%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU039+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 : n004.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 12:47:06 PM UTC 2026
% Result : Theorem 1.63s 1.15s
% Output : Refutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 64 ( 12 unt; 0 def)
% Number of atoms : 352 ( 82 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 485 ( 197 ~; 190 |; 77 &)
% ( 11 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 167 ( 146 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f6,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f7,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(f8,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f15,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0) )
=> ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f39,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f42,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( in(X1,relation_dom(X2))
& in(X1,X0) )
=> in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_funct_1) ).
fof(f43,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( in(X1,relation_dom(X2))
& in(X1,X0) )
=> in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0))) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f47,plain,
? [X0,X1,X2] :
( ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0)))
& in(X1,relation_dom(X2))
& in(X1,X0)
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f43]) ).
fof(f48,plain,
? [X0,X1,X2] :
( ~ in(apply(X2,X1),relation_rng(relation_dom_restriction(X2,X0)))
& in(X1,relation_dom(X2))
& in(X1,X0)
& relation(X2)
& function(X2) ),
inference(flattening,[],[f47]) ).
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,[],[f7]) ).
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(f62,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f63,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f62]) ).
fof(f65,plain,
! [X0,X1] :
( ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f66,plain,
! [X0,X1] :
( ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f71,plain,
( ~ in(apply(sK2,sK1),relation_rng(relation_dom_restriction(sK2,sK0)))
& in(sK1,relation_dom(sK2))
& in(sK1,sK0)
& relation(sK2)
& function(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f48]) ).
fof(f72,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(f73,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,[],[f72]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK3(X0,X1) )
| ~ in(sK3(X0,X1),X1) )
& ( ( in(sK4(X0,X1),relation_dom(X0))
& sK3(X0,X1) = apply(X0,sK4(X0,X1)) )
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK5(X0,X5),relation_dom(X0))
& apply(X0,sK5(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X7,sK5(X0,X5))],[f73]) ).
fof(f77,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X1 = relation_dom_restriction(X2,X0)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(nnf_transformation,[],[f63]) ).
fof(f78,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X1 = relation_dom_restriction(X2,X0)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X1 = relation_dom_restriction(X2,X0)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X1 = relation_dom_restriction(X2,X0)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ( apply(X1,sK8(X1,X2)) != apply(X2,sK8(X1,X2))
& in(sK8(X1,X2),relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X3,sK8(X1,X2))],[f79]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f86]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK13(X0,X1,X2),X0)
| ~ in(sK13(X0,X1,X2),X1)
| ~ in(sK13(X0,X1,X2),X2) )
& ( ( in(sK13(X0,X1,X2),X0)
& in(sK13(X0,X1,X2),X1) )
| in(sK13(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X3,sK13(X0,X1,X2))],[f87]) ).
fof(f89,plain,
function(sK2),
inference(cnf_transformation,[],[f71]) ).
fof(f90,plain,
relation(sK2),
inference(cnf_transformation,[],[f71]) ).
fof(f91,plain,
in(sK1,sK0),
inference(cnf_transformation,[],[f71]) ).
fof(f92,plain,
in(sK1,relation_dom(sK2)),
inference(cnf_transformation,[],[f71]) ).
fof(f93,plain,
~ in(apply(sK2,sK1),relation_rng(relation_dom_restriction(sK2,sK0))),
inference(cnf_transformation,[],[f71]) ).
fof(f101,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f115,plain,
! [X2,X0,X1,X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1))
| relation_dom_restriction(X2,X0) != X1
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f116,plain,
! [X2,X0,X1] :
( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
| relation_dom_restriction(X2,X0) != X1
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f124,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f126,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f134,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f88]) ).
fof(f138,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f139,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f101]) ).
fof(f140,plain,
! [X0,X6] :
( in(apply(X0,X6),relation_rng(X0))
| ~ in(X6,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f139]) ).
fof(f143,plain,
! [X2,X0] :
( set_intersection2(relation_dom(X2),X0) = relation_dom(relation_dom_restriction(X2,X0))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(relation_dom_restriction(X2,X0))
| ~ function(relation_dom_restriction(X2,X0)) ),
inference(equality_resolution,[],[f116]) ).
fof(f144,plain,
! [X2,X0,X4] :
( apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
| ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(relation_dom_restriction(X2,X0))
| ~ function(relation_dom_restriction(X2,X0)) ),
inference(equality_resolution,[],[f115]) ).
fof(f145,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f134]) ).
fof(f270,plain,
! [X2,X0] :
( set_intersection2(relation_dom(X2),X0) = relation_dom(relation_dom_restriction(X2,X0))
| ~ relation(X2)
| ~ function(X2)
| ~ function(relation_dom_restriction(X2,X0)) ),
inference(forward_subsumption_resolution,[],[f143,f126]) ).
fof(f271,plain,
! [X2,X0] :
( set_intersection2(relation_dom(X2),X0) = relation_dom(relation_dom_restriction(X2,X0))
| ~ relation(X2)
| ~ function(X2) ),
inference(forward_subsumption_resolution,[],[f270,f124]) ).
fof(f373,plain,
! [X2,X0,X4] :
( apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
| ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
| ~ relation(X2)
| ~ function(X2)
| ~ function(relation_dom_restriction(X2,X0)) ),
inference(forward_subsumption_resolution,[],[f144,f126]) ).
fof(f374,plain,
! [X2,X0,X4] :
( apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
| ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(forward_subsumption_resolution,[],[f373,f124]) ).
fof(f382,plain,
! [X2,X0,X1] :
( in(apply(X0,X1),relation_rng(relation_dom_restriction(X0,X2)))
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ relation(relation_dom_restriction(X0,X2))
| ~ function(relation_dom_restriction(X0,X2))
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[],[f140,f374]) ).
fof(f385,plain,
! [X2,X0,X1] :
( in(apply(X0,X1),relation_rng(relation_dom_restriction(X0,X2)))
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ relation(relation_dom_restriction(X0,X2))
| ~ function(relation_dom_restriction(X0,X2))
| ~ relation(X0)
| ~ function(X0) ),
inference(duplicate_literal_removal,[],[f382]) ).
fof(f389,plain,
! [X2,X0,X1] :
( in(apply(X0,X1),relation_rng(relation_dom_restriction(X0,X2)))
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ function(relation_dom_restriction(X0,X2))
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f385,f126]) ).
fof(f395,plain,
! [X2,X0,X1] :
( in(apply(X0,X1),relation_rng(relation_dom_restriction(X0,X2)))
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f389,f124]) ).
fof(f596,plain,
( ~ in(sK1,relation_dom(relation_dom_restriction(sK2,sK0)))
| ~ relation(sK2)
| ~ function(sK2) ),
inference(resolution,[],[f395,f93]) ).
fof(f611,plain,
( ~ in(sK1,relation_dom(relation_dom_restriction(sK2,sK0)))
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f596,f90]) ).
fof(f614,plain,
~ in(sK1,relation_dom(relation_dom_restriction(sK2,sK0))),
inference(forward_subsumption_resolution,[],[f611,f89]) ).
fof(f615,plain,
( ~ in(sK1,set_intersection2(relation_dom(sK2),sK0))
| ~ relation(sK2)
| ~ function(sK2) ),
inference(superposition,[],[f614,f271]) ).
fof(f616,plain,
( ~ in(sK1,set_intersection2(relation_dom(sK2),sK0))
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f615,f90]) ).
fof(f617,plain,
~ in(sK1,set_intersection2(relation_dom(sK2),sK0)),
inference(forward_subsumption_resolution,[],[f616,f89]) ).
fof(f618,plain,
~ in(sK1,set_intersection2(sK0,relation_dom(sK2))),
inference(forward_demodulation,[],[f617,f138]) ).
fof(f619,plain,
( ~ in(sK1,sK0)
| ~ in(sK1,relation_dom(sK2)) ),
inference(resolution,[],[f618,f145]) ).
fof(f623,plain,
~ in(sK1,relation_dom(sK2)),
inference(forward_subsumption_resolution,[],[f619,f91]) ).
fof(f624,plain,
$false,
inference(forward_subsumption_resolution,[],[f623,f92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU039+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n004.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Mon Sep 28 03:24:36 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 1.63/1.15 % (4120141)Detected formulas, will run a generic FOF schedule.
% 1.63/1.15 % (4120150)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=755038099:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.63/1.15 % (4120150)First to succeed.
% 1.63/1.15 % (4120150)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4120141"
% 1.63/1.15 % (4120149)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1413267774:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.63/1.15 % (4120146)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=1771726561:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.63/1.15 % (4120148)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=311905949:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.63/1.15 % (4120147)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=1603753324:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.63/1.15 % (4120149)Refutation not found, incomplete strategy
% 1.63/1.15 % (4120149)------------------------------
% 1.63/1.15 % (4120149)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.63/1.15 % (4120149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/1.15 % (4120149)CaDiCaL version: 2.1.3
% 1.63/1.15 % (4120149)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.15 % (4120149)Time elapsed: 0.003 s
% 1.63/1.15 % (4120149)Peak memory usage: 88 MB
% 1.63/1.15 % (4120149)Instructions burned: 2 (million)
% 1.63/1.15 % (4120152)dis-21_1_sil=8000:lcm=predicate:random_seed=1615048734: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)
% 1.63/1.15 % (4120151)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1600742367:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.63/1.15 % (4120152)Instruction limit reached!
% 1.63/1.15 % (4120152)------------------------------
% 1.63/1.15 % (4120152)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.63/1.15 % (4120152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/1.15 % (4120152)CaDiCaL version: 2.1.3
% 1.63/1.15 % (4120152)Termination reason: Instruction limit
% 1.63/1.15 % (4120152)Termination phase: Saturation
% 1.63/1.15 % (4120152)Time elapsed: 0.068 s
% 1.63/1.15 % (4120152)Peak memory usage: 89 MB
% 1.63/1.15 % (4120152)Instructions burned: 131 (million)
% 1.63/1.15 % (4120151)Instruction limit reached!
% 1.63/1.15 % (4120151)------------------------------
% 1.63/1.15 % (4120151)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.63/1.15 % (4120151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/1.15 % (4120151)CaDiCaL version: 2.1.3
% 1.63/1.15 % (4120151)Termination reason: Instruction limit
% 1.63/1.15 % (4120151)Termination phase: Saturation
% 1.63/1.15 % (4120151)Time elapsed: 0.092 s
% 1.63/1.15 % (4120151)Peak memory usage: 90 MB
% 1.63/1.15 % (4120151)Instructions burned: 139 (million)
% 1.63/1.15 % (4120150)Refutation found. Thanks to Tanya!
% 1.63/1.15 % SZS status Theorem for theBenchmark
% 1.63/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.52/1.34 % (4120150)------------------------------
% 2.52/1.34 % (4120150)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/1.34 % (4120150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/1.34 % (4120150)CaDiCaL version: 2.1.3
% 2.52/1.34 % (4120150)Termination reason: Refutation
% 2.52/1.34 % (4120150)Time elapsed: 0.009 s
% 2.52/1.34 % (4120150)Peak memory usage: 88 MB
% 2.52/1.34 % (4120150)Instructions burned: 23 (million)
% 2.52/1.34 % (4120150)------------------------------
% 2.52/1.34 % (4120150)------------------------------
% 2.52/1.34 % (4120141)Success in time 0.272 s
% 2.52/1.34 % Vampire exiting
%------------------------------------------------------------------------------