%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET661+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 : n008.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 12:41:34 PM UTC 2026
% Result : Theorem 6.61s 1.99s
% Output : Refutation 8.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 30
% Syntax : Number of formulae : 236 ( 35 unt; 14 def)
% Number of atoms : 863 ( 98 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1099 ( 472 ~; 499 |; 60 &)
% ( 21 <=>; 45 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 11 con; 0-3 aty)
% Number of variables : 324 ( 0 sgn 306 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( member(X0,domain_of(X1))
<=> ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X0,X2),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( member(X0,range_of(X1))
<=> ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X0),X1) ) ) ) ),
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,binary_relation_type)
=> ( member(ordered_pair(X0,X1),X2)
=> ( member(X0,domain_of(X2))
& member(X1,range_of(X2)) ) ) ) ) ),
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,binary_relation_type)
=> ( member(ordered_pair(X0,X1),inverse(X2))
<=> member(ordered_pair(X1,X0),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
<=> member(X2,X1) ) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(f6,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',p6) ).
fof(f12,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ilf_type(inverse(X0),binary_relation_type) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(f14,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',p14) ).
fof(f18,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( X0 = X1
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
<=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18) ).
fof(f28,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',p28) ).
fof(f31,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> domain(X0,X1,X2) = domain_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).
fof(f33,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> range(X0,X1,X2) = range_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33) ).
fof(f35,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> inverse3(X0,X1,X2) = inverse(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p35) ).
fof(f36,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(inverse3(X0,X1,X2),relation_type(X1,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p36) ).
fof(f37,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p37) ).
fof(f38,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( domain(X1,X0,inverse3(X0,X1,X2)) = range(X0,X1,X2)
& range(X1,X0,inverse3(X0,X1,X2)) = domain(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_24) ).
fof(f39,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( domain(X1,X0,inverse3(X0,X1,X2)) = range(X0,X1,X2)
& range(X1,X0,inverse3(X0,X1,X2)) = domain(X0,X1,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ( member(X0,domain_of(X1))
<=> ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X0,X2),X1) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( ( member(X0,range_of(X1))
<=> ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X0),X1) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f42,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X0,domain_of(X2))
& member(X1,range_of(X2)) )
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f3]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X0,domain_of(X2))
& member(X1,range_of(X2)) )
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(ordered_pair(X0,X1),inverse(X2))
<=> member(ordered_pair(X1,X0),X2) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( ( member(X2,X0)
<~> member(X2,X1) )
& ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f5]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( ( member(X2,X0)
<~> member(X2,X1) )
& ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f45]) ).
fof(f47,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,[],[f6]) ).
fof(f53,plain,
! [X0] :
( ilf_type(inverse(X0),binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f12]) ).
fof(f55,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f14]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1
<=> ! [X2] :
( ( member(X2,X0)
<=> member(X2,X1) )
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f18]) ).
fof(f74,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,[],[f28]) ).
fof(f78,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f31]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f33]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( inverse3(X0,X1,X2) = inverse(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f35]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(inverse3(X0,X1,X2),relation_type(X1,X0))
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f36]) ).
fof(f84,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( range(X0,X1,X2) != domain(X1,X0,inverse3(X0,X1,X2))
| domain(X0,X1,X2) != range(X1,X0,inverse3(X0,X1,X2)) )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f39]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,domain_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X2),X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X0,X2),X1) )
| ~ member(X0,domain_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f40]) ).
fof(f86,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,domain_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X2),X1) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X0,X3),X1) )
| ~ member(X0,domain_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f85]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,domain_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X2),X1) ) )
& ( ( ilf_type(sK0(X0,X1),set_type)
& member(ordered_pair(X0,sK0(X0,X1)),X1) )
| ~ member(X0,domain_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f86]) ).
fof(f88,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,range_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X0),X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X0),X1) )
| ~ member(X0,range_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f41]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,range_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X0),X1) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X0),X1) )
| ~ member(X0,range_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f88]) ).
fof(f90,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,range_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X0),X1) ) )
& ( ( ilf_type(sK1(X0,X1),set_type)
& member(ordered_pair(sK1(X0,X1),X0),X1) )
| ~ member(X0,range_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f89]) ).
fof(f91,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(ordered_pair(X0,X1),inverse(X2))
| ~ member(ordered_pair(X1,X0),X2) )
& ( member(ordered_pair(X1,X0),X2)
| ~ member(ordered_pair(X0,X1),inverse(X2)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f44]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f46]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ( ( ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0) )
& ( member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0) )
& ilf_type(sK2(X0,X1),set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f93]) ).
fof(f98,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,[],[f55]) ).
fof(f99,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,[],[f98]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| ~ ilf_type(X2,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f58]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| ~ ilf_type(X2,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f103]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( ( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| ~ ilf_type(X3,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f104]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ( ( ~ member(sK6(X0,X1),X1)
| ~ member(sK6(X0,X1),X0) )
& ( member(sK6(X0,X1),X1)
| member(sK6(X0,X1),X0) )
& ilf_type(sK6(X0,X1),set_type) ) )
& ( ! [X3] :
( ( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| ~ ilf_type(X3,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f105]) ).
fof(f121,plain,
( ( range(sK14,sK15,sK16) != domain(sK15,sK14,inverse3(sK14,sK15,sK16))
| domain(sK14,sK15,sK16) != range(sK15,sK14,inverse3(sK14,sK15,sK16)) )
& ilf_type(sK16,relation_type(sK14,sK15))
& ilf_type(sK15,set_type)
& ilf_type(sK14,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X0,sK14),skolemize(X1,sK15),skolemize(X2,sK16)],[f84]) ).
fof(f122,plain,
! [X0,X1] :
( member(ordered_pair(X0,sK0(X0,X1)),X1)
| ~ member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f87]) ).
fof(f125,plain,
! [X0,X1] :
( member(ordered_pair(sK1(X0,X1),X0),X1)
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f90]) ).
fof(f128,plain,
! [X2,X0,X1] :
( member(X1,range_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f43]) ).
fof(f129,plain,
! [X2,X0,X1] :
( member(X0,domain_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f43]) ).
fof(f130,plain,
! [X2,X0,X1] :
( member(ordered_pair(X1,X0),X2)
| ~ member(ordered_pair(X0,X1),inverse(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f91]) ).
fof(f131,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,X1),inverse(X2))
| ~ member(ordered_pair(X1,X0),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f91]) ).
fof(f133,plain,
! [X0,X1] :
( X0 = X1
| member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f94]) ).
fof(f134,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f94]) ).
fof(f135,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,[],[f47]) ).
fof(f144,plain,
! [X0] :
( ilf_type(inverse(X0),binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f53]) ).
fof(f148,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f99]) ).
fof(f156,plain,
! [X0,X1] :
( X0 = X1
| member(sK6(X0,X1),X1)
| member(sK6(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f106]) ).
fof(f157,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK6(X0,X1),X1)
| ~ member(sK6(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f106]) ).
fof(f180,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,[],[f74]) ).
fof(f185,plain,
! [X2,X0,X1] :
( domain_of(X2) = domain(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f78]) ).
fof(f187,plain,
! [X2,X0,X1] :
( range_of(X2) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f80]) ).
fof(f189,plain,
! [X2,X0,X1] :
( inverse(X2) = inverse3(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f82]) ).
fof(f190,plain,
! [X2,X0,X1] :
( ilf_type(inverse3(X0,X1,X2),relation_type(X1,X0))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f191,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f37]) ).
fof(f194,plain,
ilf_type(sK16,relation_type(sK14,sK15)),
inference(cnf_transformation,[],[f121]) ).
fof(f195,plain,
( range(sK14,sK15,sK16) != domain(sK15,sK14,inverse3(sK14,sK15,sK16))
| domain(sK14,sK15,sK16) != range(sK15,sK14,inverse3(sK14,sK15,sK16)) ),
inference(cnf_transformation,[],[f121]) ).
fof(f201,definition,
sF17 = range(sK14,sK15,sK16),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f202,plain,
range(sK14,sK15,sK16) = sF17,
inference(reorient_equations,[],[f201]) ).
fof(f203,definition,
sF18 = inverse3(sK14,sK15,sK16),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f204,plain,
inverse3(sK14,sK15,sK16) = sF18,
inference(reorient_equations,[],[f203]) ).
fof(f205,definition,
sF19 = domain(sK15,sK14,sF18),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f206,plain,
domain(sK15,sK14,sF18) = sF19,
inference(reorient_equations,[],[f205]) ).
fof(f207,definition,
sF20 = domain(sK14,sK15,sK16),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f208,plain,
domain(sK14,sK15,sK16) = sF20,
inference(reorient_equations,[],[f207]) ).
fof(f209,definition,
sF21 = range(sK15,sK14,sF18),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
fof(f210,plain,
range(sK15,sK14,sF18) = sF21,
inference(reorient_equations,[],[f209]) ).
fof(f211,plain,
( sF17 != sF19
| sF20 != sF21 ),
inference(definition_folding,[],[f195,f210,f204,f208,f206,f204,f202]) ).
fof(f212,definition,
sF22 = relation_type(sK14,sK15),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f213,plain,
relation_type(sK14,sK15) = sF22,
inference(reorient_equations,[],[f212]) ).
fof(f214,plain,
ilf_type(sK16,sF22),
inference(definition_folding,[],[f194,f213]) ).
fof(f218,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f148]) ).
fof(f222,definition,
( spl23_1
<=> sF20 = sF21 ),
introduced(definition,[new_symbols(definition,[spl23_1])],[avatar_definition]) ).
fof(f224,plain,
( sF20 != sF21
| spl23_1 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f226,definition,
( spl23_2
<=> sF17 = sF19 ),
introduced(definition,[new_symbols(definition,[spl23_2])],[avatar_definition]) ).
fof(f228,plain,
( sF17 != sF19
| spl23_2 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f229,plain,
( ~ spl23_1
| ~ spl23_2 ),
inference(avatar_split_clause,[],[f211,f226,f222]) ).
fof(f230,plain,
! [X2,X0,X1] :
( ilf_type(inverse3(X0,X1,X2),relation_type(X1,X0))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f190,f191]) ).
fof(f231,plain,
! [X2,X0,X1] :
( inverse(X2) = inverse3(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f189,f191]) ).
fof(f233,plain,
! [X2,X0,X1] :
( range_of(X2) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f187,f191]) ).
fof(f235,plain,
! [X2,X0,X1] :
( domain_of(X2) = domain(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f185,f191]) ).
fof(f239,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,[],[f180,f191]) ).
fof(f254,plain,
! [X0,X1] :
( X0 = X1
| member(sK6(X0,X1),X1)
| member(sK6(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f156,f191]) ).
fof(f255,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK6(X0,X1),X1)
| ~ member(sK6(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f157,f191]) ).
fof(f260,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f218,f191]) ).
fof(f265,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,[],[f135,f191]) ).
fof(f267,plain,
! [X0,X1] :
( X0 = X1
| member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f133,f191]) ).
fof(f268,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f134,f191]) ).
fof(f269,plain,
! [X2,X0,X1] :
( member(ordered_pair(X1,X0),X2)
| ~ member(ordered_pair(X0,X1),inverse(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f130,f191]) ).
fof(f270,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,X1),inverse(X2))
| ~ member(ordered_pair(X1,X0),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f131,f191]) ).
fof(f271,plain,
! [X2,X0,X1] :
( member(X1,range_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f128,f191]) ).
fof(f272,plain,
! [X2,X0,X1] :
( member(X0,domain_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f129,f191]) ).
fof(f273,plain,
! [X0,X1] :
( member(ordered_pair(sK1(X0,X1),X0),X1)
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f125,f191]) ).
fof(f275,plain,
! [X0,X1] :
( member(ordered_pair(X0,sK0(X0,X1)),X1)
| ~ member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f122,f191]) ).
fof(f277,plain,
! [X2,X0,X1] :
( ilf_type(inverse3(X0,X1,X2),relation_type(X1,X0))
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f230,f191]) ).
fof(f278,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| inverse(X2) = inverse3(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f231,f191]) ).
fof(f280,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| range_of(X2) = range(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f233,f191]) ).
fof(f282,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| domain_of(X2) = domain(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f235,f191]) ).
fof(f284,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(forward_subsumption_resolution,[],[f239,f191]) ).
fof(f295,plain,
! [X0,X1] :
( member(sK6(X0,X1),X1)
| member(sK6(X0,X1),X0)
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f254,f191]) ).
fof(f296,plain,
! [X0,X1] :
( ~ member(sK6(X0,X1),X1)
| X0 = X1
| ~ member(sK6(X0,X1),X0) ),
inference(forward_subsumption_resolution,[],[f255,f191]) ).
fof(f301,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f265,f191]) ).
fof(f303,plain,
! [X0,X1] :
( member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0)
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f267,f191]) ).
fof(f304,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| X0 = X1
| ~ member(sK2(X0,X1),X0) ),
inference(forward_subsumption_resolution,[],[f268,f191]) ).
fof(f305,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X0,X1),inverse(X2))
| member(ordered_pair(X1,X0),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f269,f191]) ).
fof(f306,plain,
! [X2,X0,X1] :
( member(ordered_pair(X0,X1),inverse(X2))
| ~ member(ordered_pair(X1,X0),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f270,f191]) ).
fof(f307,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X0,X1),X2)
| member(X1,range_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f271,f191]) ).
fof(f308,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X0,X1),X2)
| member(X0,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f272,f191]) ).
fof(f315,plain,
! [X0] :
( ~ ilf_type(X0,sF22)
| range_of(X0) = range(sK14,sK15,X0) ),
inference(superposition,[],[f280,f213]) ).
fof(f316,plain,
range(sK14,sK15,sK16) = range_of(sK16),
inference(resolution,[],[f315,f214]) ).
fof(f317,plain,
sF17 = range_of(sK16),
inference(forward_demodulation,[],[f316,f202]) ).
fof(f318,plain,
! [X0] :
( ~ ilf_type(X0,sF22)
| domain_of(X0) = domain(sK14,sK15,X0) ),
inference(superposition,[],[f282,f213]) ).
fof(f319,plain,
domain(sK14,sK15,sK16) = domain_of(sK16),
inference(resolution,[],[f318,f214]) ).
fof(f320,plain,
sF20 = domain_of(sK16),
inference(forward_demodulation,[],[f319,f208]) ).
fof(f325,definition,
( spl23_3
<=> ilf_type(sF18,relation_type(sK15,sK14)) ),
introduced(definition,[new_symbols(definition,[spl23_3])],[avatar_definition]) ).
fof(f326,plain,
( ilf_type(sF18,relation_type(sK15,sK14))
| ~ spl23_3 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f327,plain,
( ~ ilf_type(sF18,relation_type(sK15,sK14))
| spl23_3 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f335,plain,
! [X0] :
( ~ ilf_type(X0,sF22)
| inverse(X0) = inverse3(sK14,sK15,X0) ),
inference(superposition,[],[f278,f213]) ).
fof(f342,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(resolution,[],[f301,f284]) ).
fof(f343,plain,
! [X0] :
( ~ ilf_type(X0,sF22)
| relation_like(X0) ),
inference(superposition,[],[f342,f213]) ).
fof(f344,plain,
relation_like(sK16),
inference(resolution,[],[f343,f214]) ).
fof(f355,plain,
inverse3(sK14,sK15,sK16) = inverse(sK16),
inference(resolution,[],[f335,f214]) ).
fof(f356,plain,
sF18 = inverse(sK16),
inference(forward_demodulation,[],[f355,f204]) ).
fof(f357,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),sF18)
| ~ member(ordered_pair(X1,X0),sK16)
| ~ ilf_type(sK16,binary_relation_type) ),
inference(superposition,[],[f306,f356]) ).
fof(f360,definition,
( spl23_5
<=> ilf_type(sK16,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl23_5])],[avatar_definition]) ).
fof(f361,plain,
( ilf_type(sK16,binary_relation_type)
| ~ spl23_5 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f362,plain,
( ~ ilf_type(sK16,binary_relation_type)
| spl23_5 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f368,definition,
( spl23_7
<=> ! [X0,X1] :
( member(ordered_pair(X0,X1),sF18)
| ~ member(ordered_pair(X1,X0),sK16) ) ),
introduced(definition,[new_symbols(definition,[spl23_7])],[avatar_definition]) ).
fof(f369,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(X1,X0),sK16)
| member(ordered_pair(X0,X1),sF18) )
| ~ spl23_7 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f370,plain,
( ~ spl23_5
| spl23_7 ),
inference(avatar_split_clause,[],[f357,f368,f360]) ).
fof(f371,plain,
( ~ relation_like(sK16)
| spl23_5 ),
inference(resolution,[],[f362,f260]) ).
fof(f372,plain,
( $false
| spl23_5 ),
inference(forward_subsumption_resolution,[],[f371,f344]) ).
fof(f373,plain,
spl23_5,
inference(avatar_contradiction_clause,[],[f372]) ).
fof(f376,plain,
! [X0,X1] :
( ~ member(X0,range_of(inverse(X1)))
| ~ ilf_type(inverse(X1),binary_relation_type)
| member(ordered_pair(X0,sK1(X0,inverse(X1))),X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(resolution,[],[f273,f305]) ).
fof(f377,plain,
( ! [X0] :
( ~ member(X0,range_of(sK16))
| ~ ilf_type(sK16,binary_relation_type)
| member(ordered_pair(X0,sK1(X0,sK16)),sF18) )
| ~ spl23_7 ),
inference(resolution,[],[f273,f369]) ).
fof(f382,definition,
( spl23_8
<=> ilf_type(sF18,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl23_8])],[avatar_definition]) ).
fof(f383,plain,
( ilf_type(sF18,binary_relation_type)
| ~ spl23_8 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f384,plain,
( ~ ilf_type(sF18,binary_relation_type)
| spl23_8 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f389,plain,
( ! [X0] :
( ~ member(X0,range_of(sK16))
| member(ordered_pair(X0,sK1(X0,sK16)),sF18) )
| ~ spl23_5
| ~ spl23_7 ),
inference(forward_subsumption_resolution,[],[f377,f361]) ).
fof(f390,plain,
! [X0,X1] :
( member(ordered_pair(X0,sK1(X0,inverse(X1))),X1)
| ~ member(X0,range_of(inverse(X1)))
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f376,f144]) ).
fof(f391,plain,
( ! [X0] :
( member(ordered_pair(X0,sK1(X0,sK16)),sF18)
| ~ member(X0,sF17) )
| ~ spl23_5
| ~ spl23_7 ),
inference(forward_demodulation,[],[f389,f317]) ).
fof(f393,plain,
( ! [X0] :
( ~ member(X0,sF17)
| member(X0,domain_of(sF18))
| ~ ilf_type(sF18,binary_relation_type) )
| ~ spl23_5
| ~ spl23_7 ),
inference(resolution,[],[f391,f308]) ).
fof(f398,plain,
! [X0,X1] :
( ~ member(X0,range_of(inverse(X1)))
| ~ ilf_type(X1,binary_relation_type)
| member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(resolution,[],[f390,f308]) ).
fof(f405,plain,
! [X0,X1] :
( ~ member(X0,range_of(inverse(X1)))
| ~ ilf_type(X1,binary_relation_type)
| member(X0,domain_of(X1)) ),
inference(duplicate_literal_removal,[],[f398]) ).
fof(f412,plain,
( ~ relation_like(sF18)
| spl23_8 ),
inference(resolution,[],[f384,f260]) ).
fof(f415,plain,
! [X0,X1] :
( ~ member(X0,domain_of(inverse(X1)))
| ~ ilf_type(inverse(X1),binary_relation_type)
| member(ordered_pair(sK0(X0,inverse(X1)),X0),X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(resolution,[],[f275,f305]) ).
fof(f416,plain,
( ! [X0] :
( ~ member(X0,domain_of(sK16))
| ~ ilf_type(sK16,binary_relation_type)
| member(ordered_pair(sK0(X0,sK16),X0),sF18) )
| ~ spl23_7 ),
inference(resolution,[],[f275,f369]) ).
fof(f420,plain,
( ! [X0] :
( ~ member(X0,domain_of(sK16))
| member(ordered_pair(sK0(X0,sK16),X0),sF18) )
| ~ spl23_5
| ~ spl23_7 ),
inference(forward_subsumption_resolution,[],[f416,f361]) ).
fof(f421,plain,
! [X0,X1] :
( member(ordered_pair(sK0(X0,inverse(X1)),X0),X1)
| ~ member(X0,domain_of(inverse(X1)))
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f415,f144]) ).
fof(f422,plain,
( ! [X0] :
( member(ordered_pair(sK0(X0,sK16),X0),sF18)
| ~ member(X0,sF20) )
| ~ spl23_5
| ~ spl23_7 ),
inference(forward_demodulation,[],[f420,f320]) ).
fof(f425,plain,
( ! [X0] :
( ~ member(X0,sF20)
| member(X0,range_of(sF18))
| ~ ilf_type(sF18,binary_relation_type) )
| ~ spl23_5
| ~ spl23_7 ),
inference(resolution,[],[f422,f307]) ).
fof(f439,plain,
! [X0,X1] :
( ~ member(X0,domain_of(inverse(X1)))
| ~ ilf_type(X1,binary_relation_type)
| member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(resolution,[],[f421,f307]) ).
fof(f444,plain,
! [X0,X1] :
( ~ member(X0,domain_of(inverse(X1)))
| ~ ilf_type(X1,binary_relation_type)
| member(X0,range_of(X1)) ),
inference(duplicate_literal_removal,[],[f439]) ).
fof(f461,plain,
! [X0] :
( ~ member(X0,domain_of(sF18))
| ~ ilf_type(sK16,binary_relation_type)
| member(X0,range_of(sK16)) ),
inference(superposition,[],[f444,f356]) ).
fof(f462,plain,
( ! [X0] :
( ~ member(X0,domain_of(sF18))
| member(X0,range_of(sK16)) )
| ~ spl23_5 ),
inference(forward_subsumption_resolution,[],[f461,f361]) ).
fof(f463,plain,
( ! [X0] :
( ~ member(X0,domain_of(sF18))
| member(X0,sF17) )
| ~ spl23_5 ),
inference(forward_demodulation,[],[f462,f317]) ).
fof(f505,plain,
! [X0] :
( ~ member(X0,range_of(sF18))
| ~ ilf_type(sK16,binary_relation_type)
| member(X0,domain_of(sK16)) ),
inference(superposition,[],[f405,f356]) ).
fof(f506,plain,
( ! [X0] :
( ~ member(X0,range_of(sF18))
| member(X0,domain_of(sK16)) )
| ~ spl23_5 ),
inference(forward_subsumption_resolution,[],[f505,f361]) ).
fof(f507,plain,
( ! [X0] :
( ~ member(X0,range_of(sF18))
| member(X0,sF20) )
| ~ spl23_5 ),
inference(forward_demodulation,[],[f506,f320]) ).
fof(f515,plain,
( ! [X0] :
( member(sK6(X0,range_of(sF18)),sF20)
| member(sK6(X0,range_of(sF18)),X0)
| range_of(sF18) = X0 )
| ~ spl23_5 ),
inference(resolution,[],[f507,f295]) ).
fof(f573,plain,
( ilf_type(sF18,relation_type(sK15,sK14))
| ~ ilf_type(sK16,relation_type(sK14,sK15)) ),
inference(superposition,[],[f277,f204]) ).
fof(f575,plain,
( ~ ilf_type(sK16,relation_type(sK14,sK15))
| spl23_3 ),
inference(forward_subsumption_resolution,[],[f573,f327]) ).
fof(f576,plain,
( ~ ilf_type(sK16,sF22)
| spl23_3 ),
inference(forward_demodulation,[],[f575,f213]) ).
fof(f577,plain,
( $false
| spl23_3 ),
inference(forward_subsumption_resolution,[],[f576,f214]) ).
fof(f578,plain,
spl23_3,
inference(avatar_contradiction_clause,[],[f577]) ).
fof(f649,plain,
( member(sK6(sF20,range_of(sF18)),sF20)
| sF20 = range_of(sF18)
| ~ spl23_5 ),
inference(factoring,[],[f515]) ).
fof(f653,definition,
( spl23_25
<=> sF20 = range_of(sF18) ),
introduced(definition,[new_symbols(definition,[spl23_25])],[avatar_definition]) ).
fof(f655,plain,
( sF20 = range_of(sF18)
| ~ spl23_25 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f657,definition,
( spl23_26
<=> member(sK6(sF20,range_of(sF18)),sF20) ),
introduced(definition,[new_symbols(definition,[spl23_26])],[avatar_definition]) ).
fof(f659,plain,
( member(sK6(sF20,range_of(sF18)),sF20)
| ~ spl23_26 ),
inference(avatar_component_clause,[],[f657]) ).
fof(f660,plain,
( spl23_25
| spl23_26
| ~ spl23_5 ),
inference(avatar_split_clause,[],[f649,f360,f657,f653]) ).
fof(f671,plain,
( relation_like(sF18)
| ~ spl23_3 ),
inference(resolution,[],[f326,f342]) ).
fof(f673,plain,
( domain(sK15,sK14,sF18) = domain_of(sF18)
| ~ spl23_3 ),
inference(resolution,[],[f326,f282]) ).
fof(f674,plain,
( range(sK15,sK14,sF18) = range_of(sF18)
| ~ spl23_3 ),
inference(resolution,[],[f326,f280]) ).
fof(f675,plain,
( sF20 = range(sK15,sK14,sF18)
| ~ spl23_3
| ~ spl23_25 ),
inference(forward_demodulation,[],[f674,f655]) ).
fof(f677,plain,
( $false
| ~ spl23_3
| spl23_8 ),
inference(forward_subsumption_resolution,[],[f671,f412]) ).
fof(f678,plain,
( ~ spl23_3
| spl23_8 ),
inference(avatar_contradiction_clause,[],[f677]) ).
fof(f679,plain,
( sF20 = sF21
| ~ spl23_3
| ~ spl23_25 ),
inference(forward_demodulation,[],[f675,f210]) ).
fof(f681,plain,
( $false
| spl23_1
| ~ spl23_3
| ~ spl23_25 ),
inference(forward_subsumption_resolution,[],[f679,f224]) ).
fof(f682,plain,
( spl23_1
| ~ spl23_3
| ~ spl23_25 ),
inference(avatar_contradiction_clause,[],[f681]) ).
fof(f684,plain,
( sF21 = range_of(sF18)
| ~ spl23_3 ),
inference(forward_demodulation,[],[f674,f210]) ).
fof(f686,plain,
( ! [X0] :
( member(X0,domain_of(sF18))
| ~ member(X0,sF17) )
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8 ),
inference(forward_subsumption_resolution,[],[f393,f383]) ).
fof(f688,plain,
( ! [X0] :
( ~ member(X0,sF20)
| member(X0,range_of(sF18)) )
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8 ),
inference(forward_subsumption_resolution,[],[f425,f383]) ).
fof(f696,plain,
( ! [X0] :
( ~ member(X0,sF20)
| member(X0,sF21) )
| ~ spl23_3
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8 ),
inference(forward_demodulation,[],[f688,f684]) ).
fof(f771,plain,
( member(sK6(sF20,range_of(sF18)),sF21)
| ~ spl23_3
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8
| ~ spl23_26 ),
inference(resolution,[],[f659,f696]) ).
fof(f772,plain,
( member(sK6(sF20,sF21),sF20)
| ~ spl23_3
| ~ spl23_26 ),
inference(superposition,[],[f659,f684]) ).
fof(f773,plain,
( member(sK6(sF20,sF21),sF21)
| ~ spl23_3
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8
| ~ spl23_26 ),
inference(forward_demodulation,[],[f771,f684]) ).
fof(f774,plain,
( sF20 = sF21
| ~ member(sK6(sF20,sF21),sF20)
| ~ spl23_3
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8
| ~ spl23_26 ),
inference(resolution,[],[f773,f296]) ).
fof(f775,plain,
( ~ member(sK6(sF20,sF21),sF20)
| spl23_1
| ~ spl23_3
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8
| ~ spl23_26 ),
inference(forward_subsumption_resolution,[],[f774,f224]) ).
fof(f776,plain,
( $false
| spl23_1
| ~ spl23_3
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8
| ~ spl23_26 ),
inference(forward_subsumption_resolution,[],[f775,f772]) ).
fof(f777,plain,
( spl23_1
| ~ spl23_3
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8
| ~ spl23_26 ),
inference(avatar_contradiction_clause,[],[f776]) ).
fof(f780,plain,
( sF19 = domain_of(sF18)
| ~ spl23_3 ),
inference(forward_demodulation,[],[f673,f206]) ).
fof(f821,plain,
( ! [X0] :
( ~ member(X0,sF19)
| member(X0,sF17) )
| ~ spl23_3
| ~ spl23_5 ),
inference(superposition,[],[f463,f780]) ).
fof(f871,plain,
( ! [X0] :
( member(sK2(X0,sF19),sF17)
| member(sK2(X0,sF19),X0)
| sF19 = X0 )
| ~ spl23_3
| ~ spl23_5 ),
inference(resolution,[],[f821,f303]) ).
fof(f920,plain,
( member(sK2(sF17,sF19),sF17)
| sF17 = sF19
| ~ spl23_3
| ~ spl23_5 ),
inference(factoring,[],[f871]) ).
fof(f924,plain,
( member(sK2(sF17,sF19),sF17)
| spl23_2
| ~ spl23_3
| ~ spl23_5 ),
inference(forward_subsumption_resolution,[],[f920,f228]) ).
fof(f1045,plain,
( ! [X0] :
( ~ member(sK2(X0,domain_of(sF18)),sF17)
| domain_of(sF18) = X0
| ~ member(sK2(X0,domain_of(sF18)),X0) )
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8 ),
inference(resolution,[],[f686,f304]) ).
fof(f1051,plain,
( ! [X0] :
( ~ member(sK2(X0,sF19),sF17)
| domain_of(sF18) = X0
| ~ member(sK2(X0,domain_of(sF18)),X0) )
| ~ spl23_3
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8 ),
inference(forward_demodulation,[],[f1045,f780]) ).
fof(f1054,plain,
( ! [X0] :
( sF19 = X0
| ~ member(sK2(X0,sF19),sF17)
| ~ member(sK2(X0,domain_of(sF18)),X0) )
| ~ spl23_3
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8 ),
inference(forward_demodulation,[],[f1051,f780]) ).
fof(f1056,plain,
( ! [X0] :
( ~ member(sK2(X0,sF19),sF17)
| sF19 = X0
| ~ member(sK2(X0,sF19),X0) )
| ~ spl23_3
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8 ),
inference(forward_demodulation,[],[f1054,f780]) ).
fof(f1058,plain,
( sF17 = sF19
| ~ member(sK2(sF17,sF19),sF17)
| spl23_2
| ~ spl23_3
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8 ),
inference(resolution,[],[f1056,f924]) ).
fof(f1060,plain,
( ~ member(sK2(sF17,sF19),sF17)
| spl23_2
| ~ spl23_3
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8 ),
inference(forward_subsumption_resolution,[],[f1058,f228]) ).
fof(f1061,plain,
( $false
| spl23_2
| ~ spl23_3
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8 ),
inference(forward_subsumption_resolution,[],[f1060,f924]) ).
fof(f1062,plain,
( spl23_2
| ~ spl23_3
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8 ),
inference(avatar_contradiction_clause,[],[f1061]) ).
cnf(s1,plain,
( ~ spl23_1
| ~ spl23_2 ),
inference(sat_conversion,[],[f229]) ).
cnf(s4,plain,
( ~ spl23_5
| spl23_7 ),
inference(sat_conversion,[],[f370]) ).
cnf(s5,plain,
spl23_5,
inference(sat_conversion,[],[f373]) ).
cnf(s16,plain,
spl23_3,
inference(sat_conversion,[],[f578]) ).
cnf(s19,plain,
( ~ spl23_5
| spl23_25
| spl23_26 ),
inference(sat_conversion,[],[f660]) ).
cnf(s20,plain,
( ~ spl23_3
| spl23_8 ),
inference(sat_conversion,[],[f678]) ).
cnf(s21,plain,
( spl23_1
| ~ spl23_3
| ~ spl23_25 ),
inference(sat_conversion,[],[f682]) ).
cnf(s27,plain,
( spl23_1
| ~ spl23_3
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8
| ~ spl23_26 ),
inference(sat_conversion,[],[f777]) ).
cnf(s29,plain,
( spl23_2
| ~ spl23_3
| ~ spl23_5
| ~ spl23_7
| ~ spl23_8 ),
inference(sat_conversion,[],[f1062]) ).
cnf(s30,plain,
spl23_8,
inference(rat,[],[s20,s16]) ).
cnf(s33,plain,
spl23_7,
inference(rat,[],[s4,s5]) ).
cnf(s34,plain,
spl23_2,
inference(rat,[],[s29,s30,s5,s16,s33]) ).
cnf(s37,plain,
~ spl23_1,
inference(rat,[],[s1,s34]) ).
cnf(s38,plain,
~ spl23_26,
inference(rat,[],[s27,s33,s30,s5,s16,s37]) ).
cnf(s39,plain,
~ spl23_25,
inference(rat,[],[s21,s16,s37]) ).
cnf(s40,plain,
$false,
inference(rat,[],[s19,s5,s38,s39]) ).
fof(f1063,plain,
$false,
inference(avatar_sat_refutation,[],[s40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET661+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 02:29:25 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.61/1.99 % (1811321)Detected formulas, will run a generic FOF schedule.
% 6.61/1.99 % (1811332)dis-21_1_sil=8000:lcm=predicate:random_seed=3308527321: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)
% 6.61/1.99 % (1811332)Instruction limit reached!
% 6.61/1.99 % (1811332)------------------------------
% 6.61/1.99 % (1811332)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.61/1.99 % (1811332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.61/1.99 % (1811332)CaDiCaL version: 2.1.3
% 6.61/1.99 % (1811332)Termination reason: Instruction limit
% 6.61/1.99 % (1811332)Termination phase: Saturation
% 6.61/1.99 % (1811332)Time elapsed: 0.044 s
% 6.61/1.99 % (1811332)Peak memory usage: 90 MB
% 6.61/1.99 % (1811332)Instructions burned: 130 (million)
% 6.61/1.99 % (1811329)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1033329945:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.61/1.99 % (1811330)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1139682714:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.61/1.99 % (1811326)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=1868949696:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.61/1.99 % (1811327)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=1532475421:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.61/1.99 % (1811328)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=3066595266:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.61/1.99 % (1811331)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2288428941:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.61/1.99 % (1811329)Refutation not found, incomplete strategy
% 6.61/1.99 % (1811329)------------------------------
% 6.61/1.99 % (1811329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.61/1.99 % (1811329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.61/1.99 % (1811329)CaDiCaL version: 2.1.3
% 6.61/1.99 % (1811329)Termination reason: Refutation not found, incomplete strategy
% 6.61/1.99 % (1811329)Time elapsed: 0.003 s
% 6.61/1.99 % (1811329)Peak memory usage: 88 MB
% 6.61/1.99 % (1811329)Instructions burned: 3 (million)
% 6.61/1.99 % (1811330)Instruction limit reached!
% 6.61/1.99 % (1811330)------------------------------
% 6.61/1.99 % (1811330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.61/1.99 % (1811330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.61/1.99 % (1811330)CaDiCaL version: 2.1.3
% 6.61/1.99 % (1811330)Termination reason: Instruction limit
% 6.61/1.99 % (1811330)Termination phase: Saturation
% 6.61/1.99 % (1811330)Time elapsed: 0.070 s
% 6.61/1.99 % (1811330)Peak memory usage: 88 MB
% 6.61/1.99 % (1811330)Instructions burned: 119 (million)
% 6.61/1.99 % (1811340)lrs+10_1_sil=8000:sp=occurrence:random_seed=35646677:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.61/1.99 % (1811331)Instruction limit reached!
% 6.61/1.99 % (1811331)------------------------------
% 6.61/1.99 % (1811331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.61/1.99 % (1811331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.61/1.99 % (1811331)CaDiCaL version: 2.1.3
% 6.61/1.99 % (1811331)Termination reason: Instruction limit
% 6.61/1.99 % (1811331)Termination phase: Saturation
% 6.61/1.99 % (1811331)Time elapsed: 0.102 s
% 6.61/1.99 % (1811331)Peak memory usage: 90 MB
% 6.61/1.99 % (1811331)Instructions burned: 139 (million)
% 6.61/1.99 % (1811340)Instruction limit reached!
% 6.61/1.99 % (1811340)------------------------------
% 6.61/1.99 % (1811340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.61/1.99 % (1811340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.61/1.99 % (1811340)CaDiCaL version: 2.1.3
% 6.61/1.99 % (1811340)Termination reason: Instruction limit
% 6.61/1.99 % (1811340)Termination phase: Saturation
% 6.61/1.99 % (1811340)Time elapsed: 0.095 s
% 6.61/1.99 % (1811340)Peak memory usage: 92 MB
% 6.61/1.99 % (1811340)Instructions burned: 288 (million)
% 6.61/1.99 % (1811341)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1925812046:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.61/1.99 % (1811343)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3135232866:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.61/1.99 % (1811329)------------------------------
% 6.61/1.99 % (1811329)------------------------------
% 6.61/1.99 % (1811344)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=1810307581:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 6.61/1.99 % (1811341)Instruction limit reached!
% 6.61/1.99 % (1811341)------------------------------
% 6.61/1.99 % (1811341)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.61/1.99 % (1811341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.61/1.99 % (1811341)CaDiCaL version: 2.1.3
% 6.61/1.99 % (1811341)Termination reason: Instruction limit
% 6.61/1.99 % (1811341)Termination phase: Saturation
% 6.61/1.99 % (1811341)Time elapsed: 0.084 s
% 6.61/1.99 % (1811341)Peak memory usage: 89 MB
% 6.61/1.99 % (1811341)Instructions burned: 158 (million)
% 6.61/1.99 % (1811344)Instruction limit reached!
% 6.61/1.99 % (1811344)------------------------------
% 6.61/1.99 % (1811344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.61/1.99 % (1811344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.61/1.99 % (1811344)CaDiCaL version: 2.1.3
% 6.61/1.99 % (1811344)Termination reason: Instruction limit
% 6.61/1.99 % (1811344)Termination phase: Saturation
% 6.61/1.99 % (1811344)Time elapsed: 0.094 s
% 6.61/1.99 % (1811344)Peak memory usage: 91 MB
% 6.61/1.99 % (1811344)Instructions burned: 248 (million)
% 6.61/1.99 % (1811347)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=638662581:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.61/1.99 % (1811347)Refutation not found, incomplete strategy
% 6.61/1.99 % (1811347)------------------------------
% 6.61/1.99 % (1811347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.61/1.99 % (1811347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.61/1.99 % (1811347)CaDiCaL version: 2.1.3
% 6.61/1.99 % (1811347)Termination reason: Refutation not found, incomplete strategy
% 6.61/1.99 % (1811347)Time elapsed: 0.004 s
% 6.61/1.99 % (1811347)Peak memory usage: 88 MB
% 6.61/1.99 % (1811347)Instructions burned: 5 (million)
% 6.61/1.99 % (1811343)Instruction limit reached!
% 6.61/1.99 % (1811343)------------------------------
% 6.61/1.99 % (1811343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.61/1.99 % (1811343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.61/1.99 % (1811343)CaDiCaL version: 2.1.3
% 6.61/1.99 % (1811343)Termination reason: Instruction limit
% 6.61/1.99 % (1811343)Termination phase: Saturation
% 6.61/1.99 % (1811343)Time elapsed: 0.161 s
% 6.61/1.99 % (1811343)Peak memory usage: 90 MB
% 6.61/1.99 % (1811343)Instructions burned: 327 (million)
% 6.61/1.99 % (1811349)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2947315942:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.61/1.99 % (1811350)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2269838520:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.61/1.99 % (1811350)Instruction limit reached!
% 6.61/1.99 % (1811350)------------------------------
% 6.61/1.99 % (1811350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.61/1.99 % (1811350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.61/1.99 % (1811350)CaDiCaL version: 2.1.3
% 6.61/1.99 % (1811350)Termination reason: Instruction limit
% 6.61/1.99 % (1811350)Termination phase: Saturation
% 6.61/1.99 % (1811350)Time elapsed: 0.042 s
% 6.61/1.99 % (1811350)Peak memory usage: 90 MB
% 6.61/1.99 % (1811350)Instructions burned: 115 (million)
% 6.61/1.99 % (1811353)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=4222939153:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.61/1.99 % (1811355)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2901239105:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 6.61/1.99 % (1811353)Instruction limit reached!
% 6.61/1.99 % (1811353)------------------------------
% 6.61/1.99 % (1811353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.61/1.99 % (1811353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.61/1.99 % (1811353)CaDiCaL version: 2.1.3
% 6.61/1.99 % (1811353)Termination reason: Instruction limit
% 6.61/1.99 % (1811353)Termination phase: Saturation
% 6.61/1.99 % (1811353)Time elapsed: 0.065 s
% 6.61/1.99 % (1811353)Peak memory usage: 89 MB
% 6.61/1.99 % (1811353)Instructions burned: 128 (million)
% 6.61/1.99 % (1811355)Instruction limit reached!
% 6.61/1.99 % (1811355)------------------------------
% 6.61/1.99 % (1811355)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.61/1.99 % (1811355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.61/1.99 % (1811355)CaDiCaL version: 2.1.3
% 6.61/1.99 % (1811355)Termination reason: Instruction limit
% 6.61/1.99 % (1811355)Termination phase: Saturation
% 6.61/1.99 % (1811355)Time elapsed: 0.030 s
% 6.61/1.99 % (1811355)Peak memory usage: 89 MB
% 6.61/1.99 % (1811355)Instructions burned: 118 (million)
% 6.61/1.99 % (1811347)------------------------------
% 6.61/1.99 % (1811347)------------------------------
% 6.61/1.99 % (1811359)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3535555651:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 6.61/1.99 % (1811359)Refutation not found, incomplete strategy
% 6.61/1.99 % (1811359)------------------------------
% 6.61/1.99 % (1811359)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.61/1.99 % (1811359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.61/1.99 % (1811359)CaDiCaL version: 2.1.3
% 6.61/1.99 % (1811359)Termination reason: Refutation not found, incomplete strategy
% 6.61/1.99 % (1811359)Time elapsed: 0.002 s
% 6.61/1.99 % (1811359)Peak memory usage: 88 MB
% 6.61/1.99 % (1811359)Instructions burned: 5 (million)
% 6.61/1.99 % (1811326)First to succeed.
% 6.61/1.99 % (1811326)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1811321"
% 6.61/1.99 % (1811358)lrs+10_1_sil=8000:sp=occurrence:random_seed=923997011:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.61/1.99 % (1811360)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2692311306:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 6.61/1.99 % (1811359)------------------------------
% 6.61/1.99 % (1811359)------------------------------
% 6.61/1.99 % (1811364)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2862050215:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2989 on theBenchmark for (2989ds/134Mi)
% 6.61/1.99 % (1811326)Refutation found. Thanks to Tanya!
% 6.61/1.99 % SZS status Theorem for theBenchmark
% 6.61/1.99 % SZS output start Proof for theBenchmark
% See solution above
% 8.59/2.19 % (1811326)------------------------------
% 8.59/2.19 % (1811326)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.59/2.19 % (1811326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.59/2.19 % (1811326)CaDiCaL version: 2.1.3
% 8.59/2.19 % (1811326)Termination reason: Refutation
% 8.59/2.19 % (1811326)Time elapsed: 0.721 s
% 8.59/2.19 % (1811326)Peak memory usage: 129 MB
% 8.59/2.19 % (1811326)Instructions burned: 1067 (million)
% 8.59/2.19 % (1811326)------------------------------
% 8.59/2.19 % (1811326)------------------------------
% 8.59/2.19 % (1811321)Success in time 1.131 s
% 8.59/2.19 % Vampire exiting
%------------------------------------------------------------------------------