%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG106+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:35:32 PM UTC 2026
% Result : Theorem 2.65s 1.32s
% Output : Refutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 102 ( 17 unt; 11 def)
% Number of atoms : 403 ( 49 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 491 ( 190 ~; 184 |; 85 &)
% ( 17 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 12 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-3 aty)
% Number of variables : 115 ( 0 sgn 90 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f37,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f38,axiom,
aElement0(xc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1905) ).
fof(f39,conjecture,
( ! [X0,X1,X2] :
( ( aElementOf0(X0,slsdtgt0(xc))
& aElementOf0(X1,slsdtgt0(xc))
& aElement0(X2) )
=> ? [X3] :
( aElement0(X3)
& sdtasdt0(xc,X3) = X0
& ? [X4] :
( aElement0(X4)
& sdtasdt0(xc,X4) = X1
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2))
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc)) ) ) )
=> aIdeal0(slsdtgt0(xc)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f40,negated_conjecture,
~ ( ! [X0,X1,X2] :
( ( aElementOf0(X0,slsdtgt0(xc))
& aElementOf0(X1,slsdtgt0(xc))
& aElement0(X2) )
=> ? [X3] :
( aElement0(X3)
& sdtasdt0(xc,X3) = X0
& ? [X4] :
( aElement0(X4)
& sdtasdt0(xc,X4) = X1
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2))
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc)) ) ) )
=> aIdeal0(slsdtgt0(xc)) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f42,plain,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X1),X0) ) ) ) ) ),
inference(rectify,[],[f24]) ).
fof(f43,plain,
! [X0] :
( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X1),X0) ) ) ) )
=> aIdeal0(X0) ),
inference(unused_predicate_definition_removal,[],[f42]) ).
fof(f44,plain,
( ~ aIdeal0(slsdtgt0(xc))
& ! [X0,X1,X2] :
( ? [X3] :
( aElement0(X3)
& sdtasdt0(xc,X3) = X0
& ? [X4] :
( aElement0(X4)
& sdtasdt0(xc,X4) = X1
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2))
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc)) ) )
| ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElement0(X2) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f45,plain,
( ~ aIdeal0(slsdtgt0(xc))
& ! [X0,X1,X2] :
( ? [X3] :
( aElement0(X3)
& sdtasdt0(xc,X3) = X0
& ? [X4] :
( aElement0(X4)
& sdtasdt0(xc,X4) = X1
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2))
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc)) ) )
| ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElement0(X2) ) ),
inference(flattening,[],[f44]) ).
fof(f54,plain,
! [X0] :
( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f55,plain,
! [X0] :
( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,X0) ) ),
inference(flattening,[],[f54]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 ) ) ) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f63,plain,
( ~ aIdeal0(slsdtgt0(xc))
& ! [X0,X1,X2] :
( ( aElement0(sK0(X0,X1,X2))
& sdtasdt0(xc,sK0(X0,X1,X2)) = X0
& aElement0(sK1(X0,X1,X2))
& sdtasdt0(xc,sK1(X0,X1,X2)) = X1
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(sK0(X0,X1,X2),sK1(X0,X1,X2)))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(sK0(X0,X1,X2),X2))
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc)) )
| ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElement0(X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X4,sK1(X0,X1,X2))],[f45]) ).
fof(f64,plain,
! [X0] :
( aIdeal0(X0)
| ~ aSet0(X0)
| ( ( ( ~ aElementOf0(sdtpldt0(sK2(X0),sK3(X0)),X0)
& aElementOf0(sK3(X0),X0) )
| ( ~ aElementOf0(sdtasdt0(sK4(X0),sK2(X0)),X0)
& aElement0(sK4(X0)) ) )
& aElementOf0(sK2(X0),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X1,sK2(X0)),skolemize(X2,sK3(X0)),skolemize(X3,sK4(X0))],[f55]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| ~ aElementOf0(X2,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f62]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| ~ aElementOf0(X2,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X4] :
( aElement0(X4)
& sdtasdt0(X0,X4) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ? [X7] :
( aElement0(X7)
& sdtasdt0(X0,X7) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(rectify,[],[f66]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != sK5(X0,X1) )
| ~ aElementOf0(sK5(X0,X1),X1) )
& ( ( aElement0(sK6(X0,X1))
& sK5(X0,X1) = sdtasdt0(X0,sK6(X0,X1)) )
| aElementOf0(sK5(X0,X1),X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ( aElement0(sK7(X0,X5))
& sdtasdt0(X0,sK7(X0,X5)) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X2,sK5(X0,X1)),skolemize(X4,sK6(X0,X1)),skolemize(X7,sK7(X0,X5))],[f67]) ).
fof(f69,plain,
aElement0(xc),
inference(cnf_transformation,[],[f38]) ).
fof(f70,plain,
! [X2,X0,X1] :
( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f71,plain,
! [X2,X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f78,plain,
~ aIdeal0(slsdtgt0(xc)),
inference(cnf_transformation,[],[f63]) ).
fof(f84,plain,
! [X0] :
( aElementOf0(sK2(X0),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f85,plain,
! [X0] :
( aElementOf0(sK3(X0),X0)
| ~ aSet0(X0)
| aIdeal0(X0)
| aElement0(sK4(X0)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f86,plain,
! [X0] :
( ~ aElementOf0(sdtasdt0(sK4(X0),sK2(X0)),X0)
| ~ aSet0(X0)
| aElementOf0(sK3(X0),X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f87,plain,
! [X0] :
( ~ aElementOf0(sdtpldt0(sK2(X0),sK3(X0)),X0)
| ~ aSet0(X0)
| aIdeal0(X0)
| aElement0(sK4(X0)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f88,plain,
! [X0] :
( ~ aElementOf0(sdtasdt0(sK4(X0),sK2(X0)),X0)
| ~ aSet0(X0)
| ~ aElementOf0(sdtpldt0(sK2(X0),sK3(X0)),X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f95,plain,
! [X0,X1] :
( aSet0(X1)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f99,plain,
! [X0] :
( aSet0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f95]) ).
fof(f104,plain,
! [X2] :
( ~ aElement0(X2)
| sP8 ),
inference(cnf_transformation,[],[f104_D]) ).
fof(f104_D,definition,
( ! [X2] : ~ aElement0(X2)
<=> ~ sP8 ),
introduced(definition,[new_symbols(definition,[sP8])],[general_splitting_component_introduction]) ).
fof(f105,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ sP8 ),
inference(general_splitting,[],[f71,f104_D]) ).
fof(f106,plain,
! [X1] :
( ~ aElementOf0(X1,slsdtgt0(xc))
| sP9 ),
inference(cnf_transformation,[],[f106_D]) ).
fof(f106_D,definition,
( ! [X1] : ~ aElementOf0(X1,slsdtgt0(xc))
<=> ~ sP9 ),
introduced(definition,[new_symbols(definition,[sP9])],[general_splitting_component_introduction]) ).
fof(f107,plain,
! [X2,X0] :
( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElement0(X2)
| ~ sP9 ),
inference(general_splitting,[],[f70,f106_D]) ).
fof(f109,definition,
( spl10_1
<=> sP8 ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f113,definition,
( spl10_2
<=> ! [X2] : ~ aElement0(X2) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
fof(f114,plain,
( ! [X2] : ~ aElement0(X2)
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f115,plain,
( spl10_1
| spl10_2 ),
inference(avatar_split_clause,[],[f104,f113,f109]) ).
fof(f117,definition,
( spl10_3
<=> ! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc)) ) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
fof(f118,plain,
( ! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc)) )
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f119,plain,
( ~ spl10_1
| spl10_3 ),
inference(avatar_split_clause,[],[f105,f117,f109]) ).
fof(f121,definition,
( spl10_4
<=> sP9 ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
fof(f125,definition,
( spl10_5
<=> ! [X1] : ~ aElementOf0(X1,slsdtgt0(xc)) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
fof(f126,plain,
( ! [X1] : ~ aElementOf0(X1,slsdtgt0(xc))
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f127,plain,
( spl10_4
| spl10_5 ),
inference(avatar_split_clause,[],[f106,f125,f121]) ).
fof(f129,definition,
( spl10_6
<=> ! [X2,X0] :
( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
| ~ aElement0(X2)
| ~ aElementOf0(X0,slsdtgt0(xc)) ) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
fof(f130,plain,
( ! [X2,X0] :
( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
| ~ aElement0(X2)
| ~ aElementOf0(X0,slsdtgt0(xc)) )
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f131,plain,
( ~ spl10_4
| spl10_6 ),
inference(avatar_split_clause,[],[f107,f129,f121]) ).
fof(f136,plain,
( ~ aSet0(slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc))
| ~ spl10_5 ),
inference(resolution,[],[f126,f84]) ).
fof(f138,plain,
( ~ aSet0(slsdtgt0(xc))
| ~ spl10_5 ),
inference(forward_subsumption_resolution,[],[f136,f78]) ).
fof(f141,plain,
( ~ aElement0(xc)
| ~ spl10_5 ),
inference(resolution,[],[f138,f99]) ).
fof(f167,plain,
( $false
| ~ spl10_2 ),
inference(resolution,[],[f69,f114]) ).
fof(f168,plain,
~ spl10_2,
inference(avatar_contradiction_clause,[],[f167]) ).
fof(f170,plain,
( $false
| ~ spl10_5 ),
inference(forward_subsumption_resolution,[],[f141,f69]) ).
fof(f171,plain,
~ spl10_5,
inference(avatar_contradiction_clause,[],[f170]) ).
fof(f228,plain,
( ~ aElement0(sK4(slsdtgt0(xc)))
| ~ aElementOf0(sK2(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aSet0(slsdtgt0(xc))
| aElementOf0(sK3(slsdtgt0(xc)),slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc))
| ~ spl10_6 ),
inference(resolution,[],[f130,f86]) ).
fof(f229,plain,
( ~ aElement0(sK4(slsdtgt0(xc)))
| ~ aElementOf0(sK2(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sK2(slsdtgt0(xc)),sK3(slsdtgt0(xc))),slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc))
| ~ spl10_6 ),
inference(resolution,[],[f130,f88]) ).
fof(f244,plain,
( ~ aElementOf0(sK2(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sK2(slsdtgt0(xc)),sK3(slsdtgt0(xc))),slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc))
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f229,f87]) ).
fof(f245,plain,
( ~ aElementOf0(sK2(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aSet0(slsdtgt0(xc))
| aElementOf0(sK3(slsdtgt0(xc)),slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc))
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f228,f85]) ).
fof(f248,plain,
( ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sK2(slsdtgt0(xc)),sK3(slsdtgt0(xc))),slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc))
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f244,f84]) ).
fof(f249,plain,
( ~ aSet0(slsdtgt0(xc))
| aElementOf0(sK3(slsdtgt0(xc)),slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc))
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f245,f84]) ).
fof(f250,plain,
( ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sK2(slsdtgt0(xc)),sK3(slsdtgt0(xc))),slsdtgt0(xc))
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f248,f78]) ).
fof(f251,plain,
( ~ aSet0(slsdtgt0(xc))
| aElementOf0(sK3(slsdtgt0(xc)),slsdtgt0(xc))
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f249,f78]) ).
fof(f253,definition,
( spl10_9
<=> aElementOf0(sdtpldt0(sK2(slsdtgt0(xc)),sK3(slsdtgt0(xc))),slsdtgt0(xc)) ),
introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition]) ).
fof(f255,plain,
( ~ aElementOf0(sdtpldt0(sK2(slsdtgt0(xc)),sK3(slsdtgt0(xc))),slsdtgt0(xc))
| spl10_9 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f257,definition,
( spl10_10
<=> aSet0(slsdtgt0(xc)) ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
fof(f258,plain,
( aSet0(slsdtgt0(xc))
| ~ spl10_10 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f259,plain,
( ~ aSet0(slsdtgt0(xc))
| spl10_10 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f260,plain,
( ~ spl10_9
| ~ spl10_10
| ~ spl10_6 ),
inference(avatar_split_clause,[],[f250,f129,f257,f253]) ).
fof(f262,definition,
( spl10_11
<=> aElementOf0(sK3(slsdtgt0(xc)),slsdtgt0(xc)) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
fof(f264,plain,
( aElementOf0(sK3(slsdtgt0(xc)),slsdtgt0(xc))
| ~ spl10_11 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f265,plain,
( spl10_11
| ~ spl10_10
| ~ spl10_6 ),
inference(avatar_split_clause,[],[f251,f129,f257,f262]) ).
fof(f266,plain,
( ~ aElement0(xc)
| spl10_10 ),
inference(resolution,[],[f259,f99]) ).
fof(f267,plain,
( $false
| spl10_10 ),
inference(forward_subsumption_resolution,[],[f266,f69]) ).
fof(f268,plain,
spl10_10,
inference(avatar_contradiction_clause,[],[f267]) ).
fof(f348,plain,
( ~ aElementOf0(sK3(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElementOf0(sK2(slsdtgt0(xc)),slsdtgt0(xc))
| ~ spl10_3
| spl10_9 ),
inference(resolution,[],[f255,f118]) ).
fof(f349,plain,
( ~ aElementOf0(sK2(slsdtgt0(xc)),slsdtgt0(xc))
| ~ spl10_3
| spl10_9
| ~ spl10_11 ),
inference(forward_subsumption_resolution,[],[f348,f264]) ).
fof(f386,plain,
( ~ aSet0(slsdtgt0(xc))
| aIdeal0(slsdtgt0(xc))
| ~ spl10_3
| spl10_9
| ~ spl10_11 ),
inference(resolution,[],[f349,f84]) ).
fof(f387,plain,
( aIdeal0(slsdtgt0(xc))
| ~ spl10_3
| spl10_9
| ~ spl10_10
| ~ spl10_11 ),
inference(forward_subsumption_resolution,[],[f386,f258]) ).
fof(f388,plain,
( $false
| ~ spl10_3
| spl10_9
| ~ spl10_10
| ~ spl10_11 ),
inference(forward_subsumption_resolution,[],[f387,f78]) ).
fof(f389,plain,
( ~ spl10_3
| spl10_9
| ~ spl10_10
| ~ spl10_11 ),
inference(avatar_contradiction_clause,[],[f388]) ).
cnf(s1,plain,
( spl10_1
| spl10_2 ),
inference(sat_conversion,[],[f115]) ).
cnf(s2,plain,
( ~ spl10_1
| spl10_3 ),
inference(sat_conversion,[],[f119]) ).
cnf(s3,plain,
( spl10_4
| spl10_5 ),
inference(sat_conversion,[],[f127]) ).
cnf(s4,plain,
( ~ spl10_4
| spl10_6 ),
inference(sat_conversion,[],[f131]) ).
cnf(s5,plain,
~ spl10_2,
inference(sat_conversion,[],[f168]) ).
cnf(s6,plain,
~ spl10_5,
inference(sat_conversion,[],[f171]) ).
cnf(s12,plain,
( ~ spl10_6
| ~ spl10_9
| ~ spl10_10 ),
inference(sat_conversion,[],[f260]) ).
cnf(s13,plain,
( ~ spl10_6
| ~ spl10_10
| spl10_11 ),
inference(sat_conversion,[],[f265]) ).
cnf(s14,plain,
spl10_10,
inference(sat_conversion,[],[f268]) ).
cnf(s15,plain,
( ~ spl10_3
| spl10_9
| ~ spl10_10
| ~ spl10_11 ),
inference(sat_conversion,[],[f389]) ).
cnf(s16,plain,
( ~ spl10_6
| spl10_11 ),
inference(rat,[],[s13,s14]) ).
cnf(s17,plain,
( ~ spl10_6
| ~ spl10_9 ),
inference(rat,[],[s12,s14]) ).
cnf(s20,plain,
spl10_4,
inference(rat,[],[s3,s6]) ).
cnf(s21,plain,
spl10_6,
inference(rat,[],[s4,s20]) ).
cnf(s22,plain,
spl10_11,
inference(rat,[],[s16,s21]) ).
cnf(s23,plain,
~ spl10_9,
inference(rat,[],[s17,s21]) ).
cnf(s24,plain,
~ spl10_3,
inference(rat,[],[s15,s22,s14,s23]) ).
cnf(s25,plain,
~ spl10_1,
inference(rat,[],[s2,s24]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s1,s5,s25]) ).
fof(f390,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG106+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 % Computer : n005.cluster.edu
% 0.12/0.42 % Model : x86_64 x86_64
% 0.12/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.42 % Memory : 8046.5625MB
% 0.12/0.42 % OS : Linux 6.8.0-71-generic
% 0.12/0.42 % CPULimit : 300
% 0.12/0.42 % WCLimit : 300
% 0.12/0.42 % DateTime : Sun Sep 27 23:17:32 UTC 2026
% 0.12/0.42 % CPUTime :
% 0.12/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.45 Running first-order theorem proving
% 0.12/0.45 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
% 2.65/1.32 % (287101)Detected formulas, will run a generic FOF schedule.
% 2.65/1.32 % (287112)dis-21_1_sil=8000:lcm=predicate:random_seed=872173598:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.65/1.32 % (287110)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=210470551:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.65/1.32 % (287111)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=790497513:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.65/1.32 % (287107)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3109416533:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.65/1.32 % (287109)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=227869342:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.65/1.32 % (287106)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=2940844166:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.65/1.32 % (287108)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=489171837:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.65/1.32 % (287112)Instruction limit reached!
% 2.65/1.32 % (287112)------------------------------
% 2.65/1.32 % (287112)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.32 % (287112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.32 % (287112)CaDiCaL version: 2.1.3
% 2.65/1.32 % (287112)Termination reason: Instruction limit
% 2.65/1.32 % (287112)Termination phase: Saturation
% 2.65/1.32 % (287112)Time elapsed: 0.035 s
% 2.65/1.32 % (287112)Peak memory usage: 90 MB
% 2.65/1.32 % (287112)Instructions burned: 133 (million)
% 2.65/1.32 % (287109)First to succeed.
% 2.65/1.32 % (287109)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-287101"
% 2.65/1.32 % (287111)Also succeeded, but the first one will report.
% 2.65/1.32 % (287110)Also succeeded, but the first one will report.
% 2.65/1.32 % (287120)lrs+10_1_sil=8000:sp=occurrence:random_seed=2657269864:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.65/1.32 % (287120)Also succeeded, but the first one will report.
% 2.65/1.32 % (287109)Refutation found. Thanks to Tanya!
% 2.65/1.32 % SZS status Theorem for theBenchmark
% 2.65/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.52/1.47 % (287109)------------------------------
% 3.52/1.47 % (287109)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.47 % (287109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.47 % (287109)CaDiCaL version: 2.1.3
% 3.52/1.47 % (287109)Termination reason: Refutation
% 3.52/1.47 % (287109)Time elapsed: 0.011 s
% 3.52/1.47 % (287109)Peak memory usage: 89 MB
% 3.52/1.47 % (287109)Instructions burned: 15 (million)
% 3.52/1.47 % (287109)------------------------------
% 3.52/1.47 % (287109)------------------------------
% 3.52/1.47 % (287101)Success in time 0.422 s
% 3.52/1.47 % Vampire exiting
%------------------------------------------------------------------------------