%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU051+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:47:08 PM UTC 2026
% Result : Theorem 4.33s 1.52s
% Output : Refutation 5.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 70 ( 18 unt; 2 def)
% Number of atoms : 360 ( 59 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 457 ( 167 ~; 169 |; 90 &)
% ( 19 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 203 ( 180 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f7,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f13,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_rng_restriction(X0,X1))
& function(relation_rng_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(f27,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> subset(relation_image(relation_rng_restriction(X0,X2),X1),relation_image(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_funct_1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> subset(relation_image(relation_rng_restriction(X0,X2),X1),relation_image(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f36,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_1) ).
fof(f38,plain,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X4] :
( in(X4,relation_dom(X1))
=> apply(X2,X4) = apply(X1,X4) ) ) ) ) ),
inference(rectify,[],[f36]) ).
fof(f40,plain,
? [X0,X1,X2] :
( ~ subset(relation_image(relation_rng_restriction(X0,X2),X1),relation_image(X2,X1))
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f28]) ).
fof(f41,plain,
? [X0,X1,X2] :
( ~ subset(relation_image(relation_rng_restriction(X0,X2),X1),relation_image(X2,X1))
& relation(X2)
& function(X2) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f43,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f42]) ).
fof(f45,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f46,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ( relation(relation_rng_restriction(X0,X1))
& function(relation_rng_restriction(X0,X1)) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f48,plain,
! [X0,X1] :
( ( relation(relation_rng_restriction(X0,X1))
& function(relation_rng_restriction(X0,X1)) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f51,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f52,definition,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f53,definition,
! [X1,X0,X2] :
( ( X1 = relation_rng_restriction(X0,X2)
<=> sP0(X2,X0,X1) )
| ~ sP1(X1,X0,X2) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f54,plain,
! [X0,X1] :
( ! [X2] :
( sP1(X1,X0,X2)
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(definition_folding,[],[f46,f53,f52]) ).
fof(f55,plain,
( ~ subset(relation_image(relation_rng_restriction(sK2,sK4),sK3),relation_image(sK4,sK3))
& relation(sK4)
& function(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f41]) ).
fof(f56,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 ) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f43]) ).
fof(f57,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,relation_dom(X0))
& in(X5,X1)
& apply(X0,X5) = X3 )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6 ) )
& ( ? [X8] :
( in(X8,relation_dom(X0))
& in(X8,X1)
& apply(X0,X8) = X6 )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f56]) ).
fof(f58,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != sK5(X0,X1,X2) )
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( in(sK6(X0,X1,X2),relation_dom(X0))
& in(sK6(X0,X1,X2),X1)
& sK5(X0,X1,X2) = apply(X0,sK6(X0,X1,X2)) )
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6 ) )
& ( ( in(sK7(X0,X1,X6),relation_dom(X0))
& in(sK7(X0,X1,X6),X1)
& apply(X0,sK7(X0,X1,X6)) = X6 )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X3,sK5(X0,X1,X2)),skolemize(X5,sK6(X0,X1,X2)),skolemize(X8,sK7(X0,X1,X6))],[f57]) ).
fof(f61,plain,
! [X1,X0,X2] :
( ( ( X1 = relation_rng_restriction(X0,X2)
| ~ sP0(X2,X0,X1) )
& ( sP0(X2,X0,X1)
| relation_rng_restriction(X0,X2) != X1 ) )
| ~ sP1(X1,X0,X2) ),
inference(nnf_transformation,[],[f53]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( ( relation_rng_restriction(X1,X2) = X0
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| relation_rng_restriction(X1,X2) != X0 ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X2))
| ~ in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(X1)) )
& ( ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) )
| in(X3,relation_dom(X1)) ) )
| ? [X4] :
( apply(X2,X4) != apply(X1,X4)
& in(X4,relation_dom(X1)) ) )
& ( ( ! [X3] :
( ( in(X3,relation_dom(X1))
| ~ in(X3,relation_dom(X2))
| ~ in(apply(X2,X3),X0) )
& ( ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) )
| ~ in(X3,relation_dom(X1)) ) )
& ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ) )
| ~ sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X2))
| ~ in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(X1)) )
& ( ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) )
| in(X3,relation_dom(X1)) ) )
| ? [X4] :
( apply(X2,X4) != apply(X1,X4)
& in(X4,relation_dom(X1)) ) )
& ( ( ! [X3] :
( ( in(X3,relation_dom(X1))
| ~ in(X3,relation_dom(X2))
| ~ in(apply(X2,X3),X0) )
& ( ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) )
| ~ in(X3,relation_dom(X1)) ) )
& ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ) )
| ~ sP0(X2,X0,X1) ) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X2)) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,relation_dom(X2)) ) )
| ? [X4] :
( apply(X0,X4) != apply(X2,X4)
& in(X4,relation_dom(X2)) ) )
& ( ( ! [X5] :
( ( in(X5,relation_dom(X2))
| ~ in(X5,relation_dom(X0))
| ~ in(apply(X0,X5),X1) )
& ( ( in(X5,relation_dom(X0))
& in(apply(X0,X5),X1) )
| ~ in(X5,relation_dom(X2)) ) )
& ! [X6] :
( apply(X0,X6) = apply(X2,X6)
| ~ in(X6,relation_dom(X2)) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ~ in(sK10(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK10(X0,X1,X2)),X1)
| ~ in(sK10(X0,X1,X2),relation_dom(X2)) )
& ( ( in(sK10(X0,X1,X2),relation_dom(X0))
& in(apply(X0,sK10(X0,X1,X2)),X1) )
| in(sK10(X0,X1,X2),relation_dom(X2)) ) )
| ( apply(X0,sK11(X0,X2)) != apply(X2,sK11(X0,X2))
& in(sK11(X0,X2),relation_dom(X2)) ) )
& ( ( ! [X5] :
( ( in(X5,relation_dom(X2))
| ~ in(X5,relation_dom(X0))
| ~ in(apply(X0,X5),X1) )
& ( ( in(X5,relation_dom(X0))
& in(apply(X0,X5),X1) )
| ~ in(X5,relation_dom(X2)) ) )
& ! [X6] :
( apply(X0,X6) = apply(X2,X6)
| ~ in(X6,relation_dom(X2)) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X3,sK10(X0,X1,X2)),skolemize(X4,sK11(X0,X2))],[f65]) ).
fof(f70,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f71,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK14(X0,X1),X1)
& in(sK14(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X2,sK14(X0,X1))],[f71]) ).
fof(f73,plain,
function(sK4),
inference(cnf_transformation,[],[f55]) ).
fof(f74,plain,
relation(sK4),
inference(cnf_transformation,[],[f55]) ).
fof(f75,plain,
~ subset(relation_image(relation_rng_restriction(sK2,sK4),sK3),relation_image(sK4,sK3)),
inference(cnf_transformation,[],[f55]) ).
fof(f76,plain,
! [X2,X0,X1,X6] :
( apply(X0,sK7(X0,X1,X6)) = X6
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f77,plain,
! [X2,X0,X1,X6] :
( in(sK7(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f78,plain,
! [X2,X0,X1,X6] :
( in(sK7(X0,X1,X6),relation_dom(X0))
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f79,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f90,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| relation_rng_restriction(X1,X2) != X0
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f62]) ).
fof(f92,plain,
! [X2,X0,X1,X6] :
( ~ sP0(X0,X1,X2)
| ~ in(X6,relation_dom(X2))
| apply(X0,X6) = apply(X2,X6) ),
inference(cnf_transformation,[],[f66]) ).
fof(f94,plain,
! [X2,X0,X1,X5] :
( ~ sP0(X0,X1,X2)
| ~ in(X5,relation_dom(X2))
| in(X5,relation_dom(X0)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f102,plain,
! [X2,X0,X1] :
( sP1(X1,X0,X2)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f103,plain,
! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f105,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f115,plain,
! [X0,X1] :
( in(sK14(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f116,plain,
! [X0,X1] :
( ~ in(sK14(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f117,plain,
! [X2,X0,X1,X7] :
( in(apply(X0,X7),X2)
| ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f79]) ).
fof(f118,plain,
! [X0,X1,X7] :
( in(apply(X0,X7),relation_image(X0,X1))
| ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f117]) ).
fof(f119,plain,
! [X0,X1,X6] :
( in(sK7(X0,X1,X6),relation_dom(X0))
| ~ in(X6,relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f78]) ).
fof(f120,plain,
! [X0,X1,X6] :
( in(sK7(X0,X1,X6),X1)
| ~ in(X6,relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f77]) ).
fof(f121,plain,
! [X0,X1,X6] :
( ~ in(X6,relation_image(X0,X1))
| apply(X0,sK7(X0,X1,X6)) = X6
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f76]) ).
fof(f122,plain,
! [X2,X1] :
( ~ sP1(relation_rng_restriction(X1,X2),X1,X2)
| sP0(X2,X1,relation_rng_restriction(X1,X2)) ),
inference(equality_resolution,[],[f90]) ).
fof(f127,plain,
! [X0] : relation(relation_rng_restriction(X0,sK4)),
inference(unit_resulting_resolution,[],[f105,f74]) ).
fof(f136,plain,
! [X0] : function(relation_rng_restriction(X0,sK4)),
inference(unit_resulting_resolution,[],[f103,f73,f74]) ).
fof(f141,plain,
in(sK14(relation_image(relation_rng_restriction(sK2,sK4),sK3),relation_image(sK4,sK3)),relation_image(relation_rng_restriction(sK2,sK4),sK3)),
inference(unit_resulting_resolution,[],[f115,f75]) ).
fof(f143,plain,
~ in(sK14(relation_image(relation_rng_restriction(sK2,sK4),sK3),relation_image(sK4,sK3)),relation_image(sK4,sK3)),
inference(unit_resulting_resolution,[],[f116,f75]) ).
fof(f168,plain,
! [X0,X1] : sP1(relation_rng_restriction(X0,sK4),X1,sK4),
inference(unit_resulting_resolution,[],[f102,f136,f127,f73,f74]) ).
fof(f196,plain,
! [X0] : sP0(sK4,X0,relation_rng_restriction(X0,sK4)),
inference(unit_resulting_resolution,[],[f122,f168]) ).
fof(f206,plain,
sK14(relation_image(relation_rng_restriction(sK2,sK4),sK3),relation_image(sK4,sK3)) = apply(relation_rng_restriction(sK2,sK4),sK7(relation_rng_restriction(sK2,sK4),sK3,sK14(relation_image(relation_rng_restriction(sK2,sK4),sK3),relation_image(sK4,sK3)))),
inference(unit_resulting_resolution,[],[f121,f136,f127,f141]) ).
fof(f207,plain,
in(sK7(relation_rng_restriction(sK2,sK4),sK3,sK14(relation_image(relation_rng_restriction(sK2,sK4),sK3),relation_image(sK4,sK3))),relation_dom(relation_rng_restriction(sK2,sK4))),
inference(unit_resulting_resolution,[],[f119,f136,f127,f141]) ).
fof(f208,plain,
in(sK7(relation_rng_restriction(sK2,sK4),sK3,sK14(relation_image(relation_rng_restriction(sK2,sK4),sK3),relation_image(sK4,sK3))),sK3),
inference(unit_resulting_resolution,[],[f120,f136,f127,f141]) ).
fof(f256,plain,
apply(relation_rng_restriction(sK2,sK4),sK7(relation_rng_restriction(sK2,sK4),sK3,sK14(relation_image(relation_rng_restriction(sK2,sK4),sK3),relation_image(sK4,sK3)))) = apply(sK4,sK7(relation_rng_restriction(sK2,sK4),sK3,sK14(relation_image(relation_rng_restriction(sK2,sK4),sK3),relation_image(sK4,sK3)))),
inference(unit_resulting_resolution,[],[f92,f196,f207]) ).
fof(f258,plain,
in(sK7(relation_rng_restriction(sK2,sK4),sK3,sK14(relation_image(relation_rng_restriction(sK2,sK4),sK3),relation_image(sK4,sK3))),relation_dom(sK4)),
inference(unit_resulting_resolution,[],[f94,f196,f207]) ).
fof(f263,plain,
sK14(relation_image(relation_rng_restriction(sK2,sK4),sK3),relation_image(sK4,sK3)) = apply(sK4,sK7(relation_rng_restriction(sK2,sK4),sK3,sK14(relation_image(relation_rng_restriction(sK2,sK4),sK3),relation_image(sK4,sK3)))),
inference(forward_demodulation,[],[f256,f206]) ).
fof(f533,plain,
in(apply(sK4,sK7(relation_rng_restriction(sK2,sK4),sK3,sK14(relation_image(relation_rng_restriction(sK2,sK4),sK3),relation_image(sK4,sK3)))),relation_image(sK4,sK3)),
inference(unit_resulting_resolution,[],[f118,f73,f74,f208,f258]) ).
fof(f540,plain,
in(sK14(relation_image(relation_rng_restriction(sK2,sK4),sK3),relation_image(sK4,sK3)),relation_image(sK4,sK3)),
inference(forward_demodulation,[],[f533,f263]) ).
fof(f545,plain,
$false,
inference(forward_subsumption_resolution,[],[f540,f143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU051+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 03:28:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.33/1.52 % (3998090)Detected formulas, will run a generic FOF schedule.
% 4.33/1.52 % (3998100)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2657333004:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.33/1.52 % (3998095)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=3207248582:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.33/1.52 % (3998098)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1862847924:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.33/1.52 % (3998099)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2887861955:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.33/1.52 % (3998096)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=4006985829:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.33/1.52 % (3998097)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=3654555014:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.33/1.52 % (3998098)Refutation not found, incomplete strategy
% 4.33/1.52 % (3998098)------------------------------
% 4.33/1.52 % (3998098)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.52 % (3998098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.52 % (3998098)CaDiCaL version: 2.1.3
% 4.33/1.52 % (3998098)Termination reason: Refutation not found, incomplete strategy
% 4.33/1.52 % (3998098)Time elapsed: 0.002 s
% 4.33/1.52 % (3998098)Peak memory usage: 88 MB
% 4.33/1.52 % (3998098)Instructions burned: 2 (million)
% 4.33/1.52 % (3998100)Instruction limit reached!
% 4.33/1.52 % (3998100)------------------------------
% 4.33/1.52 % (3998100)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.52 % (3998100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.52 % (3998100)CaDiCaL version: 2.1.3
% 4.33/1.52 % (3998100)Termination reason: Instruction limit
% 4.33/1.52 % (3998100)Termination phase: Saturation
% 4.33/1.52 % (3998100)Time elapsed: 0.054 s
% 4.33/1.52 % (3998100)Peak memory usage: 89 MB
% 4.33/1.52 % (3998100)Instructions burned: 140 (million)
% 4.33/1.52 % (3998101)dis-21_1_sil=8000:lcm=predicate:random_seed=3229580256: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)
% 4.33/1.52 % (3998099)Instruction limit reached!
% 4.33/1.52 % (3998099)------------------------------
% 4.33/1.52 % (3998099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.52 % (3998099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.52 % (3998099)CaDiCaL version: 2.1.3
% 4.33/1.52 % (3998099)Termination reason: Instruction limit
% 4.33/1.52 % (3998099)Termination phase: Saturation
% 4.33/1.52 % (3998099)Time elapsed: 0.071 s
% 4.33/1.52 % (3998099)Peak memory usage: 88 MB
% 4.33/1.52 % (3998099)Instructions burned: 119 (million)
% 4.33/1.52 % (3998101)Instruction limit reached!
% 4.33/1.52 % (3998101)------------------------------
% 4.33/1.52 % (3998101)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.52 % (3998101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.52 % (3998101)CaDiCaL version: 2.1.3
% 4.33/1.52 % (3998101)Termination reason: Instruction limit
% 4.33/1.52 % (3998101)Termination phase: Saturation
% 4.33/1.52 % (3998101)Time elapsed: 0.073 s
% 4.33/1.52 % (3998101)Peak memory usage: 90 MB
% 4.33/1.52 % (3998101)Instructions burned: 130 (million)
% 4.33/1.52 % (3998109)lrs+10_1_sil=8000:sp=occurrence:random_seed=2912723511:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.33/1.52 % (3998110)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1305112127:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.33/1.52 % (3998109)Instruction limit reached!
% 4.33/1.52 % (3998109)------------------------------
% 4.33/1.52 % (3998109)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.52 % (3998109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.52 % (3998109)CaDiCaL version: 2.1.3
% 4.33/1.52 % (3998109)Termination reason: Instruction limit
% 4.33/1.52 % (3998109)Termination phase: Saturation
% 4.33/1.52 % (3998109)Time elapsed: 0.092 s
% 4.33/1.52 % (3998109)Peak memory usage: 91 MB
% 4.33/1.52 % (3998109)Instructions burned: 286 (million)
% 4.33/1.52 % (3998098)------------------------------
% 4.33/1.52 % (3998098)------------------------------
% 4.33/1.52 % (3998111)lrs+1011_1_sil=32000:sp=occurrence:random_seed=42292690:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.33/1.52 % (3998110)First to succeed.
% 4.33/1.52 % (3998110)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3998090"
% 4.33/1.52 % (3998114)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=482701601:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.33/1.52 % (3998116)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2373638992:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.33/1.52 % (3998116)Refutation not found, incomplete strategy
% 4.33/1.52 % (3998116)------------------------------
% 4.33/1.52 % (3998116)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.52 % (3998116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.52 % (3998116)CaDiCaL version: 2.1.3
% 4.33/1.52 % (3998116)Termination reason: Refutation not found, incomplete strategy
% 4.33/1.52 % (3998116)Time elapsed: 0.003 s
% 4.33/1.52 % (3998116)Peak memory usage: 88 MB
% 4.33/1.52 % (3998116)Instructions burned: 3 (million)
% 4.33/1.52 % (3998114)Instruction limit reached!
% 4.33/1.52 % (3998114)------------------------------
% 4.33/1.52 % (3998114)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.52 % (3998114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.52 % (3998114)CaDiCaL version: 2.1.3
% 4.33/1.52 % (3998114)Termination reason: Instruction limit
% 4.33/1.52 % (3998114)Termination phase: Saturation
% 4.33/1.52 % (3998114)Time elapsed: 0.070 s
% 4.33/1.52 % (3998114)Peak memory usage: 91 MB
% 4.33/1.52 % (3998114)Instructions burned: 248 (million)
% 4.33/1.52 % (3998111)Instruction limit reached!
% 4.33/1.52 % (3998111)------------------------------
% 4.33/1.52 % (3998111)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.52 % (3998111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.52 % (3998111)CaDiCaL version: 2.1.3
% 4.33/1.52 % (3998111)Termination reason: Instruction limit
% 4.33/1.52 % (3998111)Termination phase: Saturation
% 4.33/1.52 % (3998111)Time elapsed: 0.227 s
% 4.33/1.52 % (3998111)Peak memory usage: 92 MB
% 4.33/1.52 % (3998111)Instructions burned: 325 (million)
% 4.33/1.52 % (3998110)Refutation found. Thanks to Tanya!
% 4.33/1.52 % SZS status Theorem for theBenchmark
% 4.33/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 5.38/1.71 % (3998110)------------------------------
% 5.38/1.71 % (3998110)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.71 % (3998110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.71 % (3998110)CaDiCaL version: 2.1.3
% 5.38/1.71 % (3998110)Termination reason: Refutation
% 5.38/1.71 % (3998110)Time elapsed: 0.028 s
% 5.38/1.71 % (3998110)Peak memory usage: 89 MB
% 5.38/1.71 % (3998110)Instructions burned: 46 (million)
% 5.38/1.71 % (3998110)------------------------------
% 5.38/1.71 % (3998110)------------------------------
% 5.38/1.71 % (3998090)Success in time 0.678 s
% 5.38/1.71 % Vampire exiting
%------------------------------------------------------------------------------