%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET720+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:41:44 PM UTC 2026
% Result : Theorem 0.75s 1.03s
% Output : Refutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 78 ( 18 unt; 7 def)
% Number of atoms : 268 ( 14 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 302 ( 112 ~; 107 |; 52 &)
% ( 13 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 7 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 174 ( 0 sgn 157 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X3,X5,X6] :
( ( member(X3,X1)
& member(X5,X2)
& member(X6,X2) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X3,X6) )
=> X5 = X6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
<=> ! [X4,X5,X6] :
( ( member(X4,X2)
& member(X5,X3)
& member(X6,X3) )
=> ( ( apply(X0,X4,X5)
& apply(X1,X4,X6) )
=> X5 = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_maps) ).
fof(f21,axiom,
! [X0,X1,X2,X3,X4] :
( ( member(X3,X1)
& member(X4,X2) )
=> ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_function) ).
fof(f29,conjecture,
! [X0,X1,X2] :
( ( maps(X0,X1,X2)
& one_to_one(X0,X1,X2) )
=> equal_maps(inverse_function(inverse_function(X0,X1,X2),X2,X1),X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII11) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2] :
( ( maps(X0,X1,X2)
& one_to_one(X0,X1,X2) )
=> equal_maps(inverse_function(inverse_function(X0,X1,X2),X2,X1),X0,X1,X2) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X2)
& member(X7,X2) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X5,X7) )
=> X6 = X7 ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f32,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X2)
& member(X7,X2) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X5,X7) )
=> X6 = X7 ) ) ) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ! [X4,X5,X6] :
( ( member(X4,X2)
& member(X5,X3)
& member(X6,X3) )
=> ( ( apply(X0,X4,X5)
& apply(X1,X4,X6) )
=> X5 = X6 ) )
=> equal_maps(X0,X1,X2,X3) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f37,plain,
? [X0,X1,X2] :
( ~ equal_maps(inverse_function(inverse_function(X0,X1,X2),X2,X1),X0,X1,X2)
& maps(X0,X1,X2)
& one_to_one(X0,X1,X2) ),
inference(ennf_transformation,[],[f30]) ).
fof(f38,plain,
? [X0,X1,X2] :
( ~ equal_maps(inverse_function(inverse_function(X0,X1,X2),X2,X1),X0,X1,X2)
& maps(X0,X1,X2)
& one_to_one(X0,X1,X2) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
| ? [X4,X5,X6] :
( X5 != X6
& apply(X0,X4,X5)
& apply(X1,X4,X6)
& member(X4,X2)
& member(X5,X3)
& member(X6,X3) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f42,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
| ? [X4,X5,X6] :
( X5 != X6
& apply(X0,X4,X5)
& apply(X1,X4,X6)
& member(X4,X2)
& member(X5,X3)
& member(X6,X3) ) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4] :
( ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) )
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(ennf_transformation,[],[f21]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) )
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(flattening,[],[f43]) ).
fof(f49,plain,
( ~ equal_maps(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2)
& maps(sK0,sK1,sK2)
& one_to_one(sK0,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f38]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( member(sK3(X0,X2,X3),X2)
& apply(X0,X3,sK3(X0,X2,X3)) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X0,X2,X3))],[f40]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
| ( sK5(X0,X1,X2,X3) != sK6(X0,X1,X2,X3)
& apply(X0,sK4(X0,X1,X2,X3),sK5(X0,X1,X2,X3))
& apply(X1,sK4(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
& member(sK4(X0,X1,X2,X3),X2)
& member(sK5(X0,X1,X2,X3),X3)
& member(sK6(X0,X1,X2,X3),X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X4,sK4(X0,X1,X2,X3)),skolemize(X5,sK5(X0,X1,X2,X3)),skolemize(X6,sK6(X0,X1,X2,X3))],[f42]) ).
fof(f52,plain,
! [X0,X1,X2,X3,X4] :
( ( ( apply(X0,X3,X4)
| ~ apply(inverse_function(X0,X1,X2),X4,X3) )
& ( apply(inverse_function(X0,X1,X2),X4,X3)
| ~ apply(X0,X3,X4) ) )
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(nnf_transformation,[],[f44]) ).
fof(f58,plain,
maps(sK0,sK1,sK2),
inference(cnf_transformation,[],[f49]) ).
fof(f59,plain,
~ equal_maps(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),
inference(cnf_transformation,[],[f49]) ).
fof(f60,plain,
! [X2,X0,X1,X6,X7,X5] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( equal_maps(X0,X1,X2,X3)
| member(sK6(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f51]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( equal_maps(X0,X1,X2,X3)
| member(sK5(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f51]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( equal_maps(X0,X1,X2,X3)
| member(sK4(X0,X1,X2,X3),X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( equal_maps(X0,X1,X2,X3)
| apply(X1,sK4(X0,X1,X2,X3),sK6(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( equal_maps(X0,X1,X2,X3)
| apply(X0,sK4(X0,X1,X2,X3),sK5(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f68,plain,
! [X2,X3,X0,X1] :
( equal_maps(X0,X1,X2,X3)
| sK5(X0,X1,X2,X3) != sK6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f51]) ).
fof(f70,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(inverse_function(X0,X1,X2),X4,X3)
| apply(X0,X3,X4)
| ~ member(X3,X1)
| ~ member(X4,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f84,definition,
! [X0,X1] :
( sQ8_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ8_eqProxy])],[equality_proxy_definition]) ).
fof(f85,plain,
! [X2,X0,X1,X6,X7,X5] :
( sQ8_eqProxy(X6,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2)
| ~ maps(X0,X1,X2) ),
inference(equality_proxy_replacement,[],[f60,f84]) ).
fof(f86,plain,
! [X2,X3,X0,X1] :
( ~ sQ8_eqProxy(sK5(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(equality_proxy_replacement,[],[f68,f84]) ).
fof(f93,plain,
member(sK6(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK2),
inference(resolution,[],[f63,f59]) ).
fof(f94,plain,
member(sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK2),
inference(resolution,[],[f64,f59]) ).
fof(f95,plain,
member(sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK1),
inference(resolution,[],[f65,f59]) ).
fof(f106,plain,
apply(sK0,sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK6(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2)),
inference(resolution,[],[f66,f59]) ).
fof(f107,plain,
apply(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2)),
inference(resolution,[],[f67,f59]) ).
fof(f108,plain,
( apply(inverse_function(sK0,sK1,sK2),sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2))
| ~ member(sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK2)
| ~ member(sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK1) ),
inference(resolution,[],[f70,f107]) ).
fof(f112,definition,
( spl9_1
<=> member(sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK1) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f113,plain,
( ~ member(sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK1)
| spl9_1 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,definition,
( spl9_2
<=> member(sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK2) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f116,plain,
( ~ member(sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK2)
| spl9_2 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,definition,
( spl9_3
<=> apply(inverse_function(sK0,sK1,sK2),sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f119,plain,
( apply(inverse_function(sK0,sK1,sK2),sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2))
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f120,plain,
( ~ spl9_1
| ~ spl9_2
| spl9_3 ),
inference(avatar_split_clause,[],[f108,f118,f115,f112]) ).
fof(f121,plain,
( $false
| spl9_1 ),
inference(resolution,[],[f113,f95]) ).
fof(f122,plain,
spl9_1,
inference(avatar_contradiction_clause,[],[f121]) ).
fof(f123,plain,
( $false
| spl9_2 ),
inference(resolution,[],[f116,f94]) ).
fof(f124,plain,
spl9_2,
inference(avatar_contradiction_clause,[],[f123]) ).
fof(f125,plain,
( apply(sK0,sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2))
| ~ member(sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK1)
| ~ member(sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK2)
| ~ spl9_3 ),
inference(resolution,[],[f119,f70]) ).
fof(f127,definition,
( spl9_4
<=> apply(sK0,sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
fof(f129,plain,
( ~ spl9_2
| ~ spl9_1
| spl9_4
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f125,f118,f127,f112,f115]) ).
fof(f130,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ maps(X0,X6,X7)
| ~ apply(X0,X1,sK6(X2,X3,X4,X5))
| ~ member(X1,X6)
| ~ member(sK5(X2,X3,X4,X5),X7)
| ~ member(sK6(X2,X3,X4,X5),X7)
| ~ apply(X0,X1,sK5(X2,X3,X4,X5))
| equal_maps(X2,X3,X4,X5) ),
inference(resolution,[],[f85,f86]) ).
fof(f138,plain,
! [X2,X3,X0,X1,X4] :
( equal_maps(X1,X2,X3,X4)
| ~ member(X0,sK1)
| ~ member(sK5(X1,X2,X3,X4),sK2)
| ~ member(sK6(X1,X2,X3,X4),sK2)
| ~ apply(sK0,X0,sK5(X1,X2,X3,X4))
| ~ apply(sK0,X0,sK6(X1,X2,X3,X4)) ),
inference(resolution,[],[f130,f58]) ).
fof(f140,plain,
! [X0] :
( ~ member(X0,sK1)
| ~ member(sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK2)
| ~ member(sK6(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK2)
| ~ apply(sK0,X0,sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2))
| ~ apply(sK0,X0,sK6(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2)) ),
inference(resolution,[],[f138,f59]) ).
fof(f142,definition,
( spl9_5
<=> member(sK6(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK2) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
fof(f143,plain,
( ~ member(sK6(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK2)
| spl9_5 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,definition,
( spl9_6
<=> ! [X0] :
( ~ member(X0,sK1)
| ~ apply(sK0,X0,sK6(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2))
| ~ apply(sK0,X0,sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2)) ) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
fof(f146,plain,
( ! [X0] :
( ~ apply(sK0,X0,sK6(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2))
| ~ member(X0,sK1)
| ~ apply(sK0,X0,sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2)) )
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f147,plain,
( ~ spl9_5
| ~ spl9_2
| spl9_6 ),
inference(avatar_split_clause,[],[f140,f145,f115,f142]) ).
fof(f148,plain,
( $false
| spl9_5 ),
inference(resolution,[],[f143,f93]) ).
fof(f149,plain,
spl9_5,
inference(avatar_contradiction_clause,[],[f148]) ).
fof(f151,plain,
( ~ member(sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK1)
| ~ apply(sK0,sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2))
| ~ spl9_6 ),
inference(resolution,[],[f146,f106]) ).
fof(f153,plain,
( ~ spl9_4
| ~ spl9_1
| ~ spl9_6 ),
inference(avatar_split_clause,[],[f151,f145,f112,f127]) ).
cnf(s1,plain,
( ~ spl9_1
| ~ spl9_2
| spl9_3 ),
inference(sat_conversion,[],[f120]) ).
cnf(s2,plain,
spl9_1,
inference(sat_conversion,[],[f122]) ).
cnf(s3,plain,
spl9_2,
inference(sat_conversion,[],[f124]) ).
cnf(s4,plain,
( ~ spl9_1
| ~ spl9_2
| ~ spl9_3
| spl9_4 ),
inference(sat_conversion,[],[f129]) ).
cnf(s5,plain,
( ~ spl9_2
| ~ spl9_5
| spl9_6 ),
inference(sat_conversion,[],[f147]) ).
cnf(s6,plain,
spl9_5,
inference(sat_conversion,[],[f149]) ).
cnf(s7,plain,
( ~ spl9_1
| ~ spl9_4
| ~ spl9_6 ),
inference(sat_conversion,[],[f153]) ).
cnf(s9,plain,
( ~ spl9_2
| spl9_6 ),
inference(rat,[],[s5,s6]) ).
cnf(s10,plain,
spl9_6,
inference(rat,[],[s9,s3]) ).
cnf(s11,plain,
~ spl9_4,
inference(rat,[],[s7,s10,s2]) ).
cnf(s12,plain,
~ spl9_3,
inference(rat,[],[s4,s11,s3,s2]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s12,s3,s2]) ).
fof(f161,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET720+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 % Computer : n014.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Mon Sep 28 02:38:08 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 0.75/1.03 % (1381779)Detected formulas, will run a generic FOF schedule.
% 0.75/1.03 % (1381788)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3064244780:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.75/1.03 % (1381789)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4167036046:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.75/1.03 % (1381784)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=410618562:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.75/1.03 % (1381786)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=893749663:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.75/1.03 % (1381785)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=1045113130:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.75/1.03 % (1381790)dis-21_1_sil=8000:lcm=predicate:random_seed=2799390: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)
% 0.75/1.03 % (1381787)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3753845926:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.75/1.03 % (1381790)First to succeed.
% 0.75/1.03 % (1381787)Refutation not found, incomplete strategy
% 0.75/1.03 % (1381787)------------------------------
% 0.75/1.03 % (1381787)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.75/1.03 % (1381787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/1.03 % (1381787)CaDiCaL version: 2.1.3
% 0.75/1.03 % (1381787)Termination reason: Refutation not found, incomplete strategy
% 0.75/1.03 % (1381787)Time elapsed: 0.004 s
% 0.75/1.03 % (1381787)Peak memory usage: 88 MB
% 0.75/1.03 % (1381787)Instructions burned: 5 (million)
% 0.75/1.03 % (1381790)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1381779"
% 0.75/1.03 % (1381788)Instruction limit reached!
% 0.75/1.03 % (1381788)------------------------------
% 0.75/1.03 % (1381788)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.75/1.03 % (1381788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/1.03 % (1381788)CaDiCaL version: 2.1.3
% 0.75/1.03 % (1381788)Termination reason: Instruction limit
% 0.75/1.03 % (1381788)Termination phase: Saturation
% 0.75/1.03 % (1381788)Time elapsed: 0.067 s
% 0.75/1.03 % (1381788)Peak memory usage: 88 MB
% 0.75/1.03 % (1381788)Instructions burned: 120 (million)
% 0.75/1.03 % (1381789)Instruction limit reached!
% 0.75/1.03 % (1381789)------------------------------
% 0.75/1.03 % (1381789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.75/1.03 % (1381789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.75/1.03 % (1381789)CaDiCaL version: 2.1.3
% 0.75/1.03 % (1381789)Termination reason: Instruction limit
% 0.75/1.03 % (1381789)Termination phase: Saturation
% 0.75/1.03 % (1381789)Time elapsed: 0.069 s
% 0.75/1.03 % (1381789)Peak memory usage: 89 MB
% 0.75/1.03 % (1381789)Instructions burned: 139 (million)
% 0.75/1.03 % (1381798)lrs+10_1_sil=8000:sp=occurrence:random_seed=245000937:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.75/1.03 % (1381798)Also succeeded, but the first one will report.
% 0.75/1.03 % (1381799)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2939316281:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 0.75/1.03 % (1381799)Also succeeded, but the first one will report.
% 0.75/1.03 % (1381787)------------------------------
% 0.75/1.03 % (1381787)------------------------------
% 0.75/1.03 % (1381790)Refutation found. Thanks to Tanya!
% 0.75/1.03 % SZS status Theorem for theBenchmark
% 0.75/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 3.09/1.13 % (1381790)------------------------------
% 3.09/1.13 % (1381790)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.09/1.13 % (1381790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.09/1.13 % (1381790)CaDiCaL version: 2.1.3
% 3.09/1.13 % (1381790)Termination reason: Refutation
% 3.09/1.13 % (1381790)Time elapsed: 0.005 s
% 3.09/1.13 % (1381790)Peak memory usage: 89 MB
% 3.09/1.13 % (1381790)Instructions burned: 6 (million)
% 3.09/1.13 % (1381790)------------------------------
% 3.09/1.13 % (1381790)------------------------------
% 3.09/1.13 % (1381779)Success in time 0.402 s
% 3.09/1.13 % Vampire exiting
%------------------------------------------------------------------------------