%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET682+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 : n020.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 0.17s 0.49s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 16
% Syntax : Number of formulae : 127 ( 17 unt; 2 def)
% Number of atoms : 459 ( 12 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 565 ( 233 ~; 218 |; 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 : 223 ( 0 sgn 206 !; 17 ?)
% 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(X2,range_of(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,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',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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(f10,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
fof(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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',p20) ).
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/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(f23,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(range(X0,X1,X2),subset_type(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).
fof(f24,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/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(X0,X1))
=> ! [X3] :
( ilf_type(X3,member_type(X0))
=> ( member(X3,domain(X0,X1,X2))
=> ? [X4] :
( ilf_type(X4,member_type(X1))
& member(X4,range(X0,X1,X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_49) ).
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(X0,X1))
=> ! [X3] :
( ilf_type(X3,member_type(X0))
=> ( member(X3,domain(X0,X1,X2))
=> ? [X4] :
( ilf_type(X4,member_type(X1))
& member(X4,range(X0,X1,X2)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f27,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,range_of(X1)) )
| ~ member(X0,domain_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,range_of(X1)) )
| ~ member(X0,domain_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(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(f54,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f23]) ).
fof(f55,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ~ ilf_type(X4,member_type(X1))
| ~ member(X4,range(X0,X1,X2)) )
& member(X3,domain(X0,X1,X2))
& ilf_type(X3,member_type(X0)) )
& ilf_type(X2,relation_type(X0,X1)) )
& ~ 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,range(X0,X1,X2)) )
& member(X3,domain(X0,X1,X2))
& ilf_type(X3,member_type(X0)) )
& ilf_type(X2,relation_type(X0,X1)) )
& ~ 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),range_of(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(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,range(sK10,sK11,sK12)) )
& member(sK13,domain(sK10,sK11,sK12))
& ilf_type(sK13,member_type(sK10))
& ilf_type(sK12,relation_type(sK10,sK11))
& ~ 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),range_of(X1))
| ~ member(X0,domain_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(f86,plain,
! [X0] :
( empty(X0)
| member(sK3(X0),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(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(f115,plain,
! [X2,X0,X1] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f54]) ).
fof(f116,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f24]) ).
fof(f121,plain,
ilf_type(sK12,relation_type(sK10,sK11)),
inference(cnf_transformation,[],[f75]) ).
fof(f123,plain,
member(sK13,domain(sK10,sK11,sK12)),
inference(cnf_transformation,[],[f75]) ).
fof(f124,plain,
! [X4] :
( ~ member(X4,range(sK10,sK11,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(f131,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f125,f116]) ).
fof(f133,plain,
! [X0] :
( member(sK3(X0),X0)
| empty(X0) ),
inference(forward_subsumption_resolution,[],[f86,f116]) ).
fof(f156,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f84,f116]) ).
fof(f157,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[],[f156,f116]) ).
fof(f158,plain,
~ empty(domain(sK10,sK11,sK12)),
inference(resolution,[],[f157,f123]) ).
fof(f163,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(f164,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(forward_subsumption_resolution,[],[f163,f116]) ).
fof(f166,plain,
! [X0,X1] :
( ~ member(X0,domain_of(X1))
| member(sK0(X1),range_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f76,f116]) ).
fof(f167,plain,
! [X0] :
( member(sK0(X0),range_of(X0))
| ~ ilf_type(X0,binary_relation_type)
| empty(domain_of(X0)) ),
inference(resolution,[],[f166,f133]) ).
fof(f169,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(f170,plain,
! [X0,X1] :
( ~ ilf_type(X0,member_type(X1))
| member(X0,X1)
| empty(X1) ),
inference(forward_subsumption_resolution,[],[f169,f116]) ).
fof(f175,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,f157]) ).
fof(f176,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f175,f116]) ).
fof(f177,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[],[f176,f116]) ).
fof(f182,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(f183,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ),
inference(forward_subsumption_resolution,[],[f182,f116]) ).
fof(f184,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1))
| empty(power_set(X1)) ),
inference(resolution,[],[f183,f170]) ).
fof(f185,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f184,f126]) ).
fof(f217,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(f218,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f217,f116]) ).
fof(f220,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(resolution,[],[f218,f164]) ).
fof(f225,plain,
relation_like(sK12),
inference(resolution,[],[f220,f121]) ).
fof(f278,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(f279,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| domain(X0,X1,X2) = domain_of(X2) ),
inference(forward_subsumption_resolution,[],[f278,f116]) ).
fof(f280,plain,
domain(sK10,sK11,sK12) = domain_of(sK12),
inference(resolution,[],[f279,f121]) ).
fof(f283,plain,
~ empty(domain_of(sK12)),
inference(superposition,[],[f158,f280]) ).
fof(f292,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(f293,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| range(X0,X1,X2) = range_of(X2) ),
inference(forward_subsumption_resolution,[],[f292,f116]) ).
fof(f298,definition,
( spl14_11
<=> ilf_type(sK12,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl14_11])],[avatar_definition]) ).
fof(f299,plain,
( ilf_type(sK12,binary_relation_type)
| ~ spl14_11 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f300,plain,
( ~ ilf_type(sK12,binary_relation_type)
| spl14_11 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f306,plain,
range(sK10,sK11,sK12) = range_of(sK12),
inference(resolution,[],[f293,f121]) ).
fof(f308,plain,
( ~ relation_like(sK12)
| spl14_11 ),
inference(resolution,[],[f300,f131]) ).
fof(f309,plain,
( $false
| spl14_11 ),
inference(forward_subsumption_resolution,[],[f308,f225]) ).
fof(f310,plain,
spl14_11,
inference(avatar_contradiction_clause,[],[f309]) ).
fof(f311,plain,
! [X2,X0,X1] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f115,f116]) ).
fof(f312,plain,
! [X2,X0,X1] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f311,f116]) ).
fof(f318,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(f319,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f318,f116]) ).
fof(f320,plain,
! [X3,X0,X1] :
( ~ member(X0,power_set(X1))
| ~ member(X3,X0)
| member(X3,X1) ),
inference(forward_subsumption_resolution,[],[f319,f116]) ).
fof(f342,plain,
! [X0] :
( ~ member(X0,range_of(sK12))
| ~ ilf_type(X0,member_type(sK11)) ),
inference(superposition,[],[f124,f306]) ).
fof(f351,plain,
( ilf_type(range_of(sK12),subset_type(sK11))
| ~ ilf_type(sK12,relation_type(sK10,sK11)) ),
inference(superposition,[],[f312,f306]) ).
fof(f352,plain,
ilf_type(range_of(sK12),subset_type(sK11)),
inference(forward_subsumption_resolution,[],[f351,f121]) ).
fof(f356,plain,
member(range_of(sK12),power_set(sK11)),
inference(resolution,[],[f352,f185]) ).
fof(f382,plain,
! [X0] :
( ~ member(X0,range_of(sK12))
| member(X0,sK11) ),
inference(resolution,[],[f356,f320]) ).
fof(f480,plain,
( ~ ilf_type(sK0(sK12),member_type(sK11))
| ~ ilf_type(sK12,binary_relation_type)
| empty(domain_of(sK12)) ),
inference(resolution,[],[f342,f167]) ).
fof(f485,plain,
( ~ ilf_type(sK0(sK12),member_type(sK11))
| empty(domain_of(sK12))
| ~ spl14_11 ),
inference(forward_subsumption_resolution,[],[f480,f299]) ).
fof(f488,plain,
( ~ ilf_type(sK0(sK12),member_type(sK11))
| ~ spl14_11 ),
inference(forward_subsumption_resolution,[],[f485,f283]) ).
fof(f494,definition,
( spl14_25
<=> ilf_type(sK0(sK12),member_type(sK11)) ),
introduced(definition,[new_symbols(definition,[spl14_25])],[avatar_definition]) ).
fof(f496,plain,
( ~ ilf_type(sK0(sK12),member_type(sK11))
| spl14_25 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f498,plain,
( ~ spl14_25
| ~ spl14_11 ),
inference(avatar_split_clause,[],[f488,f298,f494]) ).
fof(f500,plain,
( ~ member(sK0(sK12),sK11)
| spl14_25 ),
inference(resolution,[],[f496,f177]) ).
fof(f511,plain,
( member(sK0(sK12),sK11)
| ~ ilf_type(sK12,binary_relation_type)
| empty(domain_of(sK12)) ),
inference(resolution,[],[f382,f167]) ).
fof(f519,plain,
( ~ ilf_type(sK12,binary_relation_type)
| empty(domain_of(sK12))
| spl14_25 ),
inference(forward_subsumption_resolution,[],[f511,f500]) ).
fof(f530,plain,
( empty(domain_of(sK12))
| ~ spl14_11
| spl14_25 ),
inference(forward_subsumption_resolution,[],[f519,f299]) ).
fof(f533,plain,
( $false
| ~ spl14_11
| spl14_25 ),
inference(forward_subsumption_resolution,[],[f530,f283]) ).
fof(f534,plain,
( ~ spl14_11
| spl14_25 ),
inference(avatar_contradiction_clause,[],[f533]) ).
cnf(s8,plain,
spl14_11,
inference(sat_conversion,[],[f310]) ).
cnf(s16,plain,
( ~ spl14_11
| ~ spl14_25 ),
inference(sat_conversion,[],[f498]) ).
cnf(s22,plain,
( ~ spl14_11
| spl14_25 ),
inference(sat_conversion,[],[f534]) ).
cnf(s25,plain,
spl14_25,
inference(rat,[],[s22,s8]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s16,s25,s8]) ).
fof(f538,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET682+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n020.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 02:34:04 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.17/0.49 % (3978674)Will run a generic schedule for satisfiability detection.
% 0.17/0.49 % (3978685)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2576698477:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.49 % (3978680)% WARNING: option uhcvi not known.
% 0.17/0.49 % (3978679)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=255759020_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.49 % (3978680)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2987114507:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.49 % (3978681)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=846976391:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.49 % (3978682)dis+10_1_sil=32000:sp=arity:random_seed=2760480660:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.49 % (3978683)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2289095244:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.49 % (3978684)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=535226045:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.49 % TRYING [1]
% 0.17/0.49 % TRYING [2]
% 0.17/0.49 % TRYING [3]
% 0.17/0.49 % (3978682) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3978674-3978682"...
% 0.17/0.49 % (3978682)...printing done.
% 0.17/0.49 % (3978682)Refutation found. Thanks to Tanya!
% 0.17/0.49 % SZS status Theorem for theBenchmark
% 0.17/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.50 % (3978682)------------------------------
% 0.17/0.50 % (3978682)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.50 % (3978682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.50 % (3978682)CaDiCaL version: 2.1.3
% 0.17/0.50 % (3978682)Termination reason: Refutation
% 0.17/0.50 % (3978682)Time elapsed: 0.013 s
% 0.17/0.50 % (3978682)Peak memory usage: 12 MB
% 0.17/0.50 % (3978682)Instructions burned: 17 (million)
% 0.17/0.50 % (3978674)Success in time 0.068 s
% 0.17/0.50 % Vampire exiting
%------------------------------------------------------------------------------