%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET686+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:41:39 PM UTC 2026
% Result : Theorem 2.91s 1.33s
% Output : Refutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 18
% Syntax : Number of formulae : 145 ( 14 unt; 8 def)
% Number of atoms : 702 ( 7 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 988 ( 431 ~; 395 |; 106 &)
% ( 19 <=>; 35 =>; 0 <=; 2 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-4 aty)
% Number of variables : 240 ( 0 sgn 202 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,inverse2(X2,X0))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X1,X3),X2)
& member(X3,X0) ) ) ) ) ),
file('/export/starexec/sandbox/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,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/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f5,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/sandbox/benchmark/theBenchmark.p',p5) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).
fof(f24,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/sandbox/benchmark/theBenchmark.p',p24) ).
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)
=> inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25) ).
fof(f27,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
fof(f28,conjecture,
! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X0))
=> ( member(X4,inverse4(X0,X2,X3,X1))
<=> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X4,X5),X3)
& member(X5,X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_53) ).
fof(f29,negated_conjecture,
~ ! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X0))
=> ( member(X4,inverse4(X0,X2,X3,X1))
<=> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X4,X5),X3)
& member(X5,X1) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f30,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( member(X4,inverse4(X0,X2,X3,X1))
<~> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X4,X5),X3)
& member(X5,X1) ) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f29]) ).
fof(f31,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( member(X4,inverse4(X0,X2,X3,X1))
<~> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X4,X5),X3)
& member(X5,X1) ) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(flattening,[],[f30]) ).
fof(f38,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f9]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f7]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f39]) ).
fof(f41,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,[],[f2]) ).
fof(f42,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,[],[f41]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X1,inverse2(X2,X0))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X1,X3),X2)
& member(X3,X0) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( inverse4(X0,X1,X2,X3) = inverse2(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(f54,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,[],[f5]) ).
fof(f56,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,[],[f24]) ).
fof(f57,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f15]) ).
fof(f63,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ ilf_type(X5,member_type(X2))
| ~ member(ordered_pair(X4,X5),X3)
| ~ member(X5,X1) )
| ~ member(X4,inverse4(X0,X2,X3,X1)) )
& ( ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X4,X5),X3)
& member(X5,X1) )
| member(X4,inverse4(X0,X2,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f31]) ).
fof(f64,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ ilf_type(X5,member_type(X2))
| ~ member(ordered_pair(X4,X5),X3)
| ~ member(X5,X1) )
| ~ member(X4,inverse4(X0,X2,X3,X1)) )
& ( ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X4,X5),X3)
& member(X5,X1) )
| member(X4,inverse4(X0,X2,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ ilf_type(X5,member_type(X2))
| ~ member(ordered_pair(X4,X5),X3)
| ~ member(X5,X1) )
| ~ member(X4,inverse4(X0,X2,X3,X1)) )
& ( ? [X6] :
( ilf_type(X6,member_type(X2))
& member(ordered_pair(X4,X6),X3)
& member(X6,X1) )
| member(X4,inverse4(X0,X2,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X0,X2)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(rectify,[],[f64]) ).
fof(f66,plain,
( ( ! [X5] :
( ~ ilf_type(X5,member_type(sK2))
| ~ member(ordered_pair(sK4,X5),sK3)
| ~ member(X5,sK1) )
| ~ member(sK4,inverse4(sK0,sK2,sK3,sK1)) )
& ( ( ilf_type(sK5,member_type(sK2))
& member(ordered_pair(sK4,sK5),sK3)
& member(sK5,sK1) )
| member(sK4,inverse4(sK0,sK2,sK3,sK1)) )
& ilf_type(sK4,member_type(sK0))
& ilf_type(sK3,relation_type(sK0,sK2))
& ~ empty(sK2)
& ilf_type(sK2,set_type)
& ~ empty(sK1)
& ilf_type(sK1,set_type)
& ~ empty(sK0)
& ilf_type(sK0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X6,sK5)],[f65]) ).
fof(f77,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f38]) ).
fof(f78,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK11(X0),X0)
& ilf_type(sK11(X0),set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X1,sK11(X0))],[f78]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f40]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,inverse2(X2,X0))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X1,X3),X2)
| ~ member(X3,X0) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X1,X3),X2)
& member(X3,X0) )
| ~ member(X1,inverse2(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f43]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,inverse2(X2,X0))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X1,X3),X2)
| ~ member(X3,X0) ) )
& ( ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X1,X4),X2)
& member(X4,X0) )
| ~ member(X1,inverse2(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f81]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,inverse2(X2,X0))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X1,X3),X2)
| ~ member(X3,X0) ) )
& ( ( ilf_type(sK12(X0,X1,X2),set_type)
& member(ordered_pair(X1,sK12(X0,X1,X2)),X2)
& member(sK12(X0,X1,X2),X0) )
| ~ member(X1,inverse2(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X4,sK12(X0,X1,X2))],[f82]) ).
fof(f88,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,[],[f57]) ).
fof(f89,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,[],[f88]) ).
fof(f92,plain,
ilf_type(sK0,set_type),
inference(cnf_transformation,[],[f66]) ).
fof(f96,plain,
ilf_type(sK2,set_type),
inference(cnf_transformation,[],[f66]) ).
fof(f98,plain,
ilf_type(sK3,relation_type(sK0,sK2)),
inference(cnf_transformation,[],[f66]) ).
fof(f100,plain,
( member(sK5,sK1)
| member(sK4,inverse4(sK0,sK2,sK3,sK1)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f101,plain,
( member(ordered_pair(sK4,sK5),sK3)
| member(sK4,inverse4(sK0,sK2,sK3,sK1)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f103,plain,
! [X5] :
( ~ ilf_type(X5,member_type(sK2))
| ~ member(ordered_pair(sK4,X5),sK3)
| ~ member(X5,sK1)
| ~ member(sK4,inverse4(sK0,sK2,sK3,sK1)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f104,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f27]) ).
fof(f121,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f79]) ).
fof(f125,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f80]) ).
fof(f126,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X2,X3),X4)
| member(X3,X1)
| ~ 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,[],[f42]) ).
fof(f128,plain,
! [X2,X0,X1] :
( member(sK12(X0,X1,X2),X0)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f129,plain,
! [X2,X0,X1] :
( member(ordered_pair(X1,sK12(X0,X1,X2)),X2)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ilf_type(sK12(X0,X1,X2),set_type)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X3,set_type)
| member(X1,inverse2(X2,X0))
| ~ member(X3,X0)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f140,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f52]) ).
fof(f142,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,[],[f54]) ).
fof(f146,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f56]) ).
fof(f149,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f89]) ).
fof(f160,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(duplicate_literal_removal,[],[f149]) ).
fof(f175,definition,
( spl17_4
<=> ! [X1] : ilf_type(X1,set_type) ),
introduced(definition,[new_symbols(definition,[spl17_4])],[avatar_definition]) ).
fof(f176,plain,
( ! [X1] : ilf_type(X1,set_type)
| ~ spl17_4 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f178,plain,
spl17_4,
inference(avatar_split_clause,[],[f104,f175]) ).
fof(f180,definition,
( spl17_5
<=> member(sK4,inverse4(sK0,sK2,sK3,sK1)) ),
introduced(definition,[new_symbols(definition,[spl17_5])],[avatar_definition]) ).
fof(f181,plain,
( ~ member(sK4,inverse4(sK0,sK2,sK3,sK1))
| spl17_5 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f182,plain,
( member(sK4,inverse4(sK0,sK2,sK3,sK1))
| ~ spl17_5 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f184,definition,
( spl17_6
<=> member(sK5,sK1) ),
introduced(definition,[new_symbols(definition,[spl17_6])],[avatar_definition]) ).
fof(f186,plain,
( member(sK5,sK1)
| ~ spl17_6 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f187,plain,
( spl17_5
| spl17_6 ),
inference(avatar_split_clause,[],[f100,f184,f180]) ).
fof(f189,definition,
( spl17_7
<=> member(ordered_pair(sK4,sK5),sK3) ),
introduced(definition,[new_symbols(definition,[spl17_7])],[avatar_definition]) ).
fof(f191,plain,
( member(ordered_pair(sK4,sK5),sK3)
| ~ spl17_7 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f192,plain,
( spl17_5
| spl17_7 ),
inference(avatar_split_clause,[],[f101,f189,f180]) ).
fof(f199,definition,
( spl17_9
<=> ! [X5] :
( ~ ilf_type(X5,member_type(sK2))
| ~ member(X5,sK1)
| ~ member(ordered_pair(sK4,X5),sK3) ) ),
introduced(definition,[new_symbols(definition,[spl17_9])],[avatar_definition]) ).
fof(f200,plain,
( ! [X5] :
( ~ member(ordered_pair(sK4,X5),sK3)
| ~ member(X5,sK1)
| ~ ilf_type(X5,member_type(sK2)) )
| ~ spl17_9 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f201,plain,
( ~ spl17_5
| spl17_9 ),
inference(avatar_split_clause,[],[f103,f199,f180]) ).
fof(f213,plain,
( ! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) )
| ~ spl17_4 ),
inference(resolution,[],[f160,f176]) ).
fof(f365,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(resolution,[],[f142,f146]) ).
fof(f366,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(X0) ),
inference(duplicate_literal_removal,[],[f365]) ).
fof(f367,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| relation_like(X0) )
| ~ spl17_4 ),
inference(forward_subsumption_resolution,[],[f366,f176]) ).
fof(f368,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) )
| ~ spl17_4 ),
inference(forward_subsumption_resolution,[],[f367,f176]) ).
fof(f408,definition,
( spl17_18
<=> relation_like(sK3) ),
introduced(definition,[new_symbols(definition,[spl17_18])],[avatar_definition]) ).
fof(f409,plain,
( relation_like(sK3)
| ~ spl17_18 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f410,plain,
( ~ relation_like(sK3)
| spl17_18 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f495,plain,
( relation_like(sK3)
| ~ spl17_4 ),
inference(resolution,[],[f368,f98]) ).
fof(f498,plain,
( $false
| ~ spl17_4
| spl17_18 ),
inference(forward_subsumption_resolution,[],[f495,f410]) ).
fof(f499,plain,
( ~ spl17_4
| spl17_18 ),
inference(avatar_contradiction_clause,[],[f498]) ).
fof(f561,plain,
( ! [X0] :
( ~ member(sK4,inverse2(sK3,X0))
| ~ ilf_type(sK3,binary_relation_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(sK12(X0,sK4,sK3),sK1)
| ~ ilf_type(sK12(X0,sK4,sK3),member_type(sK2)) )
| ~ spl17_9 ),
inference(resolution,[],[f129,f200]) ).
fof(f572,plain,
( ! [X0] :
( ~ member(sK4,inverse2(sK3,X0))
| ~ ilf_type(sK3,binary_relation_type)
| ~ ilf_type(sK4,set_type)
| ~ member(sK12(X0,sK4,sK3),sK1)
| ~ ilf_type(sK12(X0,sK4,sK3),member_type(sK2)) )
| ~ spl17_4
| ~ spl17_9 ),
inference(forward_subsumption_resolution,[],[f561,f176]) ).
fof(f576,plain,
( ! [X0] :
( ~ member(sK4,inverse2(sK3,X0))
| ~ ilf_type(sK3,binary_relation_type)
| ~ member(sK12(X0,sK4,sK3),sK1)
| ~ ilf_type(sK12(X0,sK4,sK3),member_type(sK2)) )
| ~ spl17_4
| ~ spl17_9 ),
inference(forward_subsumption_resolution,[],[f572,f176]) ).
fof(f581,definition,
( spl17_24
<=> ilf_type(sK3,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl17_24])],[avatar_definition]) ).
fof(f582,plain,
( ilf_type(sK3,binary_relation_type)
| ~ spl17_24 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f583,plain,
( ~ ilf_type(sK3,binary_relation_type)
| spl17_24 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f585,definition,
( spl17_25
<=> ! [X0] :
( ~ member(sK4,inverse2(sK3,X0))
| ~ ilf_type(sK12(X0,sK4,sK3),member_type(sK2))
| ~ member(sK12(X0,sK4,sK3),sK1) ) ),
introduced(definition,[new_symbols(definition,[spl17_25])],[avatar_definition]) ).
fof(f586,plain,
( ! [X0] :
( ~ ilf_type(sK12(X0,sK4,sK3),member_type(sK2))
| ~ member(sK4,inverse2(sK3,X0))
| ~ member(sK12(X0,sK4,sK3),sK1) )
| ~ spl17_25 ),
inference(avatar_component_clause,[],[f585]) ).
fof(f587,plain,
( ~ spl17_24
| spl17_25
| ~ spl17_4
| ~ spl17_9 ),
inference(avatar_split_clause,[],[f576,f199,f175,f585,f581]) ).
fof(f593,plain,
( ~ relation_like(sK3)
| ~ spl17_4
| spl17_24 ),
inference(resolution,[],[f583,f213]) ).
fof(f594,plain,
( $false
| ~ spl17_4
| ~ spl17_18
| spl17_24 ),
inference(forward_subsumption_resolution,[],[f593,f409]) ).
fof(f595,plain,
( ~ spl17_4
| ~ spl17_18
| spl17_24 ),
inference(avatar_contradiction_clause,[],[f594]) ).
fof(f622,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| inverse2(sK3,X0) = inverse4(sK0,sK2,sK3,X0)
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(sK0,set_type) ),
inference(resolution,[],[f140,f98]) ).
fof(f626,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| inverse2(sK3,X0) = inverse4(sK0,sK2,sK3,X0)
| ~ ilf_type(sK0,set_type) ),
inference(forward_subsumption_resolution,[],[f622,f96]) ).
fof(f628,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| inverse2(sK3,X0) = inverse4(sK0,sK2,sK3,X0) ),
inference(forward_subsumption_resolution,[],[f626,f92]) ).
fof(f630,plain,
( ! [X0] : inverse2(sK3,X0) = inverse4(sK0,sK2,sK3,X0)
| ~ spl17_4 ),
inference(forward_subsumption_resolution,[],[f628,f176]) ).
fof(f634,plain,
( ~ member(sK4,inverse2(sK3,sK1))
| ~ spl17_4
| spl17_5 ),
inference(superposition,[],[f181,f630]) ).
fof(f641,plain,
! [X2,X3,X0,X1,X4] :
( member(sK12(X0,X1,X2),X3)
| ~ ilf_type(X2,relation_type(X4,X3))
| ~ ilf_type(sK12(X0,X1,X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[],[f126,f129]) ).
fof(f646,plain,
! [X2,X3,X0,X1,X4] :
( member(sK12(X0,X1,X2),X3)
| ~ ilf_type(X2,relation_type(X4,X3))
| ~ ilf_type(sK12(X0,X1,X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f641]) ).
fof(f651,plain,
! [X2,X3,X0,X1,X4] :
( member(sK12(X0,X1,X2),X3)
| ~ ilf_type(X2,relation_type(X4,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f646,f130]) ).
fof(f656,plain,
( ! [X2,X3,X0,X1,X4] :
( member(sK12(X0,X1,X2),X3)
| ~ ilf_type(X2,relation_type(X4,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type) )
| ~ spl17_4 ),
inference(forward_subsumption_resolution,[],[f651,f176]) ).
fof(f661,plain,
( ! [X2,X3,X0,X1,X4] :
( member(sK12(X0,X1,X2),X3)
| ~ ilf_type(X2,relation_type(X4,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type) )
| ~ spl17_4 ),
inference(forward_subsumption_resolution,[],[f656,f176]) ).
fof(f666,plain,
( ! [X2,X3,X0,X1,X4] :
( member(sK12(X0,X1,X2),X3)
| ~ ilf_type(X2,relation_type(X4,X3))
| ~ ilf_type(X1,set_type)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type) )
| ~ spl17_4 ),
inference(forward_subsumption_resolution,[],[f661,f176]) ).
fof(f667,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,relation_type(X4,X3))
| member(sK12(X0,X1,X2),X3)
| ~ ilf_type(X2,binary_relation_type) )
| ~ spl17_4 ),
inference(forward_subsumption_resolution,[],[f666,f176]) ).
fof(f696,plain,
( ! [X0] :
( ~ ilf_type(sK5,set_type)
| member(sK4,inverse2(sK3,X0))
| ~ member(sK5,X0)
| ~ ilf_type(sK3,binary_relation_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl17_7 ),
inference(resolution,[],[f131,f191]) ).
fof(f704,plain,
( ! [X0] :
( ~ ilf_type(sK5,set_type)
| member(sK4,inverse2(sK3,X0))
| ~ member(sK5,X0)
| ~ ilf_type(sK3,binary_relation_type)
| ~ ilf_type(sK4,set_type) )
| ~ spl17_4
| ~ spl17_7 ),
inference(forward_subsumption_resolution,[],[f696,f176]) ).
fof(f709,plain,
( ! [X0] :
( ~ ilf_type(sK5,set_type)
| member(sK4,inverse2(sK3,X0))
| ~ member(sK5,X0)
| ~ ilf_type(sK3,binary_relation_type) )
| ~ spl17_4
| ~ spl17_7 ),
inference(forward_subsumption_resolution,[],[f704,f176]) ).
fof(f714,plain,
( ! [X0] :
( member(sK4,inverse2(sK3,X0))
| ~ member(sK5,X0)
| ~ ilf_type(sK3,binary_relation_type) )
| ~ spl17_4
| ~ spl17_7 ),
inference(forward_subsumption_resolution,[],[f709,f176]) ).
fof(f716,plain,
( ! [X0] :
( member(sK4,inverse2(sK3,X0))
| ~ member(sK5,X0) )
| ~ spl17_4
| ~ spl17_7
| ~ spl17_24 ),
inference(forward_subsumption_resolution,[],[f714,f582]) ).
fof(f729,plain,
( ~ member(sK5,sK1)
| ~ spl17_4
| spl17_5
| ~ spl17_7
| ~ spl17_24 ),
inference(resolution,[],[f716,f634]) ).
fof(f736,plain,
( $false
| ~ spl17_4
| spl17_5
| ~ spl17_6
| ~ spl17_7
| ~ spl17_24 ),
inference(forward_subsumption_resolution,[],[f729,f186]) ).
fof(f737,plain,
( ~ spl17_4
| spl17_5
| ~ spl17_6
| ~ spl17_7
| ~ spl17_24 ),
inference(avatar_contradiction_clause,[],[f736]) ).
fof(f744,plain,
( member(sK4,inverse2(sK3,sK1))
| ~ spl17_4
| ~ spl17_5 ),
inference(forward_demodulation,[],[f182,f630]) ).
fof(f765,plain,
( ! [X0] :
( ~ member(sK4,inverse2(sK3,X0))
| ~ member(sK12(X0,sK4,sK3),sK1)
| ~ member(sK12(X0,sK4,sK3),sK2)
| empty(sK2)
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(sK12(X0,sK4,sK3),set_type) )
| ~ spl17_25 ),
inference(resolution,[],[f586,f125]) ).
fof(f766,plain,
( ! [X0] :
( ~ member(sK4,inverse2(sK3,X0))
| ~ member(sK12(X0,sK4,sK3),sK1)
| ~ member(sK12(X0,sK4,sK3),sK2)
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(sK12(X0,sK4,sK3),set_type) )
| ~ spl17_25 ),
inference(forward_subsumption_resolution,[],[f765,f121]) ).
fof(f767,plain,
( ! [X0] :
( ~ member(sK4,inverse2(sK3,X0))
| ~ member(sK12(X0,sK4,sK3),sK1)
| ~ member(sK12(X0,sK4,sK3),sK2)
| ~ ilf_type(sK12(X0,sK4,sK3),set_type) )
| ~ spl17_25 ),
inference(forward_subsumption_resolution,[],[f766,f96]) ).
fof(f768,plain,
( ! [X0] :
( ~ member(sK12(X0,sK4,sK3),sK2)
| ~ member(sK12(X0,sK4,sK3),sK1)
| ~ member(sK4,inverse2(sK3,X0)) )
| ~ spl17_4
| ~ spl17_25 ),
inference(forward_subsumption_resolution,[],[f767,f176]) ).
fof(f1213,plain,
( ! [X0,X1] :
( ~ ilf_type(sK3,relation_type(X0,X1))
| member(sK12(sK1,sK4,sK3),X1)
| ~ ilf_type(sK3,binary_relation_type) )
| ~ spl17_4
| ~ spl17_5 ),
inference(resolution,[],[f667,f744]) ).
fof(f1229,plain,
( ! [X0,X1] :
( ~ ilf_type(sK3,relation_type(X0,X1))
| member(sK12(sK1,sK4,sK3),X1) )
| ~ spl17_4
| ~ spl17_5
| ~ spl17_24 ),
inference(forward_subsumption_resolution,[],[f1213,f582]) ).
fof(f1236,plain,
( member(sK12(sK1,sK4,sK3),sK2)
| ~ spl17_4
| ~ spl17_5
| ~ spl17_24 ),
inference(resolution,[],[f1229,f98]) ).
fof(f1405,plain,
( ~ member(sK12(sK1,sK4,sK3),sK1)
| ~ member(sK4,inverse2(sK3,sK1))
| ~ spl17_4
| ~ spl17_5
| ~ spl17_24
| ~ spl17_25 ),
inference(resolution,[],[f768,f1236]) ).
fof(f1411,plain,
( ~ member(sK12(sK1,sK4,sK3),sK1)
| ~ spl17_4
| ~ spl17_5
| ~ spl17_24
| ~ spl17_25 ),
inference(forward_subsumption_resolution,[],[f1405,f744]) ).
fof(f1413,plain,
( ~ member(sK4,inverse2(sK3,sK1))
| ~ ilf_type(sK3,binary_relation_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK1,set_type)
| ~ spl17_4
| ~ spl17_5
| ~ spl17_24
| ~ spl17_25 ),
inference(resolution,[],[f1411,f128]) ).
fof(f1414,plain,
( ~ ilf_type(sK3,binary_relation_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK1,set_type)
| ~ spl17_4
| ~ spl17_5
| ~ spl17_24
| ~ spl17_25 ),
inference(forward_subsumption_resolution,[],[f1413,f744]) ).
fof(f1415,plain,
( ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK1,set_type)
| ~ spl17_4
| ~ spl17_5
| ~ spl17_24
| ~ spl17_25 ),
inference(forward_subsumption_resolution,[],[f1414,f582]) ).
fof(f1416,plain,
( ~ ilf_type(sK4,set_type)
| ~ spl17_4
| ~ spl17_5
| ~ spl17_24
| ~ spl17_25 ),
inference(forward_subsumption_resolution,[],[f1415,f176]) ).
fof(f1417,plain,
( $false
| ~ spl17_4
| ~ spl17_5
| ~ spl17_24
| ~ spl17_25 ),
inference(forward_subsumption_resolution,[],[f1416,f176]) ).
fof(f1418,plain,
( ~ spl17_4
| ~ spl17_5
| ~ spl17_24
| ~ spl17_25 ),
inference(avatar_contradiction_clause,[],[f1417]) ).
cnf(s6,plain,
spl17_4,
inference(sat_conversion,[],[f178]) ).
cnf(s7,plain,
( spl17_5
| spl17_6 ),
inference(sat_conversion,[],[f187]) ).
cnf(s8,plain,
( spl17_5
| spl17_7 ),
inference(sat_conversion,[],[f192]) ).
cnf(s10,plain,
( ~ spl17_5
| spl17_9 ),
inference(sat_conversion,[],[f201]) ).
cnf(s17,plain,
( ~ spl17_4
| spl17_18 ),
inference(sat_conversion,[],[f499]) ).
cnf(s19,plain,
( ~ spl17_4
| ~ spl17_9
| ~ spl17_24
| spl17_25 ),
inference(sat_conversion,[],[f587]) ).
cnf(s20,plain,
( ~ spl17_4
| ~ spl17_18
| spl17_24 ),
inference(sat_conversion,[],[f595]) ).
cnf(s21,plain,
( ~ spl17_4
| spl17_5
| ~ spl17_6
| ~ spl17_7
| ~ spl17_24 ),
inference(sat_conversion,[],[f737]) ).
cnf(s31,plain,
( ~ spl17_4
| ~ spl17_5
| ~ spl17_24
| ~ spl17_25 ),
inference(sat_conversion,[],[f1418]) ).
cnf(s32,plain,
spl17_18,
inference(rat,[],[s17,s6]) ).
cnf(s33,plain,
spl17_24,
inference(rat,[],[s20,s6,s32]) ).
cnf(s34,plain,
spl17_5,
inference(rat,[],[s21,s7,s8,s6,s33]) ).
cnf(s35,plain,
~ spl17_25,
inference(rat,[],[s31,s33,s6,s34]) ).
cnf(s37,plain,
spl17_9,
inference(rat,[],[s10,s34]) ).
cnf(s38,plain,
$false,
inference(rat,[],[s19,s33,s6,s35,s37]) ).
fof(f1419,plain,
$false,
inference(avatar_sat_refutation,[],[s38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET686+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n002.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 02:34:38 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.91/1.33 % (4099149)Detected formulas, will run a generic FOF schedule.
% 2.91/1.33 % (4099158)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2560836812:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.91/1.33 % (4099157)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=105776690:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.91/1.33 % (4099156)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=166674512:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.91/1.33 % (4099160)dis-21_1_sil=8000:lcm=predicate:random_seed=396713587: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)
% 2.91/1.33 % (4099155)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=1369907845:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.91/1.33 % (4099154)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=3276148693:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.91/1.33 % (4099159)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=249200226:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.91/1.33 % (4099157)Refutation not found, incomplete strategy
% 2.91/1.33 % (4099157)------------------------------
% 2.91/1.33 % (4099157)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.91/1.33 % (4099157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/1.33 % (4099157)CaDiCaL version: 2.1.3
% 2.91/1.33 % (4099157)Termination reason: Refutation not found, incomplete strategy
% 2.91/1.33 % (4099157)Time elapsed: 0.003 s
% 2.91/1.33 % (4099157)Peak memory usage: 88 MB
% 2.91/1.33 % (4099157)Instructions burned: 3 (million)
% 2.91/1.33 % (4099158)Instruction limit reached!
% 2.91/1.33 % (4099158)------------------------------
% 2.91/1.33 % (4099158)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.91/1.33 % (4099158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/1.33 % (4099158)CaDiCaL version: 2.1.3
% 2.91/1.33 % (4099158)Termination reason: Instruction limit
% 2.91/1.33 % (4099158)Termination phase: Saturation
% 2.91/1.33 % (4099158)Time elapsed: 0.035 s
% 2.91/1.33 % (4099158)Peak memory usage: 88 MB
% 2.91/1.33 % (4099158)Instructions burned: 119 (million)
% 2.91/1.33 % (4099160)Instruction limit reached!
% 2.91/1.33 % (4099160)------------------------------
% 2.91/1.33 % (4099160)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.91/1.33 % (4099160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/1.33 % (4099160)CaDiCaL version: 2.1.3
% 2.91/1.33 % (4099160)Termination reason: Instruction limit
% 2.91/1.33 % (4099160)Termination phase: Saturation
% 2.91/1.33 % (4099160)Time elapsed: 0.079 s
% 2.91/1.33 % (4099160)Peak memory usage: 90 MB
% 2.91/1.33 % (4099160)Instructions burned: 130 (million)
% 2.91/1.33 % (4099159)Instruction limit reached!
% 2.91/1.33 % (4099159)------------------------------
% 2.91/1.33 % (4099159)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.91/1.33 % (4099159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/1.33 % (4099159)CaDiCaL version: 2.1.3
% 2.91/1.33 % (4099159)Termination reason: Instruction limit
% 2.91/1.33 % (4099159)Termination phase: Saturation
% 2.91/1.33 % (4099159)Time elapsed: 0.108 s
% 2.91/1.33 % (4099159)Peak memory usage: 90 MB
% 2.91/1.33 % (4099159)Instructions burned: 140 (million)
% 2.91/1.33 % (4099168)lrs+10_1_sil=8000:sp=occurrence:random_seed=1803442578:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.91/1.33 % (4099168)First to succeed.
% 2.91/1.33 % (4099168)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4099149"
% 2.91/1.33 % (4099169)lrs+10_1_sil=32000:urr=on:br=off:random_seed=130401165:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.91/1.33 % (4099157)------------------------------
% 2.91/1.33 % (4099157)------------------------------
% 2.91/1.33 % (4099170)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1298353915:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.91/1.33 % (4099168)Refutation found. Thanks to Tanya!
% 2.91/1.33 % SZS status Theorem for theBenchmark
% 2.91/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.88/1.44 % (4099168)------------------------------
% 3.88/1.44 % (4099168)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.44 % (4099168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.44 % (4099168)CaDiCaL version: 2.1.3
% 3.88/1.44 % (4099168)Termination reason: Refutation
% 3.88/1.44 % (4099168)Time elapsed: 0.021 s
% 3.88/1.44 % (4099168)Peak memory usage: 90 MB
% 3.88/1.44 % (4099168)Instructions burned: 59 (million)
% 3.88/1.44 % (4099168)------------------------------
% 3.88/1.44 % (4099168)------------------------------
% 3.88/1.44 % (4099149)Success in time 0.476 s
% 3.88/1.44 % Vampire exiting
%------------------------------------------------------------------------------