%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU075+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 : n017.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 12:47:11 PM UTC 2026
% Result : Theorem 3.70s 1.45s
% Output : Refutation 4.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 4
% Syntax : Number of formulae : 78 ( 15 unt; 0 def)
% Number of atoms : 378 ( 131 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 510 ( 210 ~; 209 |; 69 &)
% ( 6 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 114 ( 95 !; 19 ?)
% 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(f30,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( ( X0 = relation_rng(X1)
& relation_dom(X2) = X0
& relation_dom(X3) = X0
& relation_composition(X1,X2) = relation_composition(X1,X3) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_funct_1) ).
fof(f31,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( ( X0 = relation_rng(X1)
& relation_dom(X2) = X0
& relation_dom(X3) = X0
& relation_composition(X1,X2) = relation_composition(X1,X3) )
=> X2 = X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f33,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f41,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( relation_dom(X0) = relation_dom(X1)
& ! [X2] :
( in(X2,relation_dom(X0))
=> apply(X0,X2) = apply(X1,X2) ) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).
fof(f46,plain,
? [X0,X1] :
( ? [X2] :
( ? [X3] :
( X2 != X3
& X0 = relation_rng(X1)
& relation_dom(X2) = X0
& relation_dom(X3) = X0
& relation_composition(X1,X2) = relation_composition(X1,X3)
& relation(X3)
& function(X3) )
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f47,plain,
? [X0,X1] :
( ? [X2] :
( ? [X3] :
( X2 != X3
& X0 = relation_rng(X1)
& relation_dom(X2) = X0
& relation_dom(X3) = X0
& relation_composition(X1,X2) = relation_composition(X1,X3)
& relation(X3)
& function(X3) )
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| relation_dom(X0) != relation_dom(X1)
| ? [X2] :
( apply(X0,X2) != apply(X1,X2)
& in(X2,relation_dom(X0)) )
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| relation_dom(X0) != relation_dom(X1)
| ? [X2] :
( apply(X0,X2) != apply(X1,X2)
& in(X2,relation_dom(X0)) )
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f48]) ).
fof(f52,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f53,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f52]) ).
fof(f54,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(f55,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,[],[f54]) ).
fof(f74,plain,
( sK2 != sK3
& sK0 = relation_rng(sK1)
& sK0 = relation_dom(sK2)
& sK0 = relation_dom(sK3)
& relation_composition(sK1,sK2) = relation_composition(sK1,sK3)
& relation(sK3)
& function(sK3)
& relation(sK2)
& function(sK2)
& relation(sK1)
& function(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f47]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| relation_dom(X0) != relation_dom(X1)
| ( apply(X0,sK4(X0,X1)) != apply(X1,sK4(X0,X1))
& in(sK4(X0,X1),relation_dom(X0)) )
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f49]) ).
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,[],[f55]) ).
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) != sK5(X0,X1) )
| ~ in(sK5(X0,X1),X1) )
& ( ( in(sK6(X0,X1),relation_dom(X0))
& sK5(X0,X1) = apply(X0,sK6(X0,X1)) )
| in(sK5(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK7(X0,X5),relation_dom(X0))
& apply(X0,sK7(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X2,sK5(X0,X1)),skolemize(X4,sK6(X0,X1)),skolemize(X7,sK7(X0,X5))],[f77]) ).
fof(f85,plain,
function(sK1),
inference(cnf_transformation,[],[f74]) ).
fof(f86,plain,
relation(sK1),
inference(cnf_transformation,[],[f74]) ).
fof(f87,plain,
function(sK2),
inference(cnf_transformation,[],[f74]) ).
fof(f88,plain,
relation(sK2),
inference(cnf_transformation,[],[f74]) ).
fof(f89,plain,
function(sK3),
inference(cnf_transformation,[],[f74]) ).
fof(f90,plain,
relation(sK3),
inference(cnf_transformation,[],[f74]) ).
fof(f91,plain,
relation_composition(sK1,sK2) = relation_composition(sK1,sK3),
inference(cnf_transformation,[],[f74]) ).
fof(f92,plain,
sK0 = relation_dom(sK3),
inference(cnf_transformation,[],[f74]) ).
fof(f93,plain,
sK0 = relation_dom(sK2),
inference(cnf_transformation,[],[f74]) ).
fof(f94,plain,
sK0 = relation_rng(sK1),
inference(cnf_transformation,[],[f74]) ).
fof(f95,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f74]) ).
fof(f96,plain,
! [X0,X1] :
( in(sK4(X0,X1),relation_dom(X0))
| relation_dom(X0) != relation_dom(X1)
| X0 = X1
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f97,plain,
! [X0,X1] :
( apply(X0,sK4(X0,X1)) != apply(X1,sK4(X0,X1))
| relation_dom(X0) != relation_dom(X1)
| X0 = X1
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f100,plain,
! [X2,X0,X1] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f101,plain,
! [X0,X1,X5] :
( apply(X0,sK7(X0,X5)) = X5
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f102,plain,
! [X0,X1,X5] :
( in(sK7(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f142,plain,
! [X0,X5] :
( in(sK7(X0,X5),relation_dom(X0))
| ~ in(X5,relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f102]) ).
fof(f143,plain,
! [X0,X5] :
( apply(X0,sK7(X0,X5)) = X5
| ~ in(X5,relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f101]) ).
fof(f277,plain,
! [X0] :
( in(sK4(sK2,X0),sK0)
| relation_dom(X0) != sK0
| sK2 = X0
| ~ relation(X0)
| ~ function(X0)
| ~ relation(sK2)
| ~ function(sK2) ),
inference(superposition,[],[f96,f93]) ).
fof(f280,plain,
! [X0] :
( in(sK4(sK2,X0),sK0)
| relation_dom(X0) != sK0
| sK2 = X0
| ~ relation(X0)
| ~ function(X0)
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f277,f88]) ).
fof(f283,plain,
! [X0] :
( in(sK4(sK2,X0),sK0)
| relation_dom(X0) != sK0
| sK2 = X0
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f280,f87]) ).
fof(f285,plain,
! [X0] :
( apply(sK3,apply(sK1,X0)) = apply(relation_composition(sK1,sK2),X0)
| ~ in(X0,relation_dom(sK1))
| ~ relation(sK3)
| ~ function(sK3)
| ~ relation(sK1)
| ~ function(sK1) ),
inference(superposition,[],[f100,f91]) ).
fof(f292,plain,
! [X0] :
( apply(sK3,apply(sK1,X0)) = apply(relation_composition(sK1,sK2),X0)
| ~ in(X0,relation_dom(sK1))
| ~ function(sK3)
| ~ relation(sK1)
| ~ function(sK1) ),
inference(forward_subsumption_resolution,[],[f285,f90]) ).
fof(f296,plain,
! [X0] :
( apply(sK3,apply(sK1,X0)) = apply(relation_composition(sK1,sK2),X0)
| ~ in(X0,relation_dom(sK1))
| ~ relation(sK1)
| ~ function(sK1) ),
inference(forward_subsumption_resolution,[],[f292,f89]) ).
fof(f297,plain,
! [X0] :
( apply(sK3,apply(sK1,X0)) = apply(relation_composition(sK1,sK2),X0)
| ~ in(X0,relation_dom(sK1))
| ~ function(sK1) ),
inference(forward_subsumption_resolution,[],[f296,f86]) ).
fof(f298,plain,
! [X0] :
( ~ in(X0,relation_dom(sK1))
| apply(sK3,apply(sK1,X0)) = apply(relation_composition(sK1,sK2),X0) ),
inference(forward_subsumption_resolution,[],[f297,f85]) ).
fof(f302,plain,
! [X0] :
( apply(sK3,apply(sK1,sK7(sK1,X0))) = apply(relation_composition(sK1,sK2),sK7(sK1,X0))
| ~ in(X0,relation_rng(sK1))
| ~ relation(sK1)
| ~ function(sK1) ),
inference(resolution,[],[f298,f142]) ).
fof(f303,plain,
! [X0] :
( apply(sK3,apply(sK1,sK7(sK1,X0))) = apply(relation_composition(sK1,sK2),sK7(sK1,X0))
| ~ in(X0,relation_rng(sK1))
| ~ function(sK1) ),
inference(forward_subsumption_resolution,[],[f302,f86]) ).
fof(f305,plain,
! [X0] :
( apply(sK3,apply(sK1,sK7(sK1,X0))) = apply(relation_composition(sK1,sK2),sK7(sK1,X0))
| ~ in(X0,relation_rng(sK1)) ),
inference(forward_subsumption_resolution,[],[f303,f85]) ).
fof(f307,plain,
! [X0] :
( apply(sK3,apply(sK1,sK7(sK1,X0))) = apply(relation_composition(sK1,sK2),sK7(sK1,X0))
| ~ in(X0,sK0) ),
inference(forward_demodulation,[],[f305,f94]) ).
fof(f315,plain,
! [X0] :
( apply(sK3,apply(sK1,sK7(sK1,X0))) = apply(sK2,apply(sK1,sK7(sK1,X0)))
| ~ in(sK7(sK1,X0),relation_dom(sK1))
| ~ relation(sK2)
| ~ function(sK2)
| ~ relation(sK1)
| ~ function(sK1)
| ~ in(X0,sK0) ),
inference(superposition,[],[f100,f307]) ).
fof(f320,plain,
! [X0] :
( apply(sK3,apply(sK1,sK7(sK1,X0))) = apply(sK2,apply(sK1,sK7(sK1,X0)))
| ~ in(sK7(sK1,X0),relation_dom(sK1))
| ~ function(sK2)
| ~ relation(sK1)
| ~ function(sK1)
| ~ in(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f315,f88]) ).
fof(f324,plain,
! [X0] :
( apply(sK3,apply(sK1,sK7(sK1,X0))) = apply(sK2,apply(sK1,sK7(sK1,X0)))
| ~ in(sK7(sK1,X0),relation_dom(sK1))
| ~ relation(sK1)
| ~ function(sK1)
| ~ in(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f320,f87]) ).
fof(f326,plain,
! [X0] :
( apply(sK3,apply(sK1,sK7(sK1,X0))) = apply(sK2,apply(sK1,sK7(sK1,X0)))
| ~ in(sK7(sK1,X0),relation_dom(sK1))
| ~ function(sK1)
| ~ in(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f324,f86]) ).
fof(f328,plain,
! [X0] :
( ~ in(sK7(sK1,X0),relation_dom(sK1))
| apply(sK3,apply(sK1,sK7(sK1,X0))) = apply(sK2,apply(sK1,sK7(sK1,X0)))
| ~ in(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f326,f85]) ).
fof(f347,plain,
! [X0] :
( apply(sK3,apply(sK1,sK7(sK1,X0))) = apply(sK2,apply(sK1,sK7(sK1,X0)))
| ~ in(X0,sK0)
| ~ in(X0,relation_rng(sK1))
| ~ relation(sK1)
| ~ function(sK1) ),
inference(resolution,[],[f328,f142]) ).
fof(f348,plain,
! [X0] :
( apply(sK3,apply(sK1,sK7(sK1,X0))) = apply(sK2,apply(sK1,sK7(sK1,X0)))
| ~ in(X0,sK0)
| ~ in(X0,relation_rng(sK1))
| ~ function(sK1) ),
inference(forward_subsumption_resolution,[],[f347,f86]) ).
fof(f349,plain,
! [X0] :
( apply(sK3,apply(sK1,sK7(sK1,X0))) = apply(sK2,apply(sK1,sK7(sK1,X0)))
| ~ in(X0,sK0)
| ~ in(X0,relation_rng(sK1)) ),
inference(forward_subsumption_resolution,[],[f348,f85]) ).
fof(f350,plain,
! [X0] :
( ~ in(X0,sK0)
| apply(sK3,apply(sK1,sK7(sK1,X0))) = apply(sK2,apply(sK1,sK7(sK1,X0)))
| ~ in(X0,sK0) ),
inference(forward_demodulation,[],[f349,f94]) ).
fof(f351,plain,
! [X0] :
( apply(sK3,apply(sK1,sK7(sK1,X0))) = apply(sK2,apply(sK1,sK7(sK1,X0)))
| ~ in(X0,sK0) ),
inference(duplicate_literal_removal,[],[f350]) ).
fof(f361,plain,
! [X0] :
( apply(sK3,X0) = apply(sK2,X0)
| ~ in(X0,sK0)
| ~ in(X0,relation_rng(sK1))
| ~ relation(sK1)
| ~ function(sK1) ),
inference(superposition,[],[f351,f143]) ).
fof(f366,plain,
! [X0] :
( apply(sK3,X0) = apply(sK2,X0)
| ~ in(X0,sK0)
| ~ in(X0,relation_rng(sK1))
| ~ function(sK1) ),
inference(forward_subsumption_resolution,[],[f361,f86]) ).
fof(f369,plain,
! [X0] :
( apply(sK3,X0) = apply(sK2,X0)
| ~ in(X0,sK0)
| ~ in(X0,relation_rng(sK1)) ),
inference(forward_subsumption_resolution,[],[f366,f85]) ).
fof(f372,plain,
! [X0] :
( ~ in(X0,sK0)
| apply(sK3,X0) = apply(sK2,X0)
| ~ in(X0,sK0) ),
inference(forward_demodulation,[],[f369,f94]) ).
fof(f373,plain,
! [X0] :
( ~ in(X0,sK0)
| apply(sK3,X0) = apply(sK2,X0) ),
inference(duplicate_literal_removal,[],[f372]) ).
fof(f384,plain,
! [X0] :
( relation_dom(X0) != sK0
| apply(sK3,sK4(sK2,X0)) = apply(sK2,sK4(sK2,X0))
| sK2 = X0
| ~ relation(X0)
| ~ function(X0) ),
inference(resolution,[],[f373,f283]) ).
fof(f695,plain,
( sK0 != sK0
| apply(sK3,sK4(sK2,sK3)) = apply(sK2,sK4(sK2,sK3))
| sK2 = sK3
| ~ relation(sK3)
| ~ function(sK3) ),
inference(superposition,[],[f384,f92]) ).
fof(f697,plain,
( apply(sK3,sK4(sK2,sK3)) = apply(sK2,sK4(sK2,sK3))
| sK2 = sK3
| ~ relation(sK3)
| ~ function(sK3) ),
inference(trivial_inequality_removal,[],[f695]) ).
fof(f699,plain,
( apply(sK3,sK4(sK2,sK3)) = apply(sK2,sK4(sK2,sK3))
| ~ relation(sK3)
| ~ function(sK3) ),
inference(forward_subsumption_resolution,[],[f697,f95]) ).
fof(f701,plain,
( apply(sK3,sK4(sK2,sK3)) = apply(sK2,sK4(sK2,sK3))
| ~ function(sK3) ),
inference(forward_subsumption_resolution,[],[f699,f90]) ).
fof(f715,plain,
apply(sK3,sK4(sK2,sK3)) = apply(sK2,sK4(sK2,sK3)),
inference(forward_subsumption_resolution,[],[f701,f89]) ).
fof(f775,plain,
( apply(sK2,sK4(sK2,sK3)) != apply(sK2,sK4(sK2,sK3))
| relation_dom(sK2) != relation_dom(sK3)
| sK2 = sK3
| ~ relation(sK3)
| ~ function(sK3)
| ~ relation(sK2)
| ~ function(sK2) ),
inference(superposition,[],[f97,f715]) ).
fof(f778,plain,
( relation_dom(sK2) != relation_dom(sK3)
| sK2 = sK3
| ~ relation(sK3)
| ~ function(sK3)
| ~ relation(sK2)
| ~ function(sK2) ),
inference(trivial_inequality_removal,[],[f775]) ).
fof(f781,plain,
( relation_dom(sK2) != relation_dom(sK3)
| ~ relation(sK3)
| ~ function(sK3)
| ~ relation(sK2)
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f778,f95]) ).
fof(f784,plain,
( relation_dom(sK2) != relation_dom(sK3)
| ~ function(sK3)
| ~ relation(sK2)
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f781,f90]) ).
fof(f787,plain,
( relation_dom(sK2) != relation_dom(sK3)
| ~ relation(sK2)
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f784,f89]) ).
fof(f790,plain,
( relation_dom(sK2) != relation_dom(sK3)
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f787,f88]) ).
fof(f799,plain,
relation_dom(sK2) != relation_dom(sK3),
inference(forward_subsumption_resolution,[],[f790,f87]) ).
fof(f800,plain,
sK0 != relation_dom(sK2),
inference(forward_demodulation,[],[f799,f92]) ).
fof(f801,plain,
$false,
inference(forward_subsumption_resolution,[],[f800,f93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU075+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n017.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 03:26:21 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 3.70/1.45 % (3180776)Detected formulas, will run a generic FOF schedule.
% 3.70/1.45 % (3180787)dis-21_1_sil=8000:lcm=predicate:random_seed=3442551157: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)
% 3.70/1.45 % (3180782)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=3488452006:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.70/1.45 % (3180783)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=1549503349:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.70/1.45 % (3180781)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=1323628172:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.70/1.45 % (3180787)Instruction limit reached!
% 3.70/1.45 % (3180787)------------------------------
% 3.70/1.45 % (3180787)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.45 % (3180787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.45 % (3180787)CaDiCaL version: 2.1.3
% 3.70/1.45 % (3180787)Termination reason: Instruction limit
% 3.70/1.45 % (3180787)Termination phase: Saturation
% 3.70/1.45 % (3180787)Time elapsed: 0.042 s
% 3.70/1.45 % (3180787)Peak memory usage: 90 MB
% 3.70/1.45 % (3180787)Instructions burned: 131 (million)
% 3.70/1.45 % (3180786)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3263849574:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.70/1.45 % (3180785)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3724407997:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.70/1.45 % (3180784)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4205350597:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.70/1.45 % (3180785)Refutation not found, incomplete strategy
% 3.70/1.45 % (3180785)------------------------------
% 3.70/1.45 % (3180785)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.45 % (3180784)Refutation not found, incomplete strategy
% 3.70/1.45 % (3180784)------------------------------
% 3.70/1.45 % (3180784)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.45 % (3180784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.45 % (3180785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.45 % (3180785)CaDiCaL version: 2.1.3
% 3.70/1.45 % (3180784)CaDiCaL version: 2.1.3
% 3.70/1.45 % (3180784)Termination reason: Refutation not found, incomplete strategy
% 3.70/1.45 % (3180784)Time elapsed: 0.003 s
% 3.70/1.45 % (3180785)Termination reason: Refutation not found, incomplete strategy
% 3.70/1.45 % (3180785)Time elapsed: 0.003 s
% 3.70/1.45 % (3180785)Peak memory usage: 88 MB
% 3.70/1.45 % (3180784)Peak memory usage: 88 MB
% 3.70/1.45 % (3180785)Instructions burned: 3 (million)
% 3.70/1.45 % (3180784)Instructions burned: 2 (million)
% 3.70/1.45 % (3180792)lrs+10_1_sil=8000:sp=occurrence:random_seed=4224396188:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.70/1.45 % (3180786)Instruction limit reached!
% 3.70/1.45 % (3180786)------------------------------
% 3.70/1.45 % (3180786)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.45 % (3180786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.45 % (3180786)CaDiCaL version: 2.1.3
% 3.70/1.45 % (3180786)Termination reason: Instruction limit
% 3.70/1.45 % (3180786)Termination phase: Saturation
% 3.70/1.45 % (3180786)Time elapsed: 0.090 s
% 3.70/1.45 % (3180786)Peak memory usage: 90 MB
% 3.70/1.45 % (3180786)Instructions burned: 140 (million)
% 3.70/1.45 % (3180792)Instruction limit reached!
% 3.70/1.45 % (3180792)------------------------------
% 3.70/1.45 % (3180792)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.45 % (3180792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.45 % (3180792)CaDiCaL version: 2.1.3
% 3.70/1.45 % (3180792)Termination reason: Instruction limit
% 3.70/1.45 % (3180792)Termination phase: Saturation
% 3.70/1.45 % (3180792)Time elapsed: 0.085 s
% 3.70/1.45 % (3180792)Peak memory usage: 91 MB
% 3.70/1.45 % (3180792)Instructions burned: 287 (million)
% 3.70/1.45 % (3180797)lrs+10_1_sil=32000:urr=on:br=off:random_seed=788290475:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.70/1.45 % (3180785)------------------------------
% 3.70/1.45 % (3180785)------------------------------
% 3.70/1.45 % (3180784)------------------------------
% 3.70/1.45 % (3180784)------------------------------
% 3.70/1.45 % (3180798)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2408027616:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 3.70/1.45 % (3180798)First to succeed.
% 3.70/1.45 % (3180798)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3180776"
% 3.70/1.45 % (3180797)Instruction limit reached!
% 3.70/1.45 % (3180797)------------------------------
% 3.70/1.45 % (3180797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.45 % (3180797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.45 % (3180797)CaDiCaL version: 2.1.3
% 3.70/1.45 % (3180797)Termination reason: Instruction limit
% 3.70/1.45 % (3180797)Termination phase: Saturation
% 3.70/1.45 % (3180797)Time elapsed: 0.080 s
% 3.70/1.45 % (3180797)Peak memory usage: 90 MB
% 3.70/1.45 % (3180797)Instructions burned: 158 (million)
% 3.70/1.45 % (3180802)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1573384344:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 3.70/1.45 % (3180801)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=1811076040:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 3.70/1.45 % (3180798)Refutation found. Thanks to Tanya!
% 3.70/1.45 % SZS status Theorem for theBenchmark
% 3.70/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 4.78/1.64 % (3180798)------------------------------
% 4.78/1.64 % (3180798)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.78/1.64 % (3180798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.78/1.64 % (3180798)CaDiCaL version: 2.1.3
% 4.78/1.64 % (3180798)Termination reason: Refutation
% 4.78/1.64 % (3180798)Time elapsed: 0.013 s
% 4.78/1.64 % (3180798)Peak memory usage: 89 MB
% 4.78/1.64 % (3180798)Instructions burned: 35 (million)
% 4.78/1.64 % (3180798)------------------------------
% 4.78/1.64 % (3180798)------------------------------
% 4.78/1.64 % (3180776)Success in time 0.586 s
% 4.78/1.64 % Vampire exiting
%------------------------------------------------------------------------------