%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET671+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:41:36 PM UTC 2026
% Result : Theorem 6.86s 1.93s
% Output : Refutation 8.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of formulae : 150 ( 26 unt; 8 def)
% Number of atoms : 608 ( 37 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 789 ( 331 ~; 336 |; 61 &)
% ( 17 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-4 aty)
% Number of variables : 282 ( 0 sgn 266 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( X0 = X1
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(ordered_pair(X2,X3),X0)
<=> member(ordered_pair(X2,X3),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(ordered_pair(X1,X2),restrict(X3,X0))
<=> ( member(X1,X0)
& member(ordered_pair(X1,X2),X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X2,X0)
& member(X3,X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f6,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(f10,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
fof(f22,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(f25,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,set_type)
=> restrict4(X0,X1,X2,X3) = restrict(X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25) ).
fof(f26,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,set_type)
=> ilf_type(restrict4(X0,X1,X2,X3),relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).
fof(f27,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(f28,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X0))
=> ( subset(X1,X2)
=> restrict4(X1,X0,X3,X2) = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_34) ).
fof(f29,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X0))
=> ( subset(X1,X2)
=> restrict4(X1,X0,X3,X2) = X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f30,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1
<=> ! [X2] :
( ! [X3] :
( ( member(ordered_pair(X2,X3),X0)
<=> member(ordered_pair(X2,X3),X1) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f31,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( member(ordered_pair(X1,X2),restrict(X3,X0))
<=> ( member(X1,X0)
& member(ordered_pair(X1,X2),X3) ) )
| ~ ilf_type(X3,binary_relation_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X2,X0)
& member(X3,X1) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f3]) ).
fof(f33,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X2,X0)
& member(X3,X1) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f36,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f6]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f36]) ).
fof(f41,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f10]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f22]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( restrict4(X0,X1,X2,X3) = restrict(X2,X3)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f25]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ilf_type(restrict4(X0,X1,X2,X3),relation_type(X0,X1))
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f26]) ).
fof(f63,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( restrict4(X1,X0,X3,X2) != X3
& subset(X1,X2)
& ilf_type(X3,relation_type(X1,X0)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f29]) ).
fof(f64,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( restrict4(X1,X0,X3,X2) != X3
& subset(X1,X2)
& ilf_type(X3,relation_type(X1,X0)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2] :
( ? [X3] :
( ( ~ member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0) )
& ( member(ordered_pair(X2,X3),X1)
| member(ordered_pair(X2,X3),X0) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X2,X3),X0)
| ~ member(ordered_pair(X2,X3),X1) )
& ( member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(nnf_transformation,[],[f30]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2] :
( ? [X3] :
( ( ~ member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0) )
& ( member(ordered_pair(X2,X3),X1)
| member(ordered_pair(X2,X3),X0) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X2,X3),X0)
| ~ member(ordered_pair(X2,X3),X1) )
& ( member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2] :
( ? [X3] :
( ( ~ member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0) )
& ( member(ordered_pair(X2,X3),X1)
| member(ordered_pair(X2,X3),X0) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) )
& ( ! [X4] :
( ! [X5] :
( ( ( member(ordered_pair(X4,X5),X0)
| ~ member(ordered_pair(X4,X5),X1) )
& ( member(ordered_pair(X4,X5),X1)
| ~ member(ordered_pair(X4,X5),X0) ) )
| ~ ilf_type(X5,set_type) )
| ~ ilf_type(X4,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(rectify,[],[f66]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ( ( ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0) )
& ( member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0) )
& ilf_type(sK1(X0,X1),set_type)
& ilf_type(sK0(X0,X1),set_type) ) )
& ( ! [X4] :
( ! [X5] :
( ( ( member(ordered_pair(X4,X5),X0)
| ~ member(ordered_pair(X4,X5),X1) )
& ( member(ordered_pair(X4,X5),X1)
| ~ member(ordered_pair(X4,X5),X0) ) )
| ~ ilf_type(X5,set_type) )
| ~ ilf_type(X4,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f67]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X1,X2),restrict(X3,X0))
| ~ member(X1,X0)
| ~ member(ordered_pair(X1,X2),X3) )
& ( ( member(X1,X0)
& member(ordered_pair(X1,X2),X3) )
| ~ member(ordered_pair(X1,X2),restrict(X3,X0)) ) )
| ~ ilf_type(X3,binary_relation_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f31]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X1,X2),restrict(X3,X0))
| ~ member(X1,X0)
| ~ member(ordered_pair(X1,X2),X3) )
& ( ( member(X1,X0)
& member(ordered_pair(X1,X2),X3) )
| ~ member(ordered_pair(X1,X2),restrict(X3,X0)) ) )
| ~ ilf_type(X3,binary_relation_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f69]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f37]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0)
& ilf_type(sK3(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f73]) ).
fof(f75,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) )
& ( ( relation_like(X0)
& ilf_type(X0,set_type) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f41]) ).
fof(f76,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) )
& ( ( relation_like(X0)
& ilf_type(X0,set_type) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f75]) ).
fof(f91,plain,
( sK15 != restrict4(sK13,sK12,sK15,sK14)
& subset(sK13,sK14)
& ilf_type(sK15,relation_type(sK13,sK12))
& ilf_type(sK14,set_type)
& ilf_type(sK13,set_type)
& ilf_type(sK12,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14),skolemize(X3,sK15)],[f64]) ).
fof(f96,plain,
! [X0,X1] :
( member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| X0 = X1
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f68]) ).
fof(f97,plain,
! [X0,X1] :
( ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| X0 = X1
| ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f68]) ).
fof(f98,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X1,X2),X3)
| ~ member(ordered_pair(X1,X2),restrict(X3,X0))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f70]) ).
fof(f100,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X1,X2),restrict(X3,X0))
| ~ member(X1,X0)
| ~ member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f70]) ).
fof(f102,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f33]) ).
fof(f103,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f34]) ).
fof(f106,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f74]) ).
fof(f115,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f76]) ).
fof(f138,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f57]) ).
fof(f143,plain,
! [X2,X3,X0,X1] :
( restrict4(X0,X1,X2,X3) = restrict(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f61]) ).
fof(f144,plain,
! [X2,X3,X0,X1] :
( ilf_type(restrict4(X0,X1,X2,X3),relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f62]) ).
fof(f145,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f27]) ).
fof(f149,plain,
ilf_type(sK15,relation_type(sK13,sK12)),
inference(cnf_transformation,[],[f91]) ).
fof(f150,plain,
subset(sK13,sK14),
inference(cnf_transformation,[],[f91]) ).
fof(f151,plain,
sK15 != restrict4(sK13,sK12,sK15,sK14),
inference(cnf_transformation,[],[f91]) ).
fof(f155,definition,
sF16 = restrict4(sK13,sK12,sK15,sK14),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f156,plain,
restrict4(sK13,sK12,sK15,sK14) = sF16,
inference(reorient_equations,[],[f155]) ).
fof(f157,plain,
sK15 != sF16,
inference(definition_folding,[],[f151,f156]) ).
fof(f158,definition,
sF17 = relation_type(sK13,sK12),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f159,plain,
relation_type(sK13,sK12) = sF17,
inference(reorient_equations,[],[f158]) ).
fof(f160,plain,
ilf_type(sK15,sF17),
inference(definition_folding,[],[f149,f159]) ).
fof(f162,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f115]) ).
fof(f165,plain,
! [X2,X3,X0,X1] :
( ilf_type(restrict4(X0,X1,X2,X3),relation_type(X0,X1))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f144,f145]) ).
fof(f166,plain,
! [X2,X3,X0,X1] :
( restrict4(X0,X1,X2,X3) = restrict(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f143,f145]) ).
fof(f170,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f138,f145]) ).
fof(f186,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f162,f145]) ).
fof(f188,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f106,f145]) ).
fof(f192,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f103,f145]) ).
fof(f195,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f102,f145]) ).
fof(f196,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X1,X2),X3)
| ~ member(ordered_pair(X1,X2),restrict(X3,X0))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f98,f145]) ).
fof(f198,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X1,X2),restrict(X3,X0))
| ~ member(X1,X0)
| ~ member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f100,f145]) ).
fof(f199,plain,
! [X2,X3,X0,X1] :
( ilf_type(restrict4(X0,X1,X2,X3),relation_type(X0,X1))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f165,f145]) ).
fof(f200,plain,
! [X2,X3,X0,X1] :
( restrict4(X0,X1,X2,X3) = restrict(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f166,f145]) ).
fof(f202,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(forward_subsumption_resolution,[],[f170,f145]) ).
fof(f212,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f188,f145]) ).
fof(f216,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f192,f145]) ).
fof(f219,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f195,f145]) ).
fof(f220,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X1,X2),X3)
| ~ member(ordered_pair(X1,X2),restrict(X3,X0))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f196,f145]) ).
fof(f222,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X1,X2),restrict(X3,X0))
| ~ member(X1,X0)
| ~ member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f198,f145]) ).
fof(f223,plain,
! [X2,X3,X0,X1] :
( ilf_type(restrict4(X0,X1,X2,X3),relation_type(X0,X1))
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f199,f145]) ).
fof(f224,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| restrict4(X0,X1,X2,X3) = restrict(X2,X3) ),
inference(forward_subsumption_resolution,[],[f200,f145]) ).
fof(f228,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(forward_subsumption_resolution,[],[f212,f145]) ).
fof(f230,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f219,f145]) ).
fof(f231,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X1,X2),restrict(X3,X0))
| member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X3,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f220,f145]) ).
fof(f233,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X1,X2),restrict(X3,X0))
| ~ member(X1,X0)
| ~ member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X3,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f222,f145]) ).
fof(f235,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X2,X3),X4)
| member(X2,X0)
| ~ ilf_type(X4,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f230,f145]) ).
fof(f236,plain,
! [X0] :
( ~ member(X0,sK13)
| member(X0,sK14) ),
inference(resolution,[],[f228,f150]) ).
fof(f237,plain,
! [X0,X1] :
( ~ ilf_type(X0,sF17)
| restrict(X0,X1) = restrict4(sK13,sK12,X0,X1) ),
inference(superposition,[],[f224,f159]) ).
fof(f238,plain,
! [X0] : restrict(sK15,X0) = restrict4(sK13,sK12,sK15,X0),
inference(resolution,[],[f237,f160]) ).
fof(f240,plain,
sF16 = restrict(sK15,sK14),
inference(superposition,[],[f156,f238]) ).
fof(f241,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sF16)
| member(ordered_pair(X0,X1),sK15)
| ~ ilf_type(sK15,binary_relation_type) ),
inference(superposition,[],[f231,f240]) ).
fof(f243,definition,
( spl18_1
<=> ilf_type(sK15,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
fof(f244,plain,
( ilf_type(sK15,binary_relation_type)
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f245,plain,
( ~ ilf_type(sK15,binary_relation_type)
| spl18_1 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f247,definition,
( spl18_2
<=> ! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sF16)
| member(ordered_pair(X0,X1),sK15) ) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
fof(f248,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sF16)
| member(ordered_pair(X0,X1),sK15) )
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f249,plain,
( ~ spl18_1
| spl18_2 ),
inference(avatar_split_clause,[],[f241,f247,f243]) ).
fof(f251,plain,
( ~ relation_like(sK15)
| spl18_1 ),
inference(resolution,[],[f186,f245]) ).
fof(f299,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),sF16)
| ~ member(X0,sK14)
| ~ member(ordered_pair(X0,X1),sK15)
| ~ ilf_type(sK15,binary_relation_type) ),
inference(superposition,[],[f233,f240]) ).
fof(f304,plain,
( ilf_type(sF16,relation_type(sK13,sK12))
| ~ ilf_type(sK15,relation_type(sK13,sK12)) ),
inference(superposition,[],[f223,f156]) ).
fof(f308,plain,
( ilf_type(sF16,sF17)
| ~ ilf_type(sK15,relation_type(sK13,sK12)) ),
inference(forward_demodulation,[],[f304,f159]) ).
fof(f310,plain,
( ~ ilf_type(sK15,sF17)
| ilf_type(sF16,sF17) ),
inference(forward_demodulation,[],[f308,f159]) ).
fof(f312,plain,
ilf_type(sF16,sF17),
inference(forward_subsumption_resolution,[],[f310,f160]) ).
fof(f318,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(resolution,[],[f216,f202]) ).
fof(f321,plain,
! [X0] :
( ~ ilf_type(X0,sF17)
| relation_like(X0) ),
inference(superposition,[],[f318,f159]) ).
fof(f322,plain,
relation_like(sK15),
inference(resolution,[],[f321,f160]) ).
fof(f323,plain,
relation_like(sF16),
inference(resolution,[],[f321,f312]) ).
fof(f324,plain,
( $false
| spl18_1 ),
inference(forward_subsumption_resolution,[],[f322,f251]) ).
fof(f325,plain,
spl18_1,
inference(avatar_contradiction_clause,[],[f324]) ).
fof(f327,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sK15)
| ~ member(X0,sK14)
| member(ordered_pair(X0,X1),sF16) )
| ~ spl18_1 ),
inference(forward_subsumption_resolution,[],[f299,f244]) ).
fof(f329,plain,
( ! [X0] :
( member(ordered_pair(sK0(sF16,X0),sK1(sF16,X0)),sK15)
| member(ordered_pair(sK0(sF16,X0),sK1(sF16,X0)),X0)
| sF16 = X0
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(sF16,binary_relation_type) )
| ~ spl18_2 ),
inference(resolution,[],[f248,f96]) ).
fof(f331,definition,
( spl18_6
<=> ilf_type(sF16,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition]) ).
fof(f332,plain,
( ilf_type(sF16,binary_relation_type)
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f333,plain,
( ~ ilf_type(sF16,binary_relation_type)
| spl18_6 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f335,definition,
( spl18_7
<=> ! [X0] :
( member(ordered_pair(sK0(sF16,X0),sK1(sF16,X0)),sK15)
| ~ ilf_type(X0,binary_relation_type)
| sF16 = X0
| member(ordered_pair(sK0(sF16,X0),sK1(sF16,X0)),X0) ) ),
introduced(definition,[new_symbols(definition,[spl18_7])],[avatar_definition]) ).
fof(f336,plain,
( ! [X0] :
( member(ordered_pair(sK0(sF16,X0),sK1(sF16,X0)),sK15)
| member(ordered_pair(sK0(sF16,X0),sK1(sF16,X0)),X0)
| sF16 = X0
| ~ ilf_type(X0,binary_relation_type) )
| ~ spl18_7 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f337,plain,
( ~ spl18_6
| spl18_7
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f329,f247,f335,f331]) ).
fof(f348,plain,
( ~ relation_like(sF16)
| spl18_6 ),
inference(resolution,[],[f333,f186]) ).
fof(f349,plain,
( $false
| spl18_6 ),
inference(forward_subsumption_resolution,[],[f348,f323]) ).
fof(f350,plain,
spl18_6,
inference(avatar_contradiction_clause,[],[f349]) ).
fof(f395,plain,
( member(ordered_pair(sK0(sF16,sK15),sK1(sF16,sK15)),sK15)
| sK15 = sF16
| ~ ilf_type(sK15,binary_relation_type)
| ~ spl18_7 ),
inference(factoring,[],[f336]) ).
fof(f398,plain,
( member(ordered_pair(sK0(sF16,sK15),sK1(sF16,sK15)),sK15)
| ~ ilf_type(sK15,binary_relation_type)
| ~ spl18_7 ),
inference(forward_subsumption_resolution,[],[f395,f157]) ).
fof(f402,plain,
( member(ordered_pair(sK0(sF16,sK15),sK1(sF16,sK15)),sK15)
| ~ spl18_1
| ~ spl18_7 ),
inference(forward_subsumption_resolution,[],[f398,f244]) ).
fof(f403,plain,
( sK15 = sF16
| ~ member(ordered_pair(sK0(sF16,sK15),sK1(sF16,sK15)),sF16)
| ~ ilf_type(sK15,binary_relation_type)
| ~ ilf_type(sF16,binary_relation_type)
| ~ spl18_1
| ~ spl18_7 ),
inference(resolution,[],[f402,f97]) ).
fof(f404,plain,
( ~ member(sK0(sF16,sK15),sK14)
| member(ordered_pair(sK0(sF16,sK15),sK1(sF16,sK15)),sF16)
| ~ spl18_1
| ~ spl18_7 ),
inference(resolution,[],[f402,f327]) ).
fof(f406,plain,
( ! [X0,X1] :
( ~ ilf_type(sK15,relation_type(X0,X1))
| member(sK0(sF16,sK15),X0) )
| ~ spl18_1
| ~ spl18_7 ),
inference(resolution,[],[f402,f235]) ).
fof(f408,definition,
( spl18_11
<=> member(ordered_pair(sK0(sF16,sK15),sK1(sF16,sK15)),sF16) ),
introduced(definition,[new_symbols(definition,[spl18_11])],[avatar_definition]) ).
fof(f412,definition,
( spl18_12
<=> member(sK0(sF16,sK15),sK14) ),
introduced(definition,[new_symbols(definition,[spl18_12])],[avatar_definition]) ).
fof(f414,plain,
( ~ member(sK0(sF16,sK15),sK14)
| spl18_12 ),
inference(avatar_component_clause,[],[f412]) ).
fof(f415,plain,
( spl18_11
| ~ spl18_12
| ~ spl18_1
| ~ spl18_7 ),
inference(avatar_split_clause,[],[f404,f335,f243,f412,f408]) ).
fof(f416,plain,
( ~ member(ordered_pair(sK0(sF16,sK15),sK1(sF16,sK15)),sF16)
| ~ ilf_type(sK15,binary_relation_type)
| ~ ilf_type(sF16,binary_relation_type)
| ~ spl18_1
| ~ spl18_7 ),
inference(forward_subsumption_resolution,[],[f403,f157]) ).
fof(f417,plain,
( ~ member(ordered_pair(sK0(sF16,sK15),sK1(sF16,sK15)),sF16)
| ~ ilf_type(sF16,binary_relation_type)
| ~ spl18_1
| ~ spl18_7 ),
inference(forward_subsumption_resolution,[],[f416,f244]) ).
fof(f418,plain,
( ~ member(ordered_pair(sK0(sF16,sK15),sK1(sF16,sK15)),sF16)
| ~ spl18_1
| ~ spl18_6
| ~ spl18_7 ),
inference(forward_subsumption_resolution,[],[f417,f332]) ).
fof(f419,plain,
( ~ spl18_11
| ~ spl18_1
| ~ spl18_6
| ~ spl18_7 ),
inference(avatar_split_clause,[],[f418,f335,f331,f243,f408]) ).
fof(f445,plain,
( ~ ilf_type(sK15,sF17)
| member(sK0(sF16,sK15),sK13)
| ~ spl18_1
| ~ spl18_7 ),
inference(superposition,[],[f406,f159]) ).
fof(f446,plain,
( member(sK0(sF16,sK15),sK13)
| ~ spl18_1
| ~ spl18_7 ),
inference(forward_subsumption_resolution,[],[f445,f160]) ).
fof(f447,plain,
( member(sK0(sF16,sK15),sK14)
| ~ spl18_1
| ~ spl18_7 ),
inference(resolution,[],[f446,f236]) ).
fof(f449,plain,
( $false
| ~ spl18_1
| ~ spl18_7
| spl18_12 ),
inference(forward_subsumption_resolution,[],[f447,f414]) ).
fof(f450,plain,
( ~ spl18_1
| ~ spl18_7
| spl18_12 ),
inference(avatar_contradiction_clause,[],[f449]) ).
cnf(s1,plain,
( ~ spl18_1
| spl18_2 ),
inference(sat_conversion,[],[f249]) ).
cnf(s4,plain,
spl18_1,
inference(sat_conversion,[],[f325]) ).
cnf(s5,plain,
( ~ spl18_2
| ~ spl18_6
| spl18_7 ),
inference(sat_conversion,[],[f337]) ).
cnf(s7,plain,
spl18_6,
inference(sat_conversion,[],[f350]) ).
cnf(s9,plain,
( ~ spl18_1
| ~ spl18_7
| spl18_11
| ~ spl18_12 ),
inference(sat_conversion,[],[f415]) ).
cnf(s10,plain,
( ~ spl18_1
| ~ spl18_6
| ~ spl18_7
| ~ spl18_11 ),
inference(sat_conversion,[],[f419]) ).
cnf(s12,plain,
( ~ spl18_1
| ~ spl18_7
| spl18_12 ),
inference(sat_conversion,[],[f450]) ).
cnf(s14,plain,
( ~ spl18_2
| spl18_7 ),
inference(rat,[],[s5,s7]) ).
cnf(s15,plain,
spl18_2,
inference(rat,[],[s1,s4]) ).
cnf(s17,plain,
spl18_7,
inference(rat,[],[s14,s15]) ).
cnf(s18,plain,
spl18_12,
inference(rat,[],[s12,s4,s17]) ).
cnf(s19,plain,
spl18_11,
inference(rat,[],[s9,s18,s4,s17]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s10,s4,s7,s19,s17]) ).
fof(f451,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET671+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n015.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 02:32:16 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.86/1.93 % (2206964)Detected formulas, will run a generic FOF schedule.
% 6.86/1.93 % (2207058)dis-21_1_sil=8000:lcm=predicate:random_seed=238032980: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)
% 6.86/1.93 % (2207051)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=3353284128:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.86/1.93 % (2207055)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=667499850:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.86/1.93 % (2207052)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=3465068187:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.86/1.93 % (2207049)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=2193338372:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.86/1.93 % (2207053)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1520099347:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.86/1.93 % (2207056)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3520304515:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.86/1.93 % (2207053)Refutation not found, incomplete strategy
% 6.86/1.93 % (2207053)------------------------------
% 6.86/1.93 % (2207053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.86/1.93 % (2207053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.93 % (2207053)CaDiCaL version: 2.1.3
% 6.86/1.93 % (2207053)Termination reason: Refutation not found, incomplete strategy
% 6.86/1.93 % (2207053)Time elapsed: 0.002 s
% 6.86/1.93 % (2207053)Peak memory usage: 88 MB
% 6.86/1.93 % (2207053)Instructions burned: 1 (million)
% 6.86/1.93 % (2207058)Instruction limit reached!
% 6.86/1.93 % (2207058)------------------------------
% 6.86/1.93 % (2207058)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.86/1.93 % (2207058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.93 % (2207058)CaDiCaL version: 2.1.3
% 6.86/1.93 % (2207058)Termination reason: Instruction limit
% 6.86/1.93 % (2207058)Termination phase: Saturation
% 6.86/1.93 % (2207058)Time elapsed: 0.044 s
% 6.86/1.93 % (2207058)Peak memory usage: 90 MB
% 6.86/1.93 % (2207058)Instructions burned: 137 (million)
% 6.86/1.93 % (2207055)Instruction limit reached!
% 6.86/1.93 % (2207055)------------------------------
% 6.86/1.93 % (2207055)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.86/1.93 % (2207055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.93 % (2207055)CaDiCaL version: 2.1.3
% 6.86/1.93 % (2207055)Termination reason: Instruction limit
% 6.86/1.93 % (2207055)Termination phase: Saturation
% 6.86/1.93 % (2207055)Time elapsed: 0.069 s
% 6.86/1.93 % (2207055)Peak memory usage: 88 MB
% 6.86/1.93 % (2207055)Instructions burned: 119 (million)
% 6.86/1.93 % (2207056)Instruction limit reached!
% 6.86/1.93 % (2207056)------------------------------
% 6.86/1.93 % (2207056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.86/1.93 % (2207056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.93 % (2207056)CaDiCaL version: 2.1.3
% 6.86/1.93 % (2207056)Termination reason: Instruction limit
% 6.86/1.93 % (2207056)Termination phase: Saturation
% 6.86/1.93 % (2207056)Time elapsed: 0.101 s
% 6.86/1.93 % (2207056)Peak memory usage: 89 MB
% 6.86/1.93 % (2207056)Instructions burned: 140 (million)
% 6.86/1.93 % (2207088)lrs+10_1_sil=8000:sp=occurrence:random_seed=2313775497:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.86/1.93 % (2207088)Instruction limit reached!
% 6.86/1.93 % (2207088)------------------------------
% 6.86/1.93 % (2207088)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.86/1.93 % (2207088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.93 % (2207088)CaDiCaL version: 2.1.3
% 6.86/1.93 % (2207088)Termination reason: Instruction limit
% 6.86/1.93 % (2207088)Termination phase: Saturation
% 6.86/1.93 % (2207088)Time elapsed: 0.093 s
% 6.86/1.93 % (2207088)Peak memory usage: 91 MB
% 6.86/1.93 % (2207088)Instructions burned: 287 (million)
% 6.86/1.93 % (2207089)lrs+10_1_sil=32000:urr=on:br=off:random_seed=374751659:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.86/1.93 % (2207053)------------------------------
% 6.86/1.93 % (2207053)------------------------------
% 6.86/1.93 % (2207090)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3001073592:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.86/1.93 % (2207089)Instruction limit reached!
% 6.86/1.93 % (2207089)------------------------------
% 6.86/1.93 % (2207089)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.86/1.93 % (2207089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.93 % (2207089)CaDiCaL version: 2.1.3
% 6.86/1.93 % (2207089)Termination reason: Instruction limit
% 6.86/1.93 % (2207089)Termination phase: Saturation
% 6.86/1.93 % (2207089)Time elapsed: 0.089 s
% 6.86/1.93 % (2207089)Peak memory usage: 88 MB
% 6.86/1.93 % (2207089)Instructions burned: 159 (million)
% 6.86/1.93 % (2207092)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=3128012613:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 6.86/1.93 % (2207099)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2329565301:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.86/1.93 % (2207099)Refutation not found, incomplete strategy
% 6.86/1.93 % (2207099)------------------------------
% 6.86/1.93 % (2207099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.86/1.93 % (2207099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.93 % (2207099)CaDiCaL version: 2.1.3
% 6.86/1.93 % (2207099)Termination reason: Refutation not found, incomplete strategy
% 6.86/1.93 % (2207099)Time elapsed: 0.004 s
% 6.86/1.93 % (2207099)Peak memory usage: 88 MB
% 6.86/1.93 % (2207099)Instructions burned: 5 (million)
% 6.86/1.93 % (2207092)Instruction limit reached!
% 6.86/1.93 % (2207092)------------------------------
% 6.86/1.93 % (2207092)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.86/1.93 % (2207092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.93 % (2207092)CaDiCaL version: 2.1.3
% 6.86/1.93 % (2207092)Termination reason: Instruction limit
% 6.86/1.93 % (2207092)Termination phase: Saturation
% 6.86/1.93 % (2207092)Time elapsed: 0.090 s
% 6.86/1.93 % (2207092)Peak memory usage: 89 MB
% 6.86/1.93 % (2207092)Instructions burned: 249 (million)
% 6.86/1.93 % (2207112)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1793032282:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.86/1.93 % (2207090)Instruction limit reached!
% 6.86/1.93 % (2207090)------------------------------
% 6.86/1.93 % (2207090)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.86/1.93 % (2207090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.93 % (2207090)CaDiCaL version: 2.1.3
% 6.86/1.93 % (2207090)Termination reason: Instruction limit
% 6.86/1.93 % (2207090)Termination phase: Saturation
% 6.86/1.93 % (2207090)Time elapsed: 0.235 s
% 6.86/1.93 % (2207090)Peak memory usage: 91 MB
% 6.86/1.93 % (2207090)Instructions burned: 325 (million)
% 6.86/1.93 % (2207143)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1319191276:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.86/1.93 % (2207143)Instruction limit reached!
% 6.86/1.93 % (2207143)------------------------------
% 6.86/1.93 % (2207143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.86/1.93 % (2207143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.93 % (2207143)CaDiCaL version: 2.1.3
% 6.86/1.93 % (2207143)Termination reason: Instruction limit
% 6.86/1.93 % (2207143)Termination phase: Saturation
% 6.86/1.93 % (2207143)Time elapsed: 0.040 s
% 6.86/1.93 % (2207143)Peak memory usage: 90 MB
% 6.86/1.93 % (2207143)Instructions burned: 114 (million)
% 6.86/1.93 % (2207049)First to succeed.
% 6.86/1.93 % (2207148)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2328058063:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.86/1.93 % (2207049)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2206964"
% 6.86/1.93 % (2207099)------------------------------
% 6.86/1.93 % (2207099)------------------------------
% 6.86/1.93 % (2207150)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3900661556:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.86/1.93 % (2207148)Instruction limit reached!
% 6.86/1.93 % (2207148)------------------------------
% 6.86/1.93 % (2207148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.86/1.93 % (2207148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.93 % (2207148)CaDiCaL version: 2.1.3
% 6.86/1.93 % (2207148)Termination reason: Instruction limit
% 6.86/1.93 % (2207148)Termination phase: Saturation
% 6.86/1.93 % (2207148)Time elapsed: 0.069 s
% 6.86/1.93 % (2207148)Peak memory usage: 89 MB
% 6.86/1.93 % (2207148)Instructions burned: 128 (million)
% 6.86/1.93 % (2207150)Instruction limit reached!
% 6.86/1.93 % (2207150)------------------------------
% 6.86/1.93 % (2207150)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.86/1.93 % (2207150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.93 % (2207150)CaDiCaL version: 2.1.3
% 6.86/1.93 % (2207150)Termination reason: Instruction limit
% 6.86/1.93 % (2207150)Termination phase: Saturation
% 6.86/1.93 % (2207150)Time elapsed: 0.040 s
% 6.86/1.93 % (2207150)Peak memory usage: 89 MB
% 6.86/1.93 % (2207150)Instructions burned: 117 (million)
% 6.86/1.93 % (2207152)lrs+10_1_sil=8000:sp=occurrence:random_seed=3286902102:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.86/1.93 % (2207155)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4073432632:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 6.86/1.93 % (2207154)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=265367065:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.86/1.93 % (2207154)Refutation not found, incomplete strategy
% 6.86/1.93 % (2207154)------------------------------
% 6.86/1.93 % (2207154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.86/1.93 % (2207154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.93 % (2207154)CaDiCaL version: 2.1.3
% 6.86/1.93 % (2207154)Termination reason: Refutation not found, incomplete strategy
% 6.86/1.93 % (2207154)Time elapsed: 0.003 s
% 6.86/1.93 % (2207154)Peak memory usage: 88 MB
% 6.86/1.93 % (2207154)Instructions burned: 4 (million)
% 6.86/1.93 % (2207049)Refutation found. Thanks to Tanya!
% 6.86/1.93 % SZS status Theorem for theBenchmark
% 6.86/1.93 % SZS output start Proof for theBenchmark
% See solution above
% 8.26/2.12 % (2207049)------------------------------
% 8.26/2.12 % (2207049)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.26/2.12 % (2207049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.26/2.12 % (2207049)CaDiCaL version: 2.1.3
% 8.26/2.12 % (2207049)Termination reason: Refutation
% 8.26/2.12 % (2207049)Time elapsed: 0.662 s
% 8.26/2.12 % (2207049)Peak memory usage: 128 MB
% 8.26/2.12 % (2207049)Instructions burned: 978 (million)
% 8.26/2.12 % (2207049)------------------------------
% 8.26/2.12 % (2207049)------------------------------
% 8.26/2.12 % (2206964)Success in time 1.086 s
% 8.26/2.12 % Vampire exiting
%------------------------------------------------------------------------------