%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET683+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 12:41:38 PM UTC 2026
% Result : Theorem 2.42s 1.15s
% Output : Refutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 120 ( 16 unt; 2 def)
% Number of atoms : 441 ( 11 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 554 ( 233 ~; 207 |; 59 &)
% ( 14 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 232 ( 0 sgn 215 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(X2,domain_of(X1)) ) ) ) ),
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,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',p2) ).
fof(f4,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',p4) ).
fof(f6,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',p6) ).
fof(f10,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
fof(f12,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12) ).
fof(f14,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).
fof(f18,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',p18) ).
fof(f20,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/sandbox/benchmark/theBenchmark.p',p20) ).
fof(f21,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(domain(X0,X1,X2),subset_type(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
fof(f22,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/sandbox/benchmark/theBenchmark.p',p22) ).
fof(f24,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
fof(f25,conjecture,
! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ! [X3] :
( ilf_type(X3,member_type(X0))
=> ( member(X3,range(X1,X0,X2))
=> ? [X4] :
( ilf_type(X4,member_type(X1))
& member(X4,domain(X1,X0,X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_50) ).
fof(f26,negated_conjecture,
~ ! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ! [X3] :
( ilf_type(X3,member_type(X0))
=> ( member(X3,range(X1,X0,X2))
=> ? [X4] :
( ilf_type(X4,member_type(X1))
& member(X4,domain(X1,X0,X2)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f27,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,domain_of(X1)) )
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,domain_of(X1)) )
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f27]) ).
fof(f29,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,[],[f2]) ).
fof(f31,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,[],[f4]) ).
fof(f32,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,[],[f31]) ).
fof(f35,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f6]) ).
fof(f39,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f10]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f12]) ).
fof(f42,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f14]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0] :
( ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f15]) ).
fof(f49,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,[],[f18]) ).
fof(f51,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,[],[f20]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f53,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,[],[f22]) ).
fof(f55,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ~ ilf_type(X4,member_type(X1))
| ~ member(X4,domain(X1,X0,X2)) )
& member(X3,range(X1,X0,X2))
& ilf_type(X3,member_type(X0)) )
& ilf_type(X2,relation_type(X1,X0)) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f26]) ).
fof(f56,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ~ ilf_type(X4,member_type(X1))
| ~ member(X4,domain(X1,X0,X2)) )
& member(X3,range(X1,X0,X2))
& ilf_type(X3,member_type(X0)) )
& ilf_type(X2,relation_type(X1,X0)) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(sK0(X1),set_type)
& member(sK0(X1),domain_of(X1)) )
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X1))],[f28]) ).
fof(f59,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,[],[f32]) ).
fof(f61,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,[],[f35]) ).
fof(f62,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,[],[f61]) ).
fof(f63,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))],[f62]) ).
fof(f64,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,[],[f39]) ).
fof(f65,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,[],[f64]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) )
& ( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f40]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f43]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK6(X0,X1),X1)
& member(sK6(X0,X1),X0)
& ilf_type(sK6(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f70]) ).
fof(f75,plain,
( ! [X4] :
( ~ ilf_type(X4,member_type(sK11))
| ~ member(X4,domain(sK11,sK10,sK12)) )
& member(sK13,range(sK11,sK10,sK12))
& ilf_type(sK13,member_type(sK10))
& ilf_type(sK12,relation_type(sK11,sK10))
& ~ empty(sK11)
& ilf_type(sK11,set_type)
& ~ empty(sK10)
& ilf_type(sK10,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12),skolemize(X3,sK13)],[f56]) ).
fof(f76,plain,
! [X0,X1] :
( member(sK0(X1),domain_of(X1))
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f57]) ).
fof(f78,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,[],[f29]) ).
fof(f81,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f59]) ).
fof(f82,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,[],[f59]) ).
fof(f84,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f63]) ).
fof(f92,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f65]) ).
fof(f94,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f67]) ).
fof(f97,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f71]) ).
fof(f102,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f44]) ).
fof(f110,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,[],[f49]) ).
fof(f112,plain,
! [X2,X0,X1] :
( 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(cnf_transformation,[],[f51]) ).
fof(f113,plain,
! [X2,X0,X1] :
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f52]) ).
fof(f114,plain,
! [X2,X0,X1] :
( 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(cnf_transformation,[],[f53]) ).
fof(f116,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f24]) ).
fof(f121,plain,
ilf_type(sK12,relation_type(sK11,sK10)),
inference(cnf_transformation,[],[f75]) ).
fof(f123,plain,
member(sK13,range(sK11,sK10,sK12)),
inference(cnf_transformation,[],[f75]) ).
fof(f124,plain,
! [X4] :
( ~ member(X4,domain(sK11,sK10,sK12))
| ~ ilf_type(X4,member_type(sK11)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f125,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f92]) ).
fof(f126,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[],[f102,f116]) ).
fof(f130,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f125,f116]) ).
fof(f144,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f84,f116]) ).
fof(f145,plain,
! [X2,X0] :
( ~ empty(X0)
| ~ member(X2,X0) ),
inference(forward_subsumption_resolution,[],[f144,f116]) ).
fof(f148,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,[],[f110,f116]) ).
fof(f149,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(forward_subsumption_resolution,[],[f148,f116]) ).
fof(f150,plain,
! [X0,X1] :
( member(sK0(X1),domain_of(X1))
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f76,f116]) ).
fof(f151,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f81,f116]) ).
fof(f152,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1) ),
inference(forward_subsumption_resolution,[],[f151,f116]) ).
fof(f158,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,[],[f82,f145]) ).
fof(f159,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f158,f116]) ).
fof(f160,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[],[f159,f116]) ).
fof(f166,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f94,f116]) ).
fof(f167,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ),
inference(forward_subsumption_resolution,[],[f166,f116]) ).
fof(f181,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,[],[f78,f116]) ).
fof(f182,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f181,f116]) ).
fof(f191,plain,
! [X2,X0,X1] :
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f112,f116]) ).
fof(f192,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| domain(X0,X1,X2) = domain_of(X2) ),
inference(forward_subsumption_resolution,[],[f191,f116]) ).
fof(f193,plain,
domain(sK11,sK10,sK12) = domain_of(sK12),
inference(resolution,[],[f192,f121]) ).
fof(f196,plain,
! [X0] :
( ~ ilf_type(X0,member_type(sK11))
| ~ member(X0,domain_of(sK12)) ),
inference(superposition,[],[f124,f193]) ).
fof(f203,plain,
! [X2,X0,X1] :
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f113,f116]) ).
fof(f204,plain,
! [X2,X0,X1] :
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f203,f116]) ).
fof(f207,plain,
( ilf_type(domain_of(sK12),subset_type(sK11))
| ~ ilf_type(sK12,relation_type(sK11,sK10)) ),
inference(superposition,[],[f204,f193]) ).
fof(f208,plain,
ilf_type(domain_of(sK12),subset_type(sK11)),
inference(forward_subsumption_resolution,[],[f207,f121]) ).
fof(f209,plain,
! [X2,X0,X1] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f114,f116]) ).
fof(f210,plain,
! [X2,X0,X1] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f209,f116]) ).
fof(f221,plain,
( member(sK13,range_of(sK12))
| ~ ilf_type(sK12,relation_type(sK11,sK10)) ),
inference(superposition,[],[f123,f210]) ).
fof(f222,plain,
member(sK13,range_of(sK12)),
inference(forward_subsumption_resolution,[],[f221,f121]) ).
fof(f234,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f97,f116]) ).
fof(f235,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f234,f116]) ).
fof(f236,plain,
! [X3,X0,X1] :
( ~ member(X0,power_set(X1))
| ~ member(X3,X0)
| member(X3,X1) ),
inference(forward_subsumption_resolution,[],[f235,f116]) ).
fof(f240,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,X2)
| ~ ilf_type(X1,member_type(power_set(X2)))
| empty(power_set(X2)) ),
inference(resolution,[],[f236,f152]) ).
fof(f244,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X2)))
| member(X0,X2)
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[],[f240,f126]) ).
fof(f257,plain,
! [X0] :
( ~ member(X0,sK11)
| ~ member(X0,domain_of(sK12)) ),
inference(resolution,[],[f196,f160]) ).
fof(f279,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(X1))
| ~ member(X0,X2)
| member(X0,X1) ),
inference(resolution,[],[f244,f167]) ).
fof(f294,definition,
( spl14_8
<=> ilf_type(sK12,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl14_8])],[avatar_definition]) ).
fof(f295,plain,
( ilf_type(sK12,binary_relation_type)
| ~ spl14_8 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f296,plain,
( ~ ilf_type(sK12,binary_relation_type)
| spl14_8 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f298,definition,
( spl14_9
<=> ! [X0] : ~ member(X0,range_of(sK12)) ),
introduced(definition,[new_symbols(definition,[spl14_9])],[avatar_definition]) ).
fof(f299,plain,
( ! [X0] : ~ member(X0,range_of(sK12))
| ~ spl14_9 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f301,plain,
( ~ relation_like(sK12)
| spl14_8 ),
inference(resolution,[],[f296,f130]) ).
fof(f304,plain,
( ! [X0,X1] : ~ ilf_type(sK12,subset_type(cross_product(X0,X1)))
| spl14_8 ),
inference(resolution,[],[f301,f149]) ).
fof(f315,plain,
( ! [X0,X1] : ~ ilf_type(sK12,relation_type(X0,X1))
| spl14_8 ),
inference(resolution,[],[f304,f182]) ).
fof(f319,plain,
( $false
| spl14_8 ),
inference(resolution,[],[f315,f121]) ).
fof(f321,plain,
spl14_8,
inference(avatar_contradiction_clause,[],[f319]) ).
fof(f326,plain,
! [X0] :
( ~ member(X0,domain_of(sK12))
| member(X0,sK11) ),
inference(resolution,[],[f279,f208]) ).
fof(f331,plain,
! [X0] : ~ member(X0,domain_of(sK12)),
inference(forward_subsumption_resolution,[],[f326,f257]) ).
fof(f334,plain,
! [X0] :
( ~ member(X0,range_of(sK12))
| ~ ilf_type(sK12,binary_relation_type) ),
inference(resolution,[],[f331,f150]) ).
fof(f339,plain,
( ! [X0] : ~ member(X0,range_of(sK12))
| ~ spl14_8 ),
inference(forward_subsumption_resolution,[],[f334,f295]) ).
fof(f341,plain,
( spl14_9
| ~ spl14_8 ),
inference(avatar_split_clause,[],[f339,f294,f298]) ).
fof(f353,plain,
( $false
| ~ spl14_9 ),
inference(resolution,[],[f299,f222]) ).
fof(f354,plain,
~ spl14_9,
inference(avatar_contradiction_clause,[],[f353]) ).
cnf(s9,plain,
spl14_8,
inference(sat_conversion,[],[f321]) ).
cnf(s11,plain,
( ~ spl14_8
| spl14_9 ),
inference(sat_conversion,[],[f341]) ).
cnf(s14,plain,
~ spl14_9,
inference(sat_conversion,[],[f354]) ).
cnf(s16,plain,
~ spl14_8,
inference(rat,[],[s11,s14]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s9,s16]) ).
fof(f363,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET683+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 28 02:35:37 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 2.42/1.15 % (4100781)Detected formulas, will run a generic FOF schedule.
% 2.42/1.15 % (4100791)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1303079453:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.42/1.15 % (4100791)First to succeed.
% 2.42/1.15 % (4100791)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4100781"
% 2.42/1.15 % (4100786)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=1010928055:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.42/1.15 % (4100788)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=2228855930:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.42/1.15 % (4100789)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4117529575:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.42/1.15 % (4100787)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=2780440022:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.42/1.15 % (4100789)Refutation not found, incomplete strategy
% 2.42/1.15 % (4100789)------------------------------
% 2.42/1.15 % (4100789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/1.15 % (4100789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/1.15 % (4100789)CaDiCaL version: 2.1.3
% 2.42/1.15 % (4100789)Termination reason: Refutation not found, incomplete strategy
% 2.42/1.15 % (4100789)Time elapsed: 0.003 s
% 2.42/1.15 % (4100789)Peak memory usage: 88 MB
% 2.42/1.15 % (4100789)Instructions burned: 2 (million)
% 2.42/1.15 % (4100792)dis-21_1_sil=8000:lcm=predicate:random_seed=2597428446: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)
% 2.42/1.15 % (4100790)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1808434739:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.42/1.15 % (4100790)Refutation not found, incomplete strategy
% 2.42/1.15 % (4100790)------------------------------
% 2.42/1.15 % (4100790)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/1.15 % (4100790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/1.15 % (4100790)CaDiCaL version: 2.1.3
% 2.42/1.15 % (4100790)Termination reason: Refutation not found, incomplete strategy
% 2.42/1.15 % (4100790)Time elapsed: 0.003 s
% 2.42/1.15 % (4100790)Peak memory usage: 88 MB
% 2.42/1.15 % (4100790)Instructions burned: 3 (million)
% 2.42/1.15 % (4100792)Instruction limit reached!
% 2.42/1.15 % (4100792)------------------------------
% 2.42/1.15 % (4100792)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/1.15 % (4100792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/1.15 % (4100792)CaDiCaL version: 2.1.3
% 2.42/1.15 % (4100792)Termination reason: Instruction limit
% 2.42/1.15 % (4100792)Termination phase: Saturation
% 2.42/1.15 % (4100792)Time elapsed: 0.081 s
% 2.42/1.15 % (4100792)Peak memory usage: 90 MB
% 2.42/1.15 % (4100792)Instructions burned: 130 (million)
% 2.42/1.15 % (4100791)Refutation found. Thanks to Tanya!
% 2.42/1.15 % SZS status Theorem for theBenchmark
% 2.42/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.75/1.35 % (4100791)------------------------------
% 2.75/1.35 % (4100791)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.35 % (4100791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.35 % (4100791)CaDiCaL version: 2.1.3
% 2.75/1.35 % (4100791)Termination reason: Refutation
% 2.75/1.35 % (4100791)Time elapsed: 0.007 s
% 2.75/1.35 % (4100791)Peak memory usage: 90 MB
% 2.75/1.35 % (4100791)Instructions burned: 14 (million)
% 2.75/1.35 % (4100791)------------------------------
% 2.75/1.35 % (4100791)------------------------------
% 2.75/1.35 % (4100781)Success in time 0.315 s
% 2.75/1.35 % Vampire exiting
%------------------------------------------------------------------------------