%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU072+1 : 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 : n018.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 12:51:53 PM UTC 2026
% Result : Theorem 0.17s 0.49s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 102 ( 15 unt; 4 def)
% Number of atoms : 371 ( 94 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 459 ( 190 ~; 191 |; 51 &)
% ( 16 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 95 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f6,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f28,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( in(X0,relation_dom(X1))
=> relation_image(X1,singleton(X0)) = singleton(apply(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
fof(f29,axiom,
! [X0,X1] :
( relation(X1)
=> ( in(X0,relation_rng(X1))
<=> relation_inverse_image(X1,singleton(X0)) != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_1) ).
fof(f30,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( ! [X1] : subset(relation_inverse_image(X0,relation_image(X0,X1)),X1)
=> one_to_one(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t153_funct_1) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( ! [X1] : subset(relation_inverse_image(X0,relation_image(X0,X1)),X1)
=> one_to_one(X0) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f34,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f39,axiom,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f53,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f52]) ).
fof(f61,plain,
! [X0,X1] :
( relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f62,plain,
! [X0,X1] :
( relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ( in(X0,relation_rng(X1))
<=> relation_inverse_image(X1,singleton(X0)) != empty_set )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f64,plain,
? [X0] :
( ~ one_to_one(X0)
& ! [X1] : subset(relation_inverse_image(X0,relation_image(X0,X1)),X1)
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f65,plain,
? [X0] :
( ~ one_to_one(X0)
& ! [X1] : subset(relation_inverse_image(X0,relation_image(X0,X1)),X1)
& relation(X0)
& function(X0) ),
inference(flattening,[],[f64]) ).
fof(f73,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f39]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f51]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& apply(X0,X4) = X2 )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ? [X7] :
( in(X7,relation_dom(X0))
& apply(X0,X7) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f76]) ).
fof(f78,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK0(X0,X1) )
| ~ in(sK0(X0,X1),X1) )
& ( ( in(sK1(X0,X1),relation_dom(X0))
& sK0(X0,X1) = apply(X0,sK1(X0,X1)) )
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK2(X0,X5),relation_dom(X0))
& apply(X0,sK2(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1)),skolemize(X7,sK2(X0,X5))],[f77]) ).
fof(f79,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) ) )
& ( ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f53]) ).
fof(f80,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X3) != apply(X0,X4) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ( ( one_to_one(X0)
| ( sK3(X0) != sK4(X0)
& in(sK3(X0),relation_dom(X0))
& in(sK4(X0),relation_dom(X0))
& apply(X0,sK3(X0)) = apply(X0,sK4(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X3) != apply(X0,X4) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X1,sK3(X0)),skolemize(X2,sK4(X0))],[f80]) ).
fof(f93,plain,
! [X0,X1] :
( ( ( in(X0,relation_rng(X1))
| empty_set = relation_inverse_image(X1,singleton(X0)) )
& ( relation_inverse_image(X1,singleton(X0)) != empty_set
| ~ in(X0,relation_rng(X1)) ) )
| ~ relation(X1) ),
inference(nnf_transformation,[],[f63]) ).
fof(f94,plain,
( ~ one_to_one(sK16)
& ! [X1] : subset(relation_inverse_image(sK16,relation_image(sK16,X1)),X1)
& relation(sK16)
& function(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f65]) ).
fof(f95,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( empty_set != X0
& singleton(X1) != X0 ) )
& ( X0 = empty_set
| X0 = singleton(X1)
| ~ subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f96,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( empty_set != X0
& singleton(X1) != X0 ) )
& ( X0 = empty_set
| X0 = singleton(X1)
| ~ subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f95]) ).
fof(f106,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f111,plain,
! [X0] :
( ~ relation(X0)
| apply(X0,sK3(X0)) = apply(X0,sK4(X0))
| one_to_one(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f112,plain,
! [X0] :
( in(sK4(X0),relation_dom(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f113,plain,
! [X0] :
( in(sK3(X0),relation_dom(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f114,plain,
! [X0] :
( sK3(X0) != sK4(X0)
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f149,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f150,plain,
! [X0,X1] :
( empty_set != relation_inverse_image(X1,singleton(X0))
| ~ in(X0,relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f152,plain,
function(sK16),
inference(cnf_transformation,[],[f94]) ).
fof(f153,plain,
relation(sK16),
inference(cnf_transformation,[],[f94]) ).
fof(f154,plain,
! [X1] : subset(relation_inverse_image(sK16,relation_image(sK16,X1)),X1),
inference(cnf_transformation,[],[f94]) ).
fof(f155,plain,
~ one_to_one(sK16),
inference(cnf_transformation,[],[f94]) ).
fof(f158,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f96]) ).
fof(f166,plain,
! [X0,X1] :
( ~ subset(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f73]) ).
fof(f169,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f106]) ).
fof(f170,plain,
! [X0,X6] :
( in(apply(X0,X6),relation_rng(X0))
| ~ in(X6,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f169]) ).
fof(f308,plain,
( apply(sK16,sK3(sK16)) = apply(sK16,sK4(sK16))
| one_to_one(sK16)
| ~ function(sK16) ),
inference(resolution,[],[f111,f153]) ).
fof(f309,plain,
( apply(sK16,sK3(sK16)) = apply(sK16,sK4(sK16))
| ~ function(sK16) ),
inference(forward_subsumption_resolution,[],[f308,f155]) ).
fof(f341,plain,
apply(sK16,sK3(sK16)) = apply(sK16,sK4(sK16)),
inference(forward_subsumption_resolution,[],[f309,f152]) ).
fof(f359,plain,
( in(apply(sK16,sK3(sK16)),relation_rng(sK16))
| ~ in(sK4(sK16),relation_dom(sK16))
| ~ relation(sK16)
| ~ function(sK16) ),
inference(superposition,[],[f170,f341]) ).
fof(f360,plain,
( in(apply(sK16,sK3(sK16)),relation_rng(sK16))
| ~ in(sK4(sK16),relation_dom(sK16))
| ~ function(sK16) ),
inference(forward_subsumption_resolution,[],[f359,f153]) ).
fof(f361,plain,
( in(apply(sK16,sK3(sK16)),relation_rng(sK16))
| ~ in(sK4(sK16),relation_dom(sK16)) ),
inference(forward_subsumption_resolution,[],[f360,f152]) ).
fof(f363,definition,
( spl17_11
<=> in(sK4(sK16),relation_dom(sK16)) ),
introduced(definition,[new_symbols(definition,[spl17_11])],[avatar_definition]) ).
fof(f364,plain,
( in(sK4(sK16),relation_dom(sK16))
| ~ spl17_11 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f365,plain,
( ~ in(sK4(sK16),relation_dom(sK16))
| spl17_11 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f367,definition,
( spl17_12
<=> in(apply(sK16,sK3(sK16)),relation_rng(sK16)) ),
introduced(definition,[new_symbols(definition,[spl17_12])],[avatar_definition]) ).
fof(f369,plain,
( in(apply(sK16,sK3(sK16)),relation_rng(sK16))
| ~ spl17_12 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f370,plain,
( ~ spl17_11
| spl17_12 ),
inference(avatar_split_clause,[],[f361,f367,f363]) ).
fof(f375,plain,
( one_to_one(sK16)
| ~ relation(sK16)
| ~ function(sK16)
| spl17_11 ),
inference(resolution,[],[f365,f112]) ).
fof(f376,plain,
( ~ relation(sK16)
| ~ function(sK16)
| spl17_11 ),
inference(forward_subsumption_resolution,[],[f375,f155]) ).
fof(f377,plain,
( ~ function(sK16)
| spl17_11 ),
inference(forward_subsumption_resolution,[],[f376,f153]) ).
fof(f378,plain,
( $false
| spl17_11 ),
inference(forward_subsumption_resolution,[],[f377,f152]) ).
fof(f379,plain,
spl17_11,
inference(avatar_contradiction_clause,[],[f378]) ).
fof(f381,plain,
! [X0] :
( relation_image(X0,singleton(sK3(X0))) = singleton(apply(X0,sK3(X0)))
| ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(resolution,[],[f149,f113]) ).
fof(f384,plain,
! [X0] :
( ~ relation(X0)
| relation_image(X0,singleton(sK3(X0))) = singleton(apply(X0,sK3(X0)))
| ~ function(X0)
| one_to_one(X0) ),
inference(duplicate_literal_removal,[],[f381]) ).
fof(f386,plain,
( relation_image(sK16,singleton(sK4(sK16))) = singleton(apply(sK16,sK4(sK16)))
| ~ relation(sK16)
| ~ function(sK16)
| ~ spl17_11 ),
inference(resolution,[],[f364,f149]) ).
fof(f390,plain,
( relation_image(sK16,singleton(sK4(sK16))) = singleton(apply(sK16,sK4(sK16)))
| ~ function(sK16)
| ~ spl17_11 ),
inference(forward_subsumption_resolution,[],[f386,f153]) ).
fof(f391,plain,
( relation_image(sK16,singleton(sK4(sK16))) = singleton(apply(sK16,sK4(sK16)))
| ~ spl17_11 ),
inference(forward_subsumption_resolution,[],[f390,f152]) ).
fof(f392,plain,
( relation_image(sK16,singleton(sK4(sK16))) = singleton(apply(sK16,sK3(sK16)))
| ~ spl17_11 ),
inference(forward_demodulation,[],[f391,f341]) ).
fof(f450,plain,
( subset(relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16)))),singleton(sK4(sK16)))
| ~ spl17_11 ),
inference(superposition,[],[f154,f392]) ).
fof(f452,definition,
( spl17_13
<=> empty_set = relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16)))) ),
introduced(definition,[new_symbols(definition,[spl17_13])],[avatar_definition]) ).
fof(f453,plain,
( empty_set != relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16))))
| spl17_13 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f454,plain,
( empty_set = relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16))))
| ~ spl17_13 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f456,definition,
( spl17_14
<=> singleton(sK4(sK16)) = relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16)))) ),
introduced(definition,[new_symbols(definition,[spl17_14])],[avatar_definition]) ).
fof(f458,plain,
( singleton(sK4(sK16)) = relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16))))
| ~ spl17_14 ),
inference(avatar_component_clause,[],[f456]) ).
fof(f462,plain,
( empty_set != empty_set
| ~ in(apply(sK16,sK3(sK16)),relation_rng(sK16))
| ~ relation(sK16)
| ~ spl17_13 ),
inference(superposition,[],[f150,f454]) ).
fof(f463,plain,
( ~ in(apply(sK16,sK3(sK16)),relation_rng(sK16))
| ~ relation(sK16)
| ~ spl17_13 ),
inference(trivial_inequality_removal,[],[f462]) ).
fof(f464,plain,
( ~ relation(sK16)
| ~ spl17_12
| ~ spl17_13 ),
inference(forward_subsumption_resolution,[],[f463,f369]) ).
fof(f465,plain,
( $false
| ~ spl17_12
| ~ spl17_13 ),
inference(forward_subsumption_resolution,[],[f464,f153]) ).
fof(f466,plain,
( ~ spl17_12
| ~ spl17_13 ),
inference(avatar_contradiction_clause,[],[f465]) ).
fof(f473,plain,
( singleton(sK4(sK16)) = relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16))))
| empty_set = relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16))))
| ~ spl17_11 ),
inference(resolution,[],[f450,f158]) ).
fof(f474,plain,
( singleton(sK4(sK16)) = relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16))))
| ~ spl17_11
| spl17_13 ),
inference(forward_subsumption_resolution,[],[f473,f453]) ).
fof(f475,plain,
( spl17_14
| ~ spl17_11
| spl17_13 ),
inference(avatar_split_clause,[],[f474,f452,f363,f456]) ).
fof(f770,plain,
( singleton(apply(sK16,sK3(sK16))) = relation_image(sK16,singleton(sK3(sK16)))
| ~ function(sK16)
| one_to_one(sK16) ),
inference(resolution,[],[f384,f153]) ).
fof(f771,plain,
( singleton(apply(sK16,sK3(sK16))) = relation_image(sK16,singleton(sK3(sK16)))
| one_to_one(sK16) ),
inference(forward_subsumption_resolution,[],[f770,f152]) ).
fof(f776,plain,
singleton(apply(sK16,sK3(sK16))) = relation_image(sK16,singleton(sK3(sK16))),
inference(forward_subsumption_resolution,[],[f771,f155]) ).
fof(f1236,plain,
subset(relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16)))),singleton(sK3(sK16))),
inference(superposition,[],[f154,f776]) ).
fof(f1244,plain,
( subset(singleton(sK4(sK16)),singleton(sK3(sK16)))
| ~ spl17_14 ),
inference(forward_demodulation,[],[f1236,f458]) ).
fof(f1246,plain,
( sK3(sK16) = sK4(sK16)
| ~ spl17_14 ),
inference(resolution,[],[f1244,f166]) ).
fof(f1268,plain,
( sK3(sK16) != sK3(sK16)
| one_to_one(sK16)
| ~ relation(sK16)
| ~ function(sK16)
| ~ spl17_14 ),
inference(superposition,[],[f114,f1246]) ).
fof(f1270,plain,
( one_to_one(sK16)
| ~ relation(sK16)
| ~ function(sK16)
| ~ spl17_14 ),
inference(trivial_inequality_removal,[],[f1268]) ).
fof(f1271,plain,
( ~ relation(sK16)
| ~ function(sK16)
| ~ spl17_14 ),
inference(forward_subsumption_resolution,[],[f1270,f155]) ).
fof(f1273,plain,
( ~ function(sK16)
| ~ spl17_14 ),
inference(forward_subsumption_resolution,[],[f1271,f153]) ).
fof(f1274,plain,
( $false
| ~ spl17_14 ),
inference(forward_subsumption_resolution,[],[f1273,f152]) ).
fof(f1275,plain,
~ spl17_14,
inference(avatar_contradiction_clause,[],[f1274]) ).
cnf(s6,plain,
( ~ spl17_11
| spl17_12 ),
inference(sat_conversion,[],[f370]) ).
cnf(s7,plain,
spl17_11,
inference(sat_conversion,[],[f379]) ).
cnf(s9,plain,
( ~ spl17_12
| ~ spl17_13 ),
inference(sat_conversion,[],[f466]) ).
cnf(s10,plain,
( ~ spl17_11
| spl17_13
| spl17_14 ),
inference(sat_conversion,[],[f475]) ).
cnf(s26,plain,
~ spl17_14,
inference(sat_conversion,[],[f1275]) ).
cnf(s29,plain,
( ~ spl17_11
| spl17_13 ),
inference(rat,[],[s10,s26]) ).
cnf(s31,plain,
spl17_13,
inference(rat,[],[s29,s7]) ).
cnf(s32,plain,
~ spl17_12,
inference(rat,[],[s9,s31]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s6,s32,s7]) ).
fof(f1276,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU072+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.38 % Computer : n018.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 03:32:09 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.42 Running first-order model finding
% 0.09/0.42 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
% 0.17/0.49 % (2968504)Will run a generic schedule for satisfiability detection.
% 0.17/0.49 % (2968513)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1867617176:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.49 % (2968510)% WARNING: option uhcvi not known.
% 0.17/0.49 % (2968509)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=870947922_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.49 % (2968510)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=248613797:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.49 % (2968511)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2237726410:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.49 % (2968512)dis+10_1_sil=32000:sp=arity:random_seed=2524596417:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.49 % (2968514)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=750446846:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.49 % (2968515)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=894389634:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.49 % TRYING [1]
% 0.17/0.49 % TRYING [2]
% 0.17/0.49 % TRYING [3]
% 0.17/0.49 % TRYING [4]
% 0.17/0.49 % TRYING [5]
% 0.17/0.49 % (2968512) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2968504-2968512"...
% 0.17/0.49 % TRYING [6]
% 0.17/0.49 % (2968512)...printing done.
% 0.17/0.49 % (2968513)Instruction limit reached!
% 0.17/0.49 % (2968513)------------------------------
% 0.17/0.49 % (2968513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (2968513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (2968513)CaDiCaL version: 2.1.3
% 0.17/0.49 % (2968513)Termination reason: Instruction limit
% 0.17/0.49 % (2968513)Termination phase: Saturation
% 0.17/0.49 % (2968513)Time elapsed: 0.040 s
% 0.17/0.49 % (2968513)Peak memory usage: 13 MB
% 0.17/0.49 % (2968513)Instructions burned: 117 (million)
% 0.17/0.49 % (2968512)Refutation found. Thanks to Tanya!
% 0.17/0.49 % SZS status Theorem for theBenchmark
% 0.17/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.49 % (2968512)------------------------------
% 0.17/0.49 % (2968512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (2968512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (2968512)CaDiCaL version: 2.1.3
% 0.17/0.49 % (2968512)Termination reason: Refutation
% 0.17/0.49 % (2968512)Time elapsed: 0.030 s
% 0.17/0.49 % (2968512)Peak memory usage: 13 MB
% 0.17/0.49 % (2968512)Instructions burned: 47 (million)
% 0.17/0.49 % (2968504)Success in time 0.065 s
% 0.17/0.49 % Vampire exiting
%------------------------------------------------------------------------------