) )
=> ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X0)
& aElementOf0(X0,sdtpldt0(xS,xx))
& X0 != xx ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
=> aElementOf0(X0,xS) )
| aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,plain,
~ ( ( ( aSet0(sdtpldt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xS)
| X0 = xx ) ) ) )
=> ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtpldt0(xS,xx))
& xx != X1 ) ) )
=> ( ! [X2] :
( aElementOf0(X2,xS)
=> aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx)) )
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) )
& ( ( aSet0(sdtpldt0(xS,xx))
& ! [X3] :
( aElementOf0(X3,sdtpldt0(xS,xx))
<=> ( aElement0(X3)
& ( aElementOf0(X3,xS)
| xx = X3 ) ) ) )
=> ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X4)
& aElementOf0(X4,sdtpldt0(xS,xx))
& xx != X4 ) ) )
=> ( ! [X5] :
( aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx))
=> aElementOf0(X5,xS) )
| aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ) ) ) ),
inference(rectify,[],[f21]) ).
fof(f28,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f40,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& ( aElementOf0(X3,X0)
| X3 = X1 ) ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f41,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& ( aElementOf0(X3,X0)
| X3 = X1 ) ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f40]) ).
fof(f45,plain,
( ( ? [X2] :
( ~ aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx))
& aElementOf0(X2,xS) )
& ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtpldt0(xS,xx))
& xx != X1 ) )
& aSet0(sdtpldt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xS)
| X0 = xx ) ) ) )
| ( ? [X5] :
( ~ aElementOf0(X5,xS)
& aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X4)
& aElementOf0(X4,sdtpldt0(xS,xx))
& xx != X4 ) )
& aSet0(sdtpldt0(xS,xx))
& ! [X3] :
( aElementOf0(X3,sdtpldt0(xS,xx))
<=> ( aElement0(X3)
& ( aElementOf0(X3,xS)
| xx = X3 ) ) ) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f46,plain,
( ( ? [X2] :
( ~ aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx))
& aElementOf0(X2,xS) )
& ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtpldt0(xS,xx))
& xx != X1 ) )
& aSet0(sdtpldt0(xS,xx))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xS)
| X0 = xx ) ) ) )
| ( ? [X5] :
( ~ aElementOf0(X5,xS)
& aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(X4)
& aElementOf0(X4,sdtpldt0(xS,xx))
& xx != X4 ) )
& aSet0(sdtpldt0(xS,xx))
& ! [X3] :
( aElementOf0(X3,sdtpldt0(xS,xx))
<=> ( aElement0(X3)
& ( aElementOf0(X3,xS)
| xx = X3 ) ) ) ) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,X2)
| sdtpldt0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f79,plain,
aSet0(xS),
inference(cnf_transformation,[],[f18]) ).
fof(f80,plain,
aElement0(xx),
inference(cnf_transformation,[],[f18]) ).
fof(f81,plain,
~ aElementOf0(xx,xS),
inference(cnf_transformation,[],[f19]) ).
fof(f85,plain,
! [X3] :
( xx = X3
| aElementOf0(X3,xS)
| ~ sP9(X3) ),
inference(cnf_transformation,[],[f46]) ).
fof(f91,plain,
! [X1] :
( xx = X1
| ~ aElementOf0(X1,sdtpldt0(xS,xx))
| ~ aElement0(X1)
| aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ sP7(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f92,plain,
! [X0] :
( aElement0(X0)
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f94,plain,
! [X4] :
( xx != X4
| ~ sP10(X4) ),
inference(cnf_transformation,[],[f46]) ).
fof(f95,plain,
! [X4] :
( aElementOf0(X4,sdtpldt0(xS,xx))
| ~ sP10(X4) ),
inference(cnf_transformation,[],[f46]) ).
fof(f98,plain,
! [X2] :
( aElementOf0(X2,xS)
| ~ sP8(X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f99,plain,
! [X2] :
( ~ aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ sP8(X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f100,plain,
( aElementOf0(sK4,sdtmndt0(sdtpldt0(xS,xx),xx))
| sP8(sK5) ),
inference(cnf_transformation,[],[f46]) ).
fof(f101,plain,
( ~ aElementOf0(sK4,xS)
| sP8(sK5) ),
inference(cnf_transformation,[],[f46]) ).
fof(f106,plain,
! [X1] :
( aElementOf0(sK4,sdtmndt0(sdtpldt0(xS,xx),xx))
| sP7(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f107,plain,
! [X1] :
( ~ aElementOf0(sK4,xS)
| sP7(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f110,plain,
! [X0] :
( aElementOf0(sK4,sdtmndt0(sdtpldt0(xS,xx),xx))
| sP6(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f111,plain,
! [X0] :
( ~ aElementOf0(sK4,xS)
| sP6(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f113,plain,
! [X4] :
( sP10(X4)
| ~ aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
| sP8(sK5) ),
inference(cnf_transformation,[],[f46]) ).
fof(f119,plain,
! [X1,X4] :
( sP10(X4)
| ~ aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
| sP7(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f123,plain,
! [X0,X4] :
( sP10(X4)
| ~ aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
| sP6(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f125,plain,
! [X3] :
( sP9(X3)
| ~ aElementOf0(X3,sdtpldt0(xS,xx))
| sP8(sK5) ),
inference(cnf_transformation,[],[f46]) ).
fof(f131,plain,
! [X3,X1] :
( sP9(X3)
| ~ aElementOf0(X3,sdtpldt0(xS,xx))
| sP7(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f135,plain,
! [X3,X0] :
( sP9(X3)
| ~ aElementOf0(X3,sdtpldt0(xS,xx))
| sP6(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f159,plain,
! [X3,X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,sdtpldt0(X0,X1)) ),
inference(equality_resolution,[],[f64]) ).
fof(f168,plain,
~ sP10(xx),
inference(equality_resolution,[],[f94]) ).
fof(f172,plain,
! [X0,X1] :
( ~ aElement0(X1)
| aElementOf0(X1,X0)
| aSet0(X0) ),
inference(consistent_polarity_flipping,[],[f47]) ).
fof(f189,plain,
! [X3,X0,X1] :
( aElement0(X1)
| aSet0(X0)
| aElementOf0(X3,X0)
| aElement0(X3)
| ~ aElementOf0(X3,sdtpldt0(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f159]) ).
fof(f204,plain,
~ aElement0(xx),
inference(consistent_polarity_flipping,[],[f80]) ).
fof(f205,plain,
~ aSet0(xS),
inference(consistent_polarity_flipping,[],[f79]) ).
fof(f206,plain,
aElementOf0(xx,xS),
inference(consistent_polarity_flipping,[],[f81]) ).
fof(f223,plain,
! [X3,X0] :
( sP9(X3)
| aElementOf0(X3,sdtpldt0(xS,xx))
| ~ sP6(X0) ),
inference(consistent_polarity_flipping,[],[f135]) ).
fof(f227,plain,
! [X3,X1] :
( sP9(X3)
| aElementOf0(X3,sdtpldt0(xS,xx))
| sP7(X1) ),
inference(consistent_polarity_flipping,[],[f131]) ).
fof(f233,plain,
! [X3] :
( sP9(X3)
| aElementOf0(X3,sdtpldt0(xS,xx))
| ~ sP8(sK5) ),
inference(consistent_polarity_flipping,[],[f125]) ).
fof(f235,plain,
! [X0,X4] :
( sP10(X4)
| aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ sP6(X0) ),
inference(consistent_polarity_flipping,[],[f123]) ).
fof(f239,plain,
! [X1,X4] :
( sP10(X4)
| aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
| sP7(X1) ),
inference(consistent_polarity_flipping,[],[f119]) ).
fof(f245,plain,
! [X4] :
( sP10(X4)
| aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ sP8(sK5) ),
inference(consistent_polarity_flipping,[],[f113]) ).
fof(f247,plain,
! [X0] :
( aElementOf0(sK4,xS)
| ~ sP6(X0) ),
inference(consistent_polarity_flipping,[],[f111]) ).
fof(f248,plain,
! [X0] :
( ~ aElementOf0(sK4,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ sP6(X0) ),
inference(consistent_polarity_flipping,[],[f110]) ).
fof(f251,plain,
! [X1] :
( aElementOf0(sK4,xS)
| sP7(X1) ),
inference(consistent_polarity_flipping,[],[f107]) ).
fof(f252,plain,
! [X1] :
( ~ aElementOf0(sK4,sdtmndt0(sdtpldt0(xS,xx),xx))
| sP7(X1) ),
inference(consistent_polarity_flipping,[],[f106]) ).
fof(f257,plain,
( aElementOf0(sK4,xS)
| ~ sP8(sK5) ),
inference(consistent_polarity_flipping,[],[f101]) ).
fof(f258,plain,
( ~ aElementOf0(sK4,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ sP8(sK5) ),
inference(consistent_polarity_flipping,[],[f100]) ).
fof(f259,plain,
! [X2] :
( aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx))
| sP8(X2) ),
inference(consistent_polarity_flipping,[],[f99]) ).
fof(f260,plain,
! [X2] :
( ~ aElementOf0(X2,xS)
| sP8(X2) ),
inference(consistent_polarity_flipping,[],[f98]) ).
fof(f263,plain,
! [X4] :
( ~ aElementOf0(X4,sdtpldt0(xS,xx))
| ~ sP10(X4) ),
inference(consistent_polarity_flipping,[],[f95]) ).
fof(f265,plain,
! [X0] :
( ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(xS,xx))
| sP6(X0) ),
inference(consistent_polarity_flipping,[],[f92]) ).
fof(f266,plain,
! [X1] :
( xx = X1
| aElementOf0(X1,sdtpldt0(xS,xx))
| aElement0(X1)
| ~ aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ sP7(X1) ),
inference(consistent_polarity_flipping,[],[f91]) ).
fof(f272,plain,
! [X3] :
( ~ sP9(X3)
| ~ aElementOf0(X3,xS)
| xx = X3 ),
inference(consistent_polarity_flipping,[],[f85]) ).
fof(f286,definition,
( spl11_3
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
fof(f287,plain,
( ~ aElement0(xx)
| spl11_3 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f305,definition,
( spl11_7
<=> sP8(sK5) ),
introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition]) ).
fof(f307,plain,
( ~ sP8(sK5)
| spl11_7 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f309,definition,
( spl11_8
<=> aElementOf0(sK4,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
fof(f311,plain,
( ~ aElementOf0(sK4,sdtmndt0(sdtpldt0(xS,xx),xx))
| spl11_8 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f312,plain,
( ~ spl11_7
| ~ spl11_8 ),
inference(avatar_split_clause,[],[f258,f309,f305]) ).
fof(f314,definition,
( spl11_9
<=> aElementOf0(sK4,xS) ),
introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition]) ).
fof(f316,plain,
( aElementOf0(sK4,xS)
| ~ spl11_9 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f317,plain,
( ~ spl11_7
| spl11_9 ),
inference(avatar_split_clause,[],[f257,f314,f305]) ).
fof(f331,definition,
( spl11_12
<=> ! [X1] : sP7(X1) ),
introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition]) ).
fof(f332,plain,
( ! [X1] : sP7(X1)
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f333,plain,
( spl11_12
| ~ spl11_8 ),
inference(avatar_split_clause,[],[f252,f309,f331]) ).
fof(f334,plain,
( spl11_12
| spl11_9 ),
inference(avatar_split_clause,[],[f251,f314,f331]) ).
fof(f342,definition,
( spl11_14
<=> ! [X0] : ~ sP6(X0) ),
introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition]) ).
fof(f343,plain,
( ! [X0] : ~ sP6(X0)
| ~ spl11_14 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f344,plain,
( spl11_14
| ~ spl11_8 ),
inference(avatar_split_clause,[],[f248,f309,f342]) ).
fof(f345,plain,
( spl11_14
| spl11_9 ),
inference(avatar_split_clause,[],[f247,f314,f342]) ).
fof(f351,definition,
( spl11_16
<=> ! [X4] :
( sP10(X4)
| aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ),
introduced(definition,[new_symbols(definition,[spl11_16])],[avatar_definition]) ).
fof(f352,plain,
( ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
| sP10(X4) )
| ~ spl11_16 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f353,plain,
( ~ spl11_7
| spl11_16 ),
inference(avatar_split_clause,[],[f245,f351,f305]) ).
fof(f359,plain,
( spl11_12
| spl11_16 ),
inference(avatar_split_clause,[],[f239,f351,f331]) ).
fof(f363,plain,
( spl11_14
| spl11_16 ),
inference(avatar_split_clause,[],[f235,f351,f342]) ).
fof(f369,definition,
( spl11_18
<=> ! [X3] :
( sP9(X3)
| aElementOf0(X3,sdtpldt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[spl11_18])],[avatar_definition]) ).
fof(f370,plain,
( ! [X3] :
( aElementOf0(X3,sdtpldt0(xS,xx))
| sP9(X3) )
| ~ spl11_18 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f371,plain,
( ~ spl11_7
| spl11_18 ),
inference(avatar_split_clause,[],[f233,f369,f305]) ).
fof(f377,plain,
( spl11_12
| spl11_18 ),
inference(avatar_split_clause,[],[f227,f369,f331]) ).
fof(f381,plain,
( spl11_14
| spl11_18 ),
inference(avatar_split_clause,[],[f223,f369,f342]) ).
fof(f404,plain,
~ spl11_3,
inference(avatar_split_clause,[],[f204,f286]) ).
fof(f421,plain,
( ! [X0] :
( ~ sP10(X0)
| sP9(X0) )
| ~ spl11_18 ),
inference(resolution,[],[f370,f263]) ).
fof(f425,plain,
( ! [X0] :
( ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(xS,xx)) )
| ~ spl11_14 ),
inference(forward_subsumption_resolution,[],[f265,f343]) ).
fof(f426,plain,
( sP10(sK4)
| spl11_8
| ~ spl11_16 ),
inference(resolution,[],[f352,f311]) ).
fof(f428,plain,
( sP9(sK4)
| spl11_8
| ~ spl11_16
| ~ spl11_18 ),
inference(resolution,[],[f426,f421]) ).
fof(f430,plain,
( ~ aElementOf0(sK4,xS)
| xx = sK4
| spl11_8
| ~ spl11_16
| ~ spl11_18 ),
inference(resolution,[],[f428,f272]) ).
fof(f432,plain,
( xx = sK4
| spl11_8
| ~ spl11_9
| ~ spl11_16
| ~ spl11_18 ),
inference(forward_subsumption_resolution,[],[f430,f316]) ).
fof(f448,definition,
( spl11_23
<=> xx = sK4 ),
introduced(definition,[new_symbols(definition,[spl11_23])],[avatar_definition]) ).
fof(f450,plain,
( xx = sK4
| ~ spl11_23 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f468,plain,
( ! [X1] :
( xx = X1
| aElementOf0(X1,sdtpldt0(xS,xx))
| ~ aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ sP7(X1) )
| ~ spl11_14 ),
inference(forward_subsumption_resolution,[],[f266,f425]) ).
fof(f469,plain,
( ! [X1] :
( ~ aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
| aElementOf0(X1,sdtpldt0(xS,xx))
| xx = X1 )
| ~ spl11_12
| ~ spl11_14 ),
inference(forward_subsumption_resolution,[],[f468,f332]) ).
fof(f473,plain,
( ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| xx = X0
| sP8(X0) )
| ~ spl11_12
| ~ spl11_14 ),
inference(resolution,[],[f469,f259]) ).
fof(f478,plain,
sP8(xx),
inference(resolution,[],[f206,f260]) ).
fof(f496,plain,
( spl11_23
| spl11_8
| ~ spl11_9
| ~ spl11_16
| ~ spl11_18 ),
inference(avatar_split_clause,[],[f432,f369,f351,f314,f309,f448]) ).
fof(f506,plain,
( sP10(xx)
| spl11_8
| ~ spl11_16
| ~ spl11_23 ),
inference(superposition,[],[f426,f450]) ).
fof(f510,plain,
( $false
| spl11_8
| ~ spl11_16
| ~ spl11_23 ),
inference(forward_subsumption_resolution,[],[f506,f168]) ).
fof(f511,plain,
( spl11_8
| ~ spl11_16
| ~ spl11_23 ),
inference(avatar_contradiction_clause,[],[f510]) ).
fof(f521,definition,
( spl11_25
<=> xx = sK5 ),
introduced(definition,[new_symbols(definition,[spl11_25])],[avatar_definition]) ).
fof(f522,plain,
( xx != sK5
| spl11_25 ),
inference(avatar_component_clause,[],[f521]) ).
fof(f523,plain,
( xx = sK5
| ~ spl11_25 ),
inference(avatar_component_clause,[],[f521]) ).
fof(f692,plain,
( ~ sP8(xx)
| spl11_7
| ~ spl11_25 ),
inference(superposition,[],[f307,f523]) ).
fof(f693,plain,
( $false
| spl11_7
| ~ spl11_25 ),
inference(forward_subsumption_resolution,[],[f692,f478]) ).
fof(f694,plain,
( spl11_7
| ~ spl11_25 ),
inference(avatar_contradiction_clause,[],[f693]) ).
fof(f700,plain,
! [X3,X0,X1] :
( ~ aElementOf0(X3,sdtpldt0(X0,X1))
| aSet0(X0)
| aElementOf0(X3,X0)
| aElement0(X1) ),
inference(forward_subsumption_resolution,[],[f189,f172]) ).
fof(f960,plain,
( ! [X0] :
( xx = X0
| sP8(X0)
| aSet0(xS)
| aElementOf0(X0,xS)
| aElement0(xx) )
| ~ spl11_12
| ~ spl11_14 ),
inference(resolution,[],[f473,f700]) ).
fof(f969,plain,
( ! [X0] :
( xx = X0
| sP8(X0)
| aElementOf0(X0,xS)
| aElement0(xx) )
| ~ spl11_12
| ~ spl11_14 ),
inference(forward_subsumption_resolution,[],[f960,f205]) ).
fof(f971,plain,
( ! [X0] :
( xx = X0
| sP8(X0)
| aElementOf0(X0,xS) )
| spl11_3
| ~ spl11_12
| ~ spl11_14 ),
inference(forward_subsumption_resolution,[],[f969,f287]) ).
fof(f972,plain,
( ! [X0] :
( sP8(X0)
| xx = X0 )
| spl11_3
| ~ spl11_12
| ~ spl11_14 ),
inference(forward_subsumption_resolution,[],[f971,f260]) ).
fof(f1093,plain,
( xx = sK5
| spl11_3
| spl11_7
| ~ spl11_12
| ~ spl11_14 ),
inference(resolution,[],[f972,f307]) ).
fof(f1094,plain,
( $false
| spl11_3
| spl11_7
| ~ spl11_12
| ~ spl11_14
| spl11_25 ),
inference(forward_subsumption_resolution,[],[f1093,f522]) ).
fof(f1095,plain,
( spl11_3
| spl11_7
| ~ spl11_12
| ~ spl11_14
| spl11_25 ),
inference(avatar_contradiction_clause,[],[f1094]) ).
cnf(s4,plain,
( ~ spl11_7
| ~ spl11_8 ),
inference(sat_conversion,[],[f312]) ).
cnf(s5,plain,
( ~ spl11_7
| spl11_9 ),
inference(sat_conversion,[],[f317]) ).
cnf(s10,plain,
( ~ spl11_8
| spl11_12 ),
inference(sat_conversion,[],[f333]) ).
cnf(s11,plain,
( spl11_9
| spl11_12 ),
inference(sat_conversion,[],[f334]) ).
cnf(s14,plain,
( ~ spl11_8
| spl11_14 ),
inference(sat_conversion,[],[f344]) ).
cnf(s15,plain,
( spl11_9
| spl11_14 ),
inference(sat_conversion,[],[f345]) ).
cnf(s17,plain,
( ~ spl11_7
| spl11_16 ),
inference(sat_conversion,[],[f353]) ).
cnf(s23,plain,
( spl11_12
| spl11_16 ),
inference(sat_conversion,[],[f359]) ).
cnf(s27,plain,
( spl11_14
| spl11_16 ),
inference(sat_conversion,[],[f363]) ).
cnf(s29,plain,
( ~ spl11_7
| spl11_18 ),
inference(sat_conversion,[],[f371]) ).
cnf(s35,plain,
( spl11_12
| spl11_18 ),
inference(sat_conversion,[],[f377]) ).
cnf(s39,plain,
( spl11_14
| spl11_18 ),
inference(sat_conversion,[],[f381]) ).
cnf(s58,plain,
~ spl11_3,
inference(sat_conversion,[],[f404]) ).
cnf(s68,plain,
( spl11_8
| ~ spl11_9
| ~ spl11_16
| ~ spl11_18
| spl11_23 ),
inference(sat_conversion,[],[f496]) ).
cnf(s72,plain,
( spl11_8
| ~ spl11_16
| ~ spl11_23 ),
inference(sat_conversion,[],[f511]) ).
cnf(s92,plain,
( spl11_7
| ~ spl11_25 ),
inference(sat_conversion,[],[f694]) ).
cnf(s108,plain,
( spl11_3
| spl11_7
| ~ spl11_12
| ~ spl11_14
| spl11_25 ),
inference(sat_conversion,[],[f1095]) ).
cnf(s111,plain,
spl11_12,
inference(rat,[],[s68,s72,s10,s11,s23,s35]) ).
cnf(s114,plain,
spl11_14,
inference(rat,[],[s68,s72,s14,s15,s27,s39]) ).
cnf(s115,plain,
spl11_7,
inference(rat,[],[s108,s92,s58,s114,s111]) ).
cnf(s117,plain,
spl11_18,
inference(rat,[],[s29,s115]) ).
cnf(s119,plain,
spl11_16,
inference(rat,[],[s17,s115]) ).
cnf(s121,plain,
spl11_9,
inference(rat,[],[s5,s115]) ).
cnf(s122,plain,
~ spl11_8,
inference(rat,[],[s4,s115]) ).
cnf(s123,plain,
~ spl11_23,
inference(rat,[],[s72,s119,s122]) ).
cnf(s124,plain,
$false,
inference(rat,[],[s68,s121,s117,s119,s123,s122]) ).
fof(f1096,plain,
$false,
inference(avatar_sat_refutation,[],[s124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM537+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 27 20:23:11 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.03/0.32 Running first-order model finding
% 0.03/0.32 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
% 0.07/0.36 % (2706176)Will run a generic schedule for satisfiability detection.
% 0.07/0.36 % (2706182)% WARNING: option uhcvi not known.
% 0.07/0.36 % (2706183)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2850686057:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.36 % (2706186)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3069618244:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.36 % (2706182)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=775548792:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.36 % (2706181)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2238336017_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.36 % (2706184)dis+10_1_sil=32000:sp=arity:random_seed=633212146:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.36 % (2706185)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1235623439:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.36 % (2706187)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3055622635:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.36 % TRYING [1]
% 0.07/0.36 % TRYING [2]
% 0.07/0.36 % TRYING [3]
% 0.07/0.36 % TRYING [4]
% 0.07/0.36 % (2706182) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2706176-2706182"...
% 0.07/0.36 % TRYING [5]
% 0.07/0.36 % (2706186) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2706176-2706186"...
% 0.07/0.36 % (2706182)...printing done.
% 0.07/0.36 % (2706182)Refutation found. Thanks to Tanya!
% 0.07/0.36 % SZS status Theorem for theBenchmark
% 0.07/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.36 % (2706182)------------------------------
% 0.07/0.36 % (2706182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.36 % (2706182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.36 % (2706182)CaDiCaL version: 2.1.3
% 0.07/0.36 % (2706182)Termination reason: Refutation
% 0.07/0.36 % (2706182)Time elapsed: 0.012 s
% 0.07/0.36 % (2706182)Peak memory usage: 13 MB
% 0.07/0.36 % (2706182)Instructions burned: 30 (million)
% 0.07/0.36 % (2706176)Success in time 0.04 s
% 0.07/0.36 % Vampire exiting
%------------------------------------------------------------------------------