%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU228+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:47:52 PM UTC 2026
% Result : Theorem 3.55s 1.47s
% Output : Refutation 4.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 68 ( 15 unt; 0 def)
% Number of atoms : 386 ( 80 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 508 ( 190 ~; 194 |; 94 &)
% ( 21 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 2 con; 0-3 aty)
% Number of variables : 185 ( 158 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f6,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/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f7,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,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/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f30,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_1) ).
fof(f31,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( subset(X0,relation_rng(X1))
=> relation_image(X1,relation_inverse_image(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).
fof(f32,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( subset(X0,relation_rng(X1))
=> relation_image(X1,relation_inverse_image(X1,X0)) = X0 ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f42,plain,
? [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) != X0
& subset(X0,relation_rng(X1))
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f43,plain,
? [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) != X0
& subset(X0,relation_rng(X1))
& relation(X1)
& function(X1) ),
inference(flattening,[],[f42]) ).
fof(f46,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,[],[f9]) ).
fof(f47,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,[],[f46]) ).
fof(f48,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f49,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f48]) ).
fof(f50,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,[],[f6]) ).
fof(f51,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,[],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f53,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f52]) ).
fof(f59,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f60,plain,
( sK0 != relation_image(sK1,relation_inverse_image(sK1,sK0))
& subset(sK0,relation_rng(sK1))
& relation(sK1)
& function(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f43]) ).
fof(f61,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,[],[f47]) ).
fof(f62,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,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK2(X0,X1) )
| ~ in(sK2(X0,X1),X1) )
& ( ( in(sK3(X0,X1),relation_dom(X0))
& sK2(X0,X1) = apply(X0,sK3(X0,X1)) )
| in(sK2(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK4(X0,X5),relation_dom(X0))
& apply(X0,sK4(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X2,sK2(X0,X1)),skolemize(X4,sK3(X0,X1)),skolemize(X7,sK4(X0,X5))],[f62]) ).
fof(f64,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f49]) ).
fof(f65,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,X2) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) )
& ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f65]) ).
fof(f67,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ( ( ~ in(sK5(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK5(X0,X1,X2)),X1)
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( in(sK5(X0,X1,X2),relation_dom(X0))
& in(apply(X0,sK5(X0,X1,X2)),X1) )
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1) )
& ( ( in(X4,relation_dom(X0))
& in(apply(X0,X4),X1) )
| ~ in(X4,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f66]) ).
fof(f68,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,[],[f51]) ).
fof(f69,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,[],[f68]) ).
fof(f70,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != sK6(X0,X1,X2) )
| ~ in(sK6(X0,X1,X2),X2) )
& ( ( in(sK7(X0,X1,X2),relation_dom(X0))
& in(sK7(X0,X1,X2),X1)
& sK6(X0,X1,X2) = apply(X0,sK7(X0,X1,X2)) )
| in(sK6(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6 ) )
& ( ( in(sK8(X0,X1,X6),relation_dom(X0))
& in(sK8(X0,X1,X6),X1)
& apply(X0,sK8(X0,X1,X6)) = X6 )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X3,sK6(X0,X1,X2)),skolemize(X5,sK7(X0,X1,X2)),skolemize(X8,sK8(X0,X1,X6))],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f72,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f71]) ).
fof(f78,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,[],[f59]) ).
fof(f79,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,[],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK13(X0,X1),X1)
& in(sK13(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X2,sK13(X0,X1))],[f79]) ).
fof(f81,plain,
function(sK1),
inference(cnf_transformation,[],[f60]) ).
fof(f82,plain,
relation(sK1),
inference(cnf_transformation,[],[f60]) ).
fof(f83,plain,
subset(sK0,relation_rng(sK1)),
inference(cnf_transformation,[],[f60]) ).
fof(f84,plain,
sK0 != relation_image(sK1,relation_inverse_image(sK1,sK0)),
inference(cnf_transformation,[],[f60]) ).
fof(f87,plain,
! [X0,X1,X5] :
( apply(X0,sK4(X0,X5)) = X5
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f88,plain,
! [X0,X1,X5] :
( in(sK4(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f95,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,relation_dom(X0))
| ~ in(apply(X0,X4),X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f102,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,[],[f70]) ).
fof(f109,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f72]) ).
fof(f110,plain,
! [X0,X1] :
( subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f128,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f129,plain,
! [X0,X1] :
( in(sK13(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f130,plain,
! [X0,X1] :
( ~ in(sK13(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f133,plain,
! [X0,X5] :
( in(sK4(X0,X5),relation_dom(X0))
| ~ in(X5,relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f88]) ).
fof(f134,plain,
! [X0,X5] :
( ~ in(X5,relation_rng(X0))
| apply(X0,sK4(X0,X5)) = X5
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f87]) ).
fof(f135,plain,
! [X0,X1,X4] :
( ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,relation_inverse_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f95]) ).
fof(f138,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,[],[f102]) ).
fof(f139,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,[],[f138]) ).
fof(f195,plain,
! [X0] : subset(relation_image(sK1,relation_inverse_image(sK1,X0)),X0),
inference(unit_resulting_resolution,[],[f110,f81,f82]) ).
fof(f200,plain,
~ subset(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0))),
inference(unit_resulting_resolution,[],[f109,f84,f195]) ).
fof(f206,plain,
~ in(sK13(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0))),relation_image(sK1,relation_inverse_image(sK1,sK0))),
inference(unit_resulting_resolution,[],[f130,f200]) ).
fof(f207,plain,
in(sK13(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0))),sK0),
inference(unit_resulting_resolution,[],[f129,f200]) ).
fof(f214,plain,
in(sK13(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0))),relation_rng(sK1)),
inference(unit_resulting_resolution,[],[f128,f83,f207]) ).
fof(f216,plain,
sK13(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0))) = apply(sK1,sK4(sK1,sK13(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0))))),
inference(unit_resulting_resolution,[],[f134,f81,f82,f214]) ).
fof(f217,plain,
in(sK4(sK1,sK13(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0)))),relation_dom(sK1)),
inference(unit_resulting_resolution,[],[f133,f81,f82,f214]) ).
fof(f337,plain,
! [X0] :
( ~ in(sK13(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0))),X0)
| ~ in(sK4(sK1,sK13(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0)))),relation_dom(sK1))
| in(sK4(sK1,sK13(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0)))),relation_inverse_image(sK1,X0))
| ~ relation(sK1)
| ~ function(sK1) ),
inference(superposition,[],[f135,f216]) ).
fof(f339,plain,
! [X0] :
( ~ in(sK13(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0))),X0)
| in(sK4(sK1,sK13(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0)))),relation_inverse_image(sK1,X0))
| ~ relation(sK1)
| ~ function(sK1) ),
inference(forward_subsumption_resolution,[],[f337,f217]) ).
fof(f343,plain,
! [X0] :
( ~ in(sK13(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0))),X0)
| in(sK4(sK1,sK13(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0)))),relation_inverse_image(sK1,X0))
| ~ function(sK1) ),
inference(forward_subsumption_resolution,[],[f339,f82]) ).
fof(f347,plain,
! [X0] :
( in(sK4(sK1,sK13(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0)))),relation_inverse_image(sK1,X0))
| ~ in(sK13(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0))),X0) ),
inference(forward_subsumption_resolution,[],[f343,f81]) ).
fof(f546,plain,
in(sK4(sK1,sK13(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0)))),relation_inverse_image(sK1,sK0)),
inference(unit_resulting_resolution,[],[f347,f207]) ).
fof(f551,plain,
in(apply(sK1,sK4(sK1,sK13(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0))))),relation_image(sK1,relation_inverse_image(sK1,sK0))),
inference(unit_resulting_resolution,[],[f139,f81,f82,f217,f546]) ).
fof(f554,plain,
in(sK13(sK0,relation_image(sK1,relation_inverse_image(sK1,sK0))),relation_image(sK1,relation_inverse_image(sK1,sK0))),
inference(forward_demodulation,[],[f551,f216]) ).
fof(f555,plain,
$false,
inference(forward_subsumption_resolution,[],[f554,f206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU228+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 04:11:32 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 3.55/1.47 % (1547914)Detected formulas, will run a generic FOF schedule.
% 3.55/1.47 % (1547925)dis-21_1_sil=8000:lcm=predicate:random_seed=2734160885: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)
% 3.55/1.47 % (1547922)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3038365983:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.55/1.47 % (1547923)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3299152852:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.55/1.47 % (1547920)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=3398360566:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.55/1.47 % (1547919)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=1321262830:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.55/1.47 % (1547921)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=46334750:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.55/1.47 % (1547924)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2931238494:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.55/1.47 % (1547925)Instruction limit reached!
% 3.55/1.47 % (1547925)------------------------------
% 3.55/1.47 % (1547925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.47 % (1547925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.47 % (1547925)CaDiCaL version: 2.1.3
% 3.55/1.47 % (1547925)Termination reason: Instruction limit
% 3.55/1.47 % (1547925)Termination phase: Saturation
% 3.55/1.47 % (1547925)Time elapsed: 0.042 s
% 3.55/1.47 % (1547925)Peak memory usage: 91 MB
% 3.55/1.47 % (1547925)Instructions burned: 131 (million)
% 3.55/1.47 % (1547922)Instruction limit reached!
% 3.55/1.47 % (1547922)------------------------------
% 3.55/1.47 % (1547922)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.47 % (1547922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.47 % (1547922)CaDiCaL version: 2.1.3
% 3.55/1.47 % (1547922)Termination reason: Instruction limit
% 3.55/1.47 % (1547922)Termination phase: Saturation
% 3.55/1.47 % (1547922)Time elapsed: 0.057 s
% 3.55/1.47 % (1547922)Peak memory usage: 90 MB
% 3.55/1.47 % (1547922)Instructions burned: 109 (million)
% 3.55/1.47 % (1547923)Instruction limit reached!
% 3.55/1.47 % (1547923)------------------------------
% 3.55/1.47 % (1547923)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.47 % (1547923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.47 % (1547923)CaDiCaL version: 2.1.3
% 3.55/1.47 % (1547923)Termination reason: Instruction limit
% 3.55/1.47 % (1547923)Termination phase: Saturation
% 3.55/1.47 % (1547923)Time elapsed: 0.076 s
% 3.55/1.47 % (1547923)Peak memory usage: 88 MB
% 3.55/1.47 % (1547923)Instructions burned: 120 (million)
% 3.55/1.47 % (1547933)lrs+10_1_sil=8000:sp=occurrence:random_seed=879495211:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.55/1.47 % (1547924)Instruction limit reached!
% 3.55/1.47 % (1547924)------------------------------
% 3.55/1.47 % (1547924)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.47 % (1547924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.47 % (1547924)CaDiCaL version: 2.1.3
% 3.55/1.47 % (1547924)Termination reason: Instruction limit
% 3.55/1.47 % (1547924)Termination phase: Saturation
% 3.55/1.47 % (1547924)Time elapsed: 0.100 s
% 3.55/1.47 % (1547924)Peak memory usage: 90 MB
% 3.55/1.47 % (1547924)Instructions burned: 139 (million)
% 3.55/1.47 % (1547933)Instruction limit reached!
% 3.55/1.47 % (1547933)------------------------------
% 3.55/1.47 % (1547933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.47 % (1547933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.47 % (1547933)CaDiCaL version: 2.1.3
% 3.55/1.47 % (1547933)Termination reason: Instruction limit
% 3.55/1.47 % (1547933)Termination phase: Saturation
% 3.55/1.47 % (1547933)Time elapsed: 0.088 s
% 3.55/1.47 % (1547933)Peak memory usage: 92 MB
% 3.55/1.47 % (1547933)Instructions burned: 286 (million)
% 3.55/1.47 % (1547934)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3352189980:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.55/1.47 % (1547935)lrs+1011_1_sil=32000:sp=occurrence:random_seed=681509249:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.55/1.47 % (1547934)First to succeed.
% 3.55/1.47 % (1547934)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1547914"
% 3.55/1.47 % (1547937)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=3219780633:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 3.55/1.47 % (1547938)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4216888476:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 3.55/1.47 % (1547938)Instruction limit reached!
% 3.55/1.47 % (1547938)------------------------------
% 3.55/1.47 % (1547938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.47 % (1547938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.47 % (1547938)CaDiCaL version: 2.1.3
% 3.55/1.47 % (1547938)Termination reason: Instruction limit
% 3.55/1.47 % (1547938)Termination phase: Saturation
% 3.55/1.47 % (1547938)Time elapsed: 0.070 s
% 3.55/1.47 % (1547938)Peak memory usage: 88 MB
% 3.55/1.47 % (1547938)Instructions burned: 297 (million)
% 3.55/1.47 % (1547937)Instruction limit reached!
% 3.55/1.47 % (1547937)------------------------------
% 3.55/1.47 % (1547937)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.47 % (1547937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.47 % (1547937)CaDiCaL version: 2.1.3
% 3.55/1.47 % (1547937)Termination reason: Instruction limit
% 3.55/1.47 % (1547937)Termination phase: Saturation
% 3.55/1.47 % (1547937)Time elapsed: 0.124 s
% 3.55/1.47 % (1547937)Peak memory usage: 91 MB
% 3.55/1.47 % (1547937)Instructions burned: 250 (million)
% 3.55/1.47 % (1547943)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1721550581:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 3.55/1.47 % (1547935)Instruction limit reached!
% 3.55/1.47 % (1547935)------------------------------
% 3.55/1.47 % (1547935)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.47 % (1547935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.47 % (1547935)CaDiCaL version: 2.1.3
% 3.55/1.47 % (1547935)Termination reason: Instruction limit
% 3.55/1.47 % (1547935)Termination phase: Saturation
% 3.55/1.47 % (1547935)Time elapsed: 0.212 s
% 3.55/1.47 % (1547935)Peak memory usage: 91 MB
% 3.55/1.47 % (1547935)Instructions burned: 325 (million)
% 3.55/1.47 % (1547934)Refutation found. Thanks to Tanya!
% 3.55/1.47 % SZS status Theorem for theBenchmark
% 3.55/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 4.95/1.67 % (1547934)------------------------------
% 4.95/1.67 % (1547934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.95/1.67 % (1547934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.67 % (1547934)CaDiCaL version: 2.1.3
% 4.95/1.67 % (1547934)Termination reason: Refutation
% 4.95/1.67 % (1547934)Time elapsed: 0.020 s
% 4.95/1.67 % (1547934)Peak memory usage: 89 MB
% 4.95/1.67 % (1547934)Instructions burned: 32 (million)
% 4.95/1.67 % (1547934)------------------------------
% 4.95/1.67 % (1547934)------------------------------
% 4.95/1.67 % (1547914)Success in time 0.62 s
% 4.95/1.67 % Vampire exiting
%------------------------------------------------------------------------------