%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET685+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 12:44:25 PM UTC 2026
% Result : Theorem 0.14s 0.46s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of formulae : 131 ( 11 unt; 6 def)
% Number of atoms : 579 ( 7 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 768 ( 320 ~; 288 |; 106 &)
% ( 17 <=>; 35 =>; 0 <=; 2 <~>)
% Maximal formula depth : 20 ( 7 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 : 263 ( 0 sgn 225 !; 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,image(X2,X0))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X1),X2)
& member(X3,X0) ) ) ) ) ),
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,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',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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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)
=> image4(X0,X1,X2,X3) = image(X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25) ).
fof(f27,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/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(X2,X0))
=> ! [X4] :
( ilf_type(X4,member_type(X0))
=> ( member(X4,image4(X2,X0,X3,X1))
<=> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X5,X4),X3)
& member(X5,X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_52) ).
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(X2,X0))
=> ! [X4] :
( ilf_type(X4,member_type(X0))
=> ( member(X4,image4(X2,X0,X3,X1))
<=> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X5,X4),X3)
& member(X5,X1) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f30,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X1,image(X2,X0))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X1),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(f31,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(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(flattening,[],[f31]) ).
fof(f35,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(f37,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(f38,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,[],[f37]) ).
fof(f41,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f9]) ).
fof(f47,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(f58,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(f59,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( image4(X0,X1,X2,X3) = image(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(f61,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( member(X4,image4(X2,X0,X3,X1))
<~> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X5,X4),X3)
& member(X5,X1) ) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X2,X0)) )
& ~ 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(f62,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( member(X4,image4(X2,X0,X3,X1))
<~> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X5,X4),X3)
& member(X5,X1) ) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X2,X0)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,image(X2,X0))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X3,X1),X2)
| ~ member(X3,X0) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X1),X2)
& member(X3,X0) )
| ~ member(X1,image(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f30]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,image(X2,X0))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X3,X1),X2)
| ~ member(X3,X0) ) )
& ( ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X4,X1),X2)
& member(X4,X0) )
| ~ member(X1,image(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,image(X2,X0))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X3,X1),X2)
| ~ member(X3,X0) ) )
& ( ( ilf_type(sK0(X0,X1,X2),set_type)
& member(ordered_pair(sK0(X0,X1,X2),X1),X2)
& member(sK0(X0,X1,X2),X0) )
| ~ member(X1,image(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,[sK0]),skolemize(X4,sK0(X0,X1,X2))],[f64]) ).
fof(f68,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,[],[f38]) ).
fof(f70,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,[],[f41]) ).
fof(f71,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,[],[f70]) ).
fof(f72,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK3(X0),X0)
& ilf_type(sK3(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,[sK3]),skolemize(X1,sK3(X0))],[f71]) ).
fof(f73,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,[],[f47]) ).
fof(f74,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,[],[f73]) ).
fof(f88,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ ilf_type(X5,member_type(X2))
| ~ member(ordered_pair(X5,X4),X3)
| ~ member(X5,X1) )
| ~ member(X4,image4(X2,X0,X3,X1)) )
& ( ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X5,X4),X3)
& member(X5,X1) )
| member(X4,image4(X2,X0,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X2,X0)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f62]) ).
fof(f89,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ ilf_type(X5,member_type(X2))
| ~ member(ordered_pair(X5,X4),X3)
| ~ member(X5,X1) )
| ~ member(X4,image4(X2,X0,X3,X1)) )
& ( ? [X5] :
( ilf_type(X5,member_type(X2))
& member(ordered_pair(X5,X4),X3)
& member(X5,X1) )
| member(X4,image4(X2,X0,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X2,X0)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ ilf_type(X5,member_type(X2))
| ~ member(ordered_pair(X5,X4),X3)
| ~ member(X5,X1) )
| ~ member(X4,image4(X2,X0,X3,X1)) )
& ( ? [X6] :
( ilf_type(X6,member_type(X2))
& member(ordered_pair(X6,X4),X3)
& member(X6,X1) )
| member(X4,image4(X2,X0,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X2,X0)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(rectify,[],[f89]) ).
fof(f91,plain,
( ( ! [X5] :
( ~ ilf_type(X5,member_type(sK13))
| ~ member(ordered_pair(X5,sK15),sK14)
| ~ member(X5,sK12) )
| ~ member(sK15,image4(sK13,sK11,sK14,sK12)) )
& ( ( ilf_type(sK16,member_type(sK13))
& member(ordered_pair(sK16,sK15),sK14)
& member(sK16,sK12) )
| member(sK15,image4(sK13,sK11,sK14,sK12)) )
& ilf_type(sK15,member_type(sK11))
& ilf_type(sK14,relation_type(sK13,sK11))
& ~ empty(sK13)
& ilf_type(sK13,set_type)
& ~ empty(sK12)
& ilf_type(sK12,set_type)
& ~ empty(sK11)
& ilf_type(sK11,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14,sK15,sK16]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13),skolemize(X3,sK14),skolemize(X4,sK15),skolemize(X6,sK16)],[f90]) ).
fof(f92,plain,
! [X2,X0,X1] :
( member(sK0(X0,X1,X2),X0)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f65]) ).
fof(f93,plain,
! [X2,X0,X1] :
( member(ordered_pair(sK0(X0,X1,X2),X1),X2)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f65]) ).
fof(f95,plain,
! [X2,X3,X0,X1] :
( member(X1,image(X2,X0))
| ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X3,X1),X2)
| ~ member(X3,X0)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f65]) ).
fof(f97,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,[],[f32]) ).
fof(f101,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,[],[f35]) ).
fof(f105,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,[],[f68]) ).
fof(f107,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f72]) ).
fof(f117,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f74]) ).
fof(f140,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,[],[f58]) ).
fof(f141,plain,
! [X2,X3,X0,X1] :
( image4(X0,X1,X2,X3) = image(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,[],[f59]) ).
fof(f143,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f27]) ).
fof(f150,plain,
ilf_type(sK14,relation_type(sK13,sK11)),
inference(cnf_transformation,[],[f91]) ).
fof(f152,plain,
( member(sK16,sK12)
| member(sK15,image4(sK13,sK11,sK14,sK12)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f153,plain,
( member(ordered_pair(sK16,sK15),sK14)
| member(sK15,image4(sK13,sK11,sK14,sK12)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f155,plain,
! [X5] :
( ~ ilf_type(X5,member_type(sK13))
| ~ member(ordered_pair(X5,sK15),sK14)
| ~ member(X5,sK12)
| ~ member(sK15,image4(sK13,sK11,sK14,sK12)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f162,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f117]) ).
fof(f164,definition,
( spl17_1
<=> member(sK15,image4(sK13,sK11,sK14,sK12)) ),
introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition]) ).
fof(f165,plain,
( ~ member(sK15,image4(sK13,sK11,sK14,sK12))
| spl17_1 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f166,plain,
( member(sK15,image4(sK13,sK11,sK14,sK12))
| ~ spl17_1 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f168,definition,
( spl17_2
<=> member(sK16,sK12) ),
introduced(definition,[new_symbols(definition,[spl17_2])],[avatar_definition]) ).
fof(f170,plain,
( member(sK16,sK12)
| ~ spl17_2 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f171,plain,
( spl17_1
| spl17_2 ),
inference(avatar_split_clause,[],[f152,f168,f164]) ).
fof(f173,definition,
( spl17_3
<=> member(ordered_pair(sK16,sK15),sK14) ),
introduced(definition,[new_symbols(definition,[spl17_3])],[avatar_definition]) ).
fof(f175,plain,
( member(ordered_pair(sK16,sK15),sK14)
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f176,plain,
( spl17_1
| spl17_3 ),
inference(avatar_split_clause,[],[f153,f173,f164]) ).
fof(f183,definition,
( spl17_5
<=> ! [X5] :
( ~ ilf_type(X5,member_type(sK13))
| ~ member(X5,sK12)
| ~ member(ordered_pair(X5,sK15),sK14) ) ),
introduced(definition,[new_symbols(definition,[spl17_5])],[avatar_definition]) ).
fof(f184,plain,
( ! [X5] :
( ~ member(ordered_pair(X5,sK15),sK14)
| ~ member(X5,sK12)
| ~ ilf_type(X5,member_type(sK13)) )
| ~ spl17_5 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f185,plain,
( ~ spl17_1
| spl17_5 ),
inference(avatar_split_clause,[],[f155,f183,f164]) ).
fof(f210,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f162,f143]) ).
fof(f216,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f107,f143]) ).
fof(f217,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[],[f216,f143]) ).
fof(f241,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,[],[f140,f143]) ).
fof(f242,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(forward_subsumption_resolution,[],[f241,f143]) ).
fof(f253,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f105,f217]) ).
fof(f254,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f253,f143]) ).
fof(f255,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[],[f254,f143]) ).
fof(f295,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,[],[f101,f143]) ).
fof(f296,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f295,f143]) ).
fof(f297,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(resolution,[],[f296,f242]) ).
fof(f316,plain,
relation_like(sK14),
inference(resolution,[],[f297,f150]) ).
fof(f397,plain,
! [X2,X0,X1] :
( member(sK0(X0,X1,X2),X0)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f92,f143]) ).
fof(f398,plain,
! [X2,X0,X1] :
( member(sK0(X0,X1,X2),X0)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f397,f143]) ).
fof(f412,plain,
! [X2,X0,X1] :
( member(ordered_pair(sK0(X0,X1,X2),X1),X2)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ),
inference(forward_subsumption_resolution,[],[f93,f143]) ).
fof(f413,plain,
! [X2,X0,X1] :
( member(ordered_pair(sK0(X0,X1,X2),X1),X2)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f412,f143]) ).
fof(f450,plain,
! [X2,X3,X0,X1] :
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f141,f143]) ).
fof(f451,plain,
! [X2,X3,X0,X1] :
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f450,f143]) ).
fof(f452,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| image4(X0,X1,X2,X3) = image(X2,X3) ),
inference(forward_subsumption_resolution,[],[f451,f143]) ).
fof(f457,plain,
! [X0] : image4(sK13,sK11,sK14,X0) = image(sK14,X0),
inference(resolution,[],[f452,f150]) ).
fof(f458,plain,
( ~ member(sK15,image(sK14,sK12))
| spl17_1 ),
inference(superposition,[],[f165,f457]) ).
fof(f461,plain,
! [X2,X3,X0,X1] :
( member(X1,image(X2,X0))
| ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X3,X1),X2)
| ~ member(X3,X0)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ),
inference(forward_subsumption_resolution,[],[f95,f143]) ).
fof(f462,plain,
! [X2,X3,X0,X1] :
( member(X1,image(X2,X0))
| ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X3,X1),X2)
| ~ member(X3,X0)
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f461,f143]) ).
fof(f463,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X3,X1),X2)
| member(X1,image(X2,X0))
| ~ member(X3,X0)
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f462,f143]) ).
fof(f464,plain,
( ! [X0] :
( member(sK15,image(sK14,X0))
| ~ member(sK16,X0)
| ~ ilf_type(sK14,binary_relation_type) )
| ~ spl17_3 ),
inference(resolution,[],[f463,f175]) ).
fof(f471,definition,
( spl17_16
<=> ilf_type(sK14,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl17_16])],[avatar_definition]) ).
fof(f472,plain,
( ilf_type(sK14,binary_relation_type)
| ~ spl17_16 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f473,plain,
( ~ ilf_type(sK14,binary_relation_type)
| spl17_16 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f475,definition,
( spl17_17
<=> ! [X0] :
( member(sK15,image(sK14,X0))
| ~ member(sK16,X0) ) ),
introduced(definition,[new_symbols(definition,[spl17_17])],[avatar_definition]) ).
fof(f476,plain,
( ! [X0] :
( member(sK15,image(sK14,X0))
| ~ member(sK16,X0) )
| ~ spl17_17 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f477,plain,
( ~ spl17_16
| spl17_17
| ~ spl17_3 ),
inference(avatar_split_clause,[],[f464,f173,f475,f471]) ).
fof(f478,plain,
( ~ relation_like(sK14)
| spl17_16 ),
inference(resolution,[],[f473,f210]) ).
fof(f479,plain,
( $false
| spl17_16 ),
inference(forward_subsumption_resolution,[],[f478,f316]) ).
fof(f480,plain,
spl17_16,
inference(avatar_contradiction_clause,[],[f479]) ).
fof(f492,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) ),
inference(forward_subsumption_resolution,[],[f97,f143]) ).
fof(f493,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) ),
inference(forward_subsumption_resolution,[],[f492,f143]) ).
fof(f494,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) ),
inference(forward_subsumption_resolution,[],[f493,f143]) ).
fof(f495,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,[],[f494,f143]) ).
fof(f501,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,relation_type(X3,X4))
| member(sK0(X0,X1,X2),X3)
| ~ ilf_type(X2,binary_relation_type) ),
inference(resolution,[],[f495,f413]) ).
fof(f505,plain,
( ~ member(sK16,sK12)
| spl17_1
| ~ spl17_17 ),
inference(resolution,[],[f476,f458]) ).
fof(f512,plain,
( $false
| spl17_1
| ~ spl17_2
| ~ spl17_17 ),
inference(forward_subsumption_resolution,[],[f505,f170]) ).
fof(f513,plain,
( spl17_1
| ~ spl17_2
| ~ spl17_17 ),
inference(avatar_contradiction_clause,[],[f512]) ).
fof(f514,plain,
( member(sK15,image(sK14,sK12))
| ~ spl17_1 ),
inference(forward_demodulation,[],[f166,f457]) ).
fof(f522,plain,
( ! [X0] :
( ~ member(sK0(X0,sK15,sK14),sK12)
| ~ ilf_type(sK0(X0,sK15,sK14),member_type(sK13))
| ~ member(sK15,image(sK14,X0))
| ~ ilf_type(sK14,binary_relation_type) )
| ~ spl17_5 ),
inference(resolution,[],[f184,f413]) ).
fof(f523,plain,
( ! [X0] :
( ~ ilf_type(sK0(X0,sK15,sK14),member_type(sK13))
| ~ member(sK0(X0,sK15,sK14),sK12)
| ~ member(sK15,image(sK14,X0)) )
| ~ spl17_5
| ~ spl17_16 ),
inference(forward_subsumption_resolution,[],[f522,f472]) ).
fof(f533,plain,
( ! [X0] :
( ~ member(sK0(X0,sK15,sK14),sK13)
| ~ member(sK15,image(sK14,X0))
| ~ member(sK0(X0,sK15,sK14),sK12) )
| ~ spl17_5
| ~ spl17_16 ),
inference(resolution,[],[f523,f255]) ).
fof(f791,plain,
( ! [X0,X1] :
( ~ ilf_type(sK14,relation_type(X0,X1))
| member(sK0(sK12,sK15,sK14),X0)
| ~ ilf_type(sK14,binary_relation_type) )
| ~ spl17_1 ),
inference(resolution,[],[f501,f514]) ).
fof(f792,plain,
( ! [X0,X1] :
( ~ ilf_type(sK14,relation_type(X0,X1))
| member(sK0(sK12,sK15,sK14),X0) )
| ~ spl17_1
| ~ spl17_16 ),
inference(forward_subsumption_resolution,[],[f791,f472]) ).
fof(f793,plain,
( member(sK0(sK12,sK15,sK14),sK13)
| ~ spl17_1
| ~ spl17_16 ),
inference(resolution,[],[f792,f150]) ).
fof(f806,plain,
( ~ member(sK15,image(sK14,sK12))
| ~ member(sK0(sK12,sK15,sK14),sK12)
| ~ spl17_1
| ~ spl17_5
| ~ spl17_16 ),
inference(resolution,[],[f793,f533]) ).
fof(f811,plain,
( ~ member(sK0(sK12,sK15,sK14),sK12)
| ~ spl17_1
| ~ spl17_5
| ~ spl17_16 ),
inference(forward_subsumption_resolution,[],[f806,f514]) ).
fof(f901,plain,
( ~ member(sK15,image(sK14,sK12))
| ~ ilf_type(sK14,binary_relation_type)
| ~ spl17_1
| ~ spl17_5
| ~ spl17_16 ),
inference(resolution,[],[f811,f398]) ).
fof(f902,plain,
( ~ ilf_type(sK14,binary_relation_type)
| ~ spl17_1
| ~ spl17_5
| ~ spl17_16 ),
inference(forward_subsumption_resolution,[],[f901,f514]) ).
fof(f903,plain,
( $false
| ~ spl17_1
| ~ spl17_5
| ~ spl17_16 ),
inference(forward_subsumption_resolution,[],[f902,f472]) ).
fof(f904,plain,
( ~ spl17_1
| ~ spl17_5
| ~ spl17_16 ),
inference(avatar_contradiction_clause,[],[f903]) ).
cnf(s1,plain,
( spl17_1
| spl17_2 ),
inference(sat_conversion,[],[f171]) ).
cnf(s2,plain,
( spl17_1
| spl17_3 ),
inference(sat_conversion,[],[f176]) ).
cnf(s4,plain,
( ~ spl17_1
| spl17_5 ),
inference(sat_conversion,[],[f185]) ).
cnf(s14,plain,
( ~ spl17_3
| ~ spl17_16
| spl17_17 ),
inference(sat_conversion,[],[f477]) ).
cnf(s15,plain,
spl17_16,
inference(sat_conversion,[],[f480]) ).
cnf(s17,plain,
( spl17_1
| ~ spl17_2
| ~ spl17_17 ),
inference(sat_conversion,[],[f513]) ).
cnf(s25,plain,
( ~ spl17_1
| ~ spl17_5
| ~ spl17_16 ),
inference(sat_conversion,[],[f904]) ).
cnf(s26,plain,
( ~ spl17_3
| spl17_17 ),
inference(rat,[],[s14,s15]) ).
cnf(s29,plain,
spl17_1,
inference(rat,[],[s17,s26,s1,s2]) ).
cnf(s30,plain,
~ spl17_5,
inference(rat,[],[s25,s15,s29]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s4,s30,s29]) ).
fof(f905,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET685+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 28 02:32:19 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 Running first-order model finding
% 0.13/0.39 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.46 % (3608380)Will run a generic schedule for satisfiability detection.
% 0.14/0.46 % (3608386)% WARNING: option uhcvi not known.
% 0.14/0.46 % (3608386)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3916341424:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.46 % (3608390)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3998578074:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.46 % (3608391)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2159102322:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.46 % (3608385)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3872386985_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.46 % (3608388)dis+10_1_sil=32000:sp=arity:random_seed=580775735:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.46 % (3608387)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2342699004:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.46 % (3608389)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3603509820:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.46 % TRYING [1]
% 0.14/0.46 % TRYING [2]
% 0.14/0.46 % TRYING [3]
% 0.14/0.46 % (3608388) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3608380-3608388"...
% 0.14/0.46 % (3608388)...printing done.
% 0.14/0.46 % (3608388)Refutation found. Thanks to Tanya!
% 0.14/0.46 % SZS status Theorem for theBenchmark
% 0.14/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.47 % (3608388)------------------------------
% 0.14/0.47 % (3608388)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.47 % (3608388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.47 % (3608388)CaDiCaL version: 2.1.3
% 0.14/0.47 % (3608388)Termination reason: Refutation
% 0.14/0.47 % (3608388)Time elapsed: 0.028 s
% 0.14/0.47 % (3608388)Peak memory usage: 13 MB
% 0.14/0.47 % (3608388)Instructions burned: 38 (million)
% 0.14/0.47 % (3608380)Success in time 0.064 s
% 0.14/0.47 % Vampire exiting
%------------------------------------------------------------------------------