%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU071+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 : 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 12:51:53 PM UTC 2026
% Result : Theorem 0.93s 0.64s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 119 ( 20 unt; 10 def)
% Number of atoms : 520 ( 77 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 668 ( 267 ~; 281 |; 84 &)
% ( 27 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 11 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-3 aty)
% Number of variables : 184 ( 0 sgn 162 !; 22 ?)
% 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] :
( ( 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/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f8,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(f27,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> subset(relation_inverse_image(X1,relation_image(X1,X0)),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_funct_1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> subset(relation_inverse_image(X1,relation_image(X1,X0)),X0) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f45,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(f46,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,[],[f45]) ).
fof(f47,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,[],[f6]) ).
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(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f50,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,[],[f8]) ).
fof(f51,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,[],[f50]) ).
fof(f56,plain,
? [X0,X1] :
( ~ subset(relation_inverse_image(X1,relation_image(X1,X0)),X0)
& one_to_one(X1)
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f57,plain,
? [X0,X1] :
( ~ subset(relation_inverse_image(X1,relation_image(X1,X0)),X0)
& one_to_one(X1)
& relation(X1)
& function(X1) ),
inference(flattening,[],[f56]) ).
fof(f67,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,[],[f46]) ).
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) )
& ( ? [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,[],[f67]) ).
fof(f69,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != sK0(X0,X1,X2) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),relation_dom(X0))
& in(sK1(X0,X1,X2),X1)
& sK0(X0,X1,X2) = apply(X0,sK1(X0,X1,X2)) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6 ) )
& ( ( in(sK2(X0,X1,X6),relation_dom(X0))
& in(sK2(X0,X1,X6),X1)
& apply(X0,sK2(X0,X1,X6)) = X6 )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2)),skolemize(X8,sK2(X0,X1,X6))],[f68]) ).
fof(f70,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,[],[f48]) ).
fof(f71,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,[],[f70]) ).
fof(f72,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,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ( ( ~ in(sK3(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK3(X0,X1,X2)),X1)
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(sK3(X0,X1,X2),relation_dom(X0))
& in(apply(X0,sK3(X0,X1,X2)),X1) )
| in(sK3(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,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f72]) ).
fof(f74,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,[],[f49]) ).
fof(f75,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,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK4(X0,X1),X1)
& in(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f75]) ).
fof(f77,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,[],[f51]) ).
fof(f78,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,X4) != apply(X0,X3) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ( ( one_to_one(X0)
| ( sK5(X0) != sK6(X0)
& in(sK5(X0),relation_dom(X0))
& in(sK6(X0),relation_dom(X0))
& apply(X0,sK5(X0)) = apply(X0,sK6(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X4) != apply(X0,X3) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X1,sK5(X0)),skolemize(X2,sK6(X0))],[f78]) ).
fof(f91,plain,
( ~ subset(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18)
& one_to_one(sK19)
& relation(sK19)
& function(sK19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19]),skolemize(X0,sK18),skolemize(X1,sK19)],[f57]) ).
fof(f99,plain,
! [X2,X0,X1,X6] :
( apply(X0,sK2(X0,X1,X6)) = X6
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f100,plain,
! [X2,X0,X1,X6] :
( in(sK2(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f101,plain,
! [X2,X0,X1,X6] :
( in(sK2(X0,X1,X6),relation_dom(X0))
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f107,plain,
! [X2,X0,X1,X4] :
( in(apply(X0,X4),X1)
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f108,plain,
! [X2,X0,X1,X4] :
( in(X4,relation_dom(X0))
| ~ in(X4,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f114,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f115,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f116,plain,
! [X3,X0,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X4) != apply(X0,X3)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f151,plain,
function(sK19),
inference(cnf_transformation,[],[f91]) ).
fof(f152,plain,
relation(sK19),
inference(cnf_transformation,[],[f91]) ).
fof(f153,plain,
one_to_one(sK19),
inference(cnf_transformation,[],[f91]) ).
fof(f154,plain,
~ subset(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18),
inference(cnf_transformation,[],[f91]) ).
fof(f166,plain,
! [X0,X1,X6] :
( in(sK2(X0,X1,X6),relation_dom(X0))
| ~ in(X6,relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f101]) ).
fof(f167,plain,
! [X0,X1,X6] :
( in(sK2(X0,X1,X6),X1)
| ~ in(X6,relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f100]) ).
fof(f168,plain,
! [X0,X1,X6] :
( apply(X0,sK2(X0,X1,X6)) = X6
| ~ in(X6,relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f99]) ).
fof(f170,plain,
! [X0,X1,X4] :
( in(X4,relation_dom(X0))
| ~ in(X4,relation_inverse_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f108]) ).
fof(f171,plain,
! [X0,X1,X4] :
( in(apply(X0,X4),X1)
| ~ in(X4,relation_inverse_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f107]) ).
fof(f183,plain,
! [X0,X1,X6] :
( ~ in(sK2(X0,X1,X6),relation_dom(X0))
| in(X6,relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(consistent_polarity_flipping,[],[f166]) ).
fof(f184,plain,
! [X0,X1,X6] :
( in(X6,relation_image(X0,X1))
| ~ in(sK2(X0,X1,X6),X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(consistent_polarity_flipping,[],[f167]) ).
fof(f185,plain,
! [X0,X1,X6] :
( in(X6,relation_image(X0,X1))
| apply(X0,sK2(X0,X1,X6)) = X6
| ~ relation(X0)
| ~ function(X0) ),
inference(consistent_polarity_flipping,[],[f168]) ).
fof(f190,plain,
! [X0,X1,X4] :
( in(X4,relation_inverse_image(X0,X1))
| ~ in(X4,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(consistent_polarity_flipping,[],[f170]) ).
fof(f191,plain,
! [X0,X1,X4] :
( in(X4,relation_inverse_image(X0,X1))
| ~ in(apply(X0,X4),X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(consistent_polarity_flipping,[],[f171]) ).
fof(f192,plain,
! [X0,X1] :
( in(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f115]) ).
fof(f193,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK4(X0,X1),X0) ),
inference(consistent_polarity_flipping,[],[f114]) ).
fof(f197,plain,
! [X3,X0,X4] :
( apply(X0,X4) != apply(X0,X3)
| in(X3,relation_dom(X0))
| in(X4,relation_dom(X0))
| X3 = X4
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(consistent_polarity_flipping,[],[f116]) ).
fof(f547,plain,
~ in(sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18),relation_inverse_image(sK19,relation_image(sK19,sK18))),
inference(resolution,[],[f193,f154]) ).
fof(f2785,plain,
( ~ in(sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18),relation_dom(sK19))
| ~ relation(sK19)
| ~ function(sK19) ),
inference(resolution,[],[f190,f547]) ).
fof(f2788,definition,
( spl20_84
<=> function(sK19) ),
introduced(definition,[new_symbols(definition,[spl20_84])],[avatar_definition]) ).
fof(f2790,plain,
( ~ function(sK19)
| spl20_84 ),
inference(avatar_component_clause,[],[f2788]) ).
fof(f2792,definition,
( spl20_85
<=> relation(sK19) ),
introduced(definition,[new_symbols(definition,[spl20_85])],[avatar_definition]) ).
fof(f2794,plain,
( ~ relation(sK19)
| spl20_85 ),
inference(avatar_component_clause,[],[f2792]) ).
fof(f2796,definition,
( spl20_86
<=> in(sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18),relation_dom(sK19)) ),
introduced(definition,[new_symbols(definition,[spl20_86])],[avatar_definition]) ).
fof(f2799,plain,
( ~ spl20_84
| ~ spl20_85
| ~ spl20_86 ),
inference(avatar_split_clause,[],[f2785,f2796,f2792,f2788]) ).
fof(f2800,plain,
( $false
| spl20_84 ),
inference(resolution,[],[f2790,f151]) ).
fof(f2802,plain,
spl20_84,
inference(avatar_contradiction_clause,[],[f2800]) ).
fof(f2803,plain,
( $false
| spl20_85 ),
inference(resolution,[],[f2794,f152]) ).
fof(f2805,plain,
spl20_85,
inference(avatar_contradiction_clause,[],[f2803]) ).
fof(f2957,plain,
( ~ in(apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18)),relation_image(sK19,sK18))
| ~ relation(sK19)
| ~ function(sK19) ),
inference(resolution,[],[f191,f547]) ).
fof(f2960,definition,
( spl20_87
<=> in(apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18)),relation_image(sK19,sK18)) ),
introduced(definition,[new_symbols(definition,[spl20_87])],[avatar_definition]) ).
fof(f2962,plain,
( ~ in(apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18)),relation_image(sK19,sK18))
| spl20_87 ),
inference(avatar_component_clause,[],[f2960]) ).
fof(f2963,plain,
( ~ spl20_84
| ~ spl20_85
| ~ spl20_87 ),
inference(avatar_split_clause,[],[f2957,f2960,f2792,f2788]) ).
fof(f3423,plain,
( ~ in(sK2(sK19,sK18,apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18))),sK18)
| ~ relation(sK19)
| ~ function(sK19)
| spl20_87 ),
inference(resolution,[],[f184,f2962]) ).
fof(f3426,definition,
( spl20_88
<=> in(sK2(sK19,sK18,apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18))),sK18) ),
introduced(definition,[new_symbols(definition,[spl20_88])],[avatar_definition]) ).
fof(f3428,plain,
( ~ in(sK2(sK19,sK18,apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18))),sK18)
| spl20_88 ),
inference(avatar_component_clause,[],[f3426]) ).
fof(f3429,plain,
( ~ spl20_84
| ~ spl20_85
| ~ spl20_88
| spl20_87 ),
inference(avatar_split_clause,[],[f3423,f2960,f3426,f2792,f2788]) ).
fof(f4240,plain,
( apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18)) = apply(sK19,sK2(sK19,sK18,apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18))))
| ~ relation(sK19)
| ~ function(sK19)
| spl20_87 ),
inference(resolution,[],[f185,f2962]) ).
fof(f4251,definition,
( spl20_149
<=> apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18)) = apply(sK19,sK2(sK19,sK18,apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18)))) ),
introduced(definition,[new_symbols(definition,[spl20_149])],[avatar_definition]) ).
fof(f4253,plain,
( apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18)) = apply(sK19,sK2(sK19,sK18,apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18))))
| ~ spl20_149 ),
inference(avatar_component_clause,[],[f4251]) ).
fof(f4254,plain,
( ~ spl20_84
| ~ spl20_85
| spl20_149
| spl20_87 ),
inference(avatar_split_clause,[],[f4240,f2960,f4251,f2792,f2788]) ).
fof(f4473,definition,
( spl20_150
<=> in(sK2(sK19,sK18,apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18))),relation_dom(sK19)) ),
introduced(definition,[new_symbols(definition,[spl20_150])],[avatar_definition]) ).
fof(f4475,plain,
( in(sK2(sK19,sK18,apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18))),relation_dom(sK19))
| ~ spl20_150 ),
inference(avatar_component_clause,[],[f4473]) ).
fof(f4480,plain,
( in(apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18)),relation_image(sK19,sK18))
| ~ relation(sK19)
| ~ function(sK19)
| ~ spl20_150 ),
inference(resolution,[],[f4475,f183]) ).
fof(f4481,plain,
( ~ spl20_84
| ~ spl20_85
| spl20_87
| ~ spl20_150 ),
inference(avatar_split_clause,[],[f4480,f4473,f2960,f2792,f2788]) ).
fof(f5743,plain,
( ! [X0] :
( apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18)) != apply(sK19,X0)
| in(X0,relation_dom(sK19))
| in(sK2(sK19,sK18,apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18))),relation_dom(sK19))
| sK2(sK19,sK18,apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18))) = X0
| ~ one_to_one(sK19)
| ~ relation(sK19)
| ~ function(sK19) )
| ~ spl20_149 ),
inference(superposition,[],[f197,f4253]) ).
fof(f5752,definition,
( spl20_307
<=> one_to_one(sK19) ),
introduced(definition,[new_symbols(definition,[spl20_307])],[avatar_definition]) ).
fof(f5754,plain,
( ~ one_to_one(sK19)
| spl20_307 ),
inference(avatar_component_clause,[],[f5752]) ).
fof(f5764,definition,
( spl20_310
<=> ! [X0] :
( apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18)) != apply(sK19,X0)
| sK2(sK19,sK18,apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18))) = X0
| in(X0,relation_dom(sK19)) ) ),
introduced(definition,[new_symbols(definition,[spl20_310])],[avatar_definition]) ).
fof(f5765,plain,
( ! [X0] :
( apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18)) != apply(sK19,X0)
| sK2(sK19,sK18,apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18))) = X0
| in(X0,relation_dom(sK19)) )
| ~ spl20_310 ),
inference(avatar_component_clause,[],[f5764]) ).
fof(f5769,plain,
( ~ spl20_84
| ~ spl20_85
| ~ spl20_307
| spl20_150
| spl20_310
| ~ spl20_149 ),
inference(avatar_split_clause,[],[f5743,f4251,f5764,f4473,f5752,f2792,f2788]) ).
fof(f5770,plain,
( $false
| spl20_307 ),
inference(resolution,[],[f5754,f153]) ).
fof(f5773,plain,
spl20_307,
inference(avatar_contradiction_clause,[],[f5770]) ).
fof(f6528,plain,
( sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18) = sK2(sK19,sK18,apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18)))
| in(sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18),relation_dom(sK19))
| ~ spl20_310 ),
inference(equality_resolution,[],[f5765]) ).
fof(f6533,definition,
( spl20_335
<=> sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18) = sK2(sK19,sK18,apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18))) ),
introduced(definition,[new_symbols(definition,[spl20_335])],[avatar_definition]) ).
fof(f6535,plain,
( sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18) = sK2(sK19,sK18,apply(sK19,sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18)))
| ~ spl20_335 ),
inference(avatar_component_clause,[],[f6533]) ).
fof(f6536,plain,
( spl20_86
| spl20_335
| ~ spl20_310 ),
inference(avatar_split_clause,[],[f6528,f5764,f6533,f2796]) ).
fof(f6552,plain,
( ~ in(sK4(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18),sK18)
| spl20_88
| ~ spl20_335 ),
inference(superposition,[],[f3428,f6535]) ).
fof(f6607,plain,
( subset(relation_inverse_image(sK19,relation_image(sK19,sK18)),sK18)
| spl20_88
| ~ spl20_335 ),
inference(resolution,[],[f6552,f192]) ).
fof(f6611,plain,
( $false
| spl20_88
| ~ spl20_335 ),
inference(resolution,[],[f6607,f154]) ).
fof(f6613,plain,
( spl20_88
| ~ spl20_335 ),
inference(avatar_contradiction_clause,[],[f6611]) ).
cnf(s120,plain,
( ~ spl20_84
| ~ spl20_85
| ~ spl20_86 ),
inference(sat_conversion,[],[f2799]) ).
cnf(s121,plain,
spl20_84,
inference(sat_conversion,[],[f2802]) ).
cnf(s122,plain,
spl20_85,
inference(sat_conversion,[],[f2805]) ).
cnf(s147,plain,
( ~ spl20_84
| ~ spl20_85
| ~ spl20_87 ),
inference(sat_conversion,[],[f2963]) ).
cnf(s271,plain,
( ~ spl20_84
| ~ spl20_85
| spl20_87
| ~ spl20_88 ),
inference(sat_conversion,[],[f3429]) ).
cnf(s347,plain,
( ~ spl20_84
| ~ spl20_85
| spl20_87
| spl20_149 ),
inference(sat_conversion,[],[f4254]) ).
cnf(s370,plain,
( ~ spl20_84
| ~ spl20_85
| spl20_87
| ~ spl20_150 ),
inference(sat_conversion,[],[f4481]) ).
cnf(s591,plain,
( ~ spl20_84
| ~ spl20_85
| ~ spl20_149
| spl20_150
| ~ spl20_307
| spl20_310 ),
inference(sat_conversion,[],[f5769]) ).
cnf(s592,plain,
spl20_307,
inference(sat_conversion,[],[f5773]) ).
cnf(s619,plain,
( spl20_86
| ~ spl20_310
| spl20_335 ),
inference(sat_conversion,[],[f6536]) ).
cnf(s623,plain,
( spl20_88
| ~ spl20_335 ),
inference(sat_conversion,[],[f6613]) ).
cnf(s624,plain,
( ~ spl20_84
| ~ spl20_85
| ~ spl20_149
| spl20_150
| spl20_310 ),
inference(rat,[],[s591,s592]) ).
cnf(s673,plain,
~ spl20_87,
inference(rat,[],[s147,s122,s121]) ).
cnf(s674,plain,
~ spl20_150,
inference(rat,[],[s370,s121,s122,s673]) ).
cnf(s675,plain,
spl20_149,
inference(rat,[],[s347,s121,s122,s673]) ).
cnf(s676,plain,
~ spl20_88,
inference(rat,[],[s271,s121,s122,s673]) ).
cnf(s679,plain,
spl20_310,
inference(rat,[],[s624,s674,s121,s122,s675]) ).
cnf(s681,plain,
~ spl20_335,
inference(rat,[],[s623,s676]) ).
cnf(s684,plain,
spl20_86,
inference(rat,[],[s619,s681,s679]) ).
cnf(s725,plain,
$false,
inference(rat,[],[s120,s684,s122,s121]) ).
fof(f6614,plain,
$false,
inference(avatar_sat_refutation,[],[s725]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU071+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n020.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:30:50 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 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
% 0.93/0.64 % (3999818)Will run a generic schedule for satisfiability detection.
% 0.93/0.64 % (3999825)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3880758315:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.93/0.64 % (3999824)% WARNING: option uhcvi not known.
% 0.93/0.64 % (3999823)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1780480006_2999 on theBenchmark for (2999ds/0Mi)
% 0.93/0.64 % (3999824)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3021673130:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.93/0.64 % (3999828)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4014132007:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.93/0.64 % (3999827)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3139968051:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.93/0.64 % (3999829)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2804022772:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.93/0.64 % (3999826)dis+10_1_sil=32000:sp=arity:random_seed=416599185:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.93/0.64 % TRYING [1]
% 0.93/0.64 % TRYING [2]
% 0.93/0.64 % TRYING [3]
% 0.93/0.64 % TRYING [4]
% 0.93/0.64 % TRYING [5]
% 0.93/0.64 % (3999826)Instruction limit reached!
% 0.93/0.64 % (3999826)------------------------------
% 0.93/0.64 % (3999826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.64 % (3999826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.64 % (3999826)CaDiCaL version: 2.1.3
% 0.93/0.64 % (3999826)Termination reason: Instruction limit
% 0.93/0.64 % (3999826)Termination phase: Saturation
% 0.93/0.64 % (3999826)Time elapsed: 0.098 s
% 0.93/0.64 % (3999826)Peak memory usage: 12 MB
% 0.93/0.64 % (3999826)Instructions burned: 103 (million)
% 0.93/0.64 % (3999827)Instruction limit reached!
% 0.93/0.64 % (3999827)------------------------------
% 0.93/0.64 % (3999827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.64 % (3999827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.64 % (3999827)CaDiCaL version: 2.1.3
% 0.93/0.64 % (3999827)Termination reason: Instruction limit
% 0.93/0.64 % (3999827)Termination phase: Saturation
% 0.93/0.64 % (3999827)Time elapsed: 0.106 s
% 0.93/0.64 % (3999827)Peak memory usage: 12 MB
% 0.93/0.64 % (3999827)Instructions burned: 117 (million)
% 0.93/0.64 % (3999828)Instruction limit reached!
% 0.93/0.64 % (3999828)------------------------------
% 0.93/0.64 % (3999828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.64 % (3999828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.64 % (3999828)CaDiCaL version: 2.1.3
% 0.93/0.64 % (3999828)Termination reason: Instruction limit
% 0.93/0.64 % (3999828)Termination phase: Saturation
% 0.93/0.64 % (3999828)Time elapsed: 0.124 s
% 0.93/0.64 % (3999828)Peak memory usage: 12 MB
% 0.93/0.64 % (3999828)Instructions burned: 131 (million)
% 0.93/0.64 % (3999839)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1657351379:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.93/0.64 % (3999838)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=84976794:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 0.93/0.64 % TRYING [6]
% 0.93/0.64 % TRYING [1]
% 0.93/0.64 % TRYING [2]
% 0.93/0.64 % TRYING [3]
% 0.93/0.64 % (3999829) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3999818-3999829"...
% 0.93/0.64 % TRYING [4]
% 0.93/0.64 % (3999840)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1805076993:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.93/0.64 % (3999829)...printing done.
% 0.93/0.64 % (3999829)Refutation found. Thanks to Tanya!
% 0.93/0.64 % SZS status Theorem for theBenchmark
% 0.93/0.64 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.64 % (3999829)------------------------------
% 0.18/0.64 % (3999829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.64 % (3999829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.64 % (3999829)CaDiCaL version: 2.1.3
% 0.18/0.64 % (3999829)Termination reason: Refutation
% 0.18/0.64 % (3999829)Time elapsed: 0.158 s
% 0.18/0.64 % (3999829)Peak memory usage: 14 MB
% 0.18/0.64 % (3999829)Instructions burned: 151 (million)
% 0.18/0.64 % (3999818)Success in time 0.2 s
% 0.18/0.64 % Vampire exiting
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