%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET684+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of formulae : 144 ( 15 unt; 7 def)
% Number of atoms : 670 ( 8 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 905 ( 379 ~; 347 |; 118 &)
% ( 18 <=>; 41 =>; 0 <=; 2 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-5 aty)
% Number of variables : 306 ( 0 sgn 258 !; 48 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(ordered_pair(X0,X1),compose(X2,X3))
<=> ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X0,X4),X2)
& member(ordered_pair(X4,X1),X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X2,X0)
& member(X3,X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).
fof(f26,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',p26) ).
fof(f27,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> compose5(X0,X1,X2,X3,X4) = compose(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
fof(f29,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p29) ).
fof(f30,conjecture,
! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,member_type(X0))
=> ! [X6] :
( ilf_type(X6,member_type(X2))
=> ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
<=> ? [X7] :
( ilf_type(X7,member_type(X1))
& member(ordered_pair(X5,X7),X3)
& member(ordered_pair(X7,X6),X4) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_51) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ! [X5] :
( ilf_type(X5,member_type(X0))
=> ! [X6] :
( ilf_type(X6,member_type(X2))
=> ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
<=> ? [X7] :
( ilf_type(X7,member_type(X1))
& member(ordered_pair(X5,X7),X3)
& member(ordered_pair(X7,X6),X4) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( member(ordered_pair(X0,X1),compose(X2,X3))
<=> ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X0,X4),X2)
& member(ordered_pair(X4,X1),X3) ) )
| ~ ilf_type(X3,binary_relation_type) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f33,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X2,X0)
& member(X3,X1) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f34,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X2,X0)
& member(X3,X1) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f33]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f5]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f7]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f39]) ).
fof(f43,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f9]) ).
fof(f49,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f15]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( 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,[],[f26]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( compose5(X0,X1,X2,X3,X4) = compose(X3,X4)
| ~ ilf_type(X4,relation_type(X1,X2)) )
| ~ ilf_type(X3,relation_type(X0,X1)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f27]) ).
fof(f66,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
<~> ? [X7] :
( ilf_type(X7,member_type(X1))
& member(ordered_pair(X5,X7),X3)
& member(ordered_pair(X7,X6),X4) ) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(X0)) )
& ilf_type(X4,relation_type(X1,X2)) )
& ilf_type(X3,relation_type(X0,X1)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f31]) ).
fof(f67,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4))
<~> ? [X7] :
( ilf_type(X7,member_type(X1))
& member(ordered_pair(X5,X7),X3)
& member(ordered_pair(X7,X6),X4) ) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(X0)) )
& ilf_type(X4,relation_type(X1,X2)) )
& ilf_type(X3,relation_type(X0,X1)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),compose(X2,X3))
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X0,X4),X2)
| ~ member(ordered_pair(X4,X1),X3) ) )
& ( ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X0,X4),X2)
& member(ordered_pair(X4,X1),X3) )
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ) )
| ~ ilf_type(X3,binary_relation_type) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f32]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),compose(X2,X3))
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X0,X4),X2)
| ~ member(ordered_pair(X4,X1),X3) ) )
& ( ? [X5] :
( ilf_type(X5,set_type)
& member(ordered_pair(X0,X5),X2)
& member(ordered_pair(X5,X1),X3) )
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ) )
| ~ ilf_type(X3,binary_relation_type) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f68]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),compose(X2,X3))
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X0,X4),X2)
| ~ member(ordered_pair(X4,X1),X3) ) )
& ( ( ilf_type(sK0(X0,X1,X2,X3),set_type)
& member(ordered_pair(X0,sK0(X0,X1,X2,X3)),X2)
& member(ordered_pair(sK0(X0,X1,X2,X3),X1),X3) )
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ) )
| ~ ilf_type(X3,binary_relation_type) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X5,sK0(X0,X1,X2,X3))],[f69]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f40]) ).
fof(f75,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,[],[f43]) ).
fof(f76,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,[],[f75]) ).
fof(f77,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))],[f76]) ).
fof(f78,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,[],[f49]) ).
fof(f79,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,[],[f78]) ).
fof(f93,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ ilf_type(X7,member_type(X1))
| ~ member(ordered_pair(X5,X7),X3)
| ~ member(ordered_pair(X7,X6),X4) )
| ~ member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ( ? [X7] :
( ilf_type(X7,member_type(X1))
& member(ordered_pair(X5,X7),X3)
& member(ordered_pair(X7,X6),X4) )
| member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(X0)) )
& ilf_type(X4,relation_type(X1,X2)) )
& ilf_type(X3,relation_type(X0,X1)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f67]) ).
fof(f94,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ ilf_type(X7,member_type(X1))
| ~ member(ordered_pair(X5,X7),X3)
| ~ member(ordered_pair(X7,X6),X4) )
| ~ member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ( ? [X7] :
( ilf_type(X7,member_type(X1))
& member(ordered_pair(X5,X7),X3)
& member(ordered_pair(X7,X6),X4) )
| member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(X0)) )
& ilf_type(X4,relation_type(X1,X2)) )
& ilf_type(X3,relation_type(X0,X1)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ! [X7] :
( ~ ilf_type(X7,member_type(X1))
| ~ member(ordered_pair(X5,X7),X3)
| ~ member(ordered_pair(X7,X6),X4) )
| ~ member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ( ? [X8] :
( ilf_type(X8,member_type(X1))
& member(ordered_pair(X5,X8),X3)
& member(ordered_pair(X8,X6),X4) )
| member(ordered_pair(X5,X6),compose5(X0,X1,X2,X3,X4)) )
& ilf_type(X6,member_type(X2)) )
& ilf_type(X5,member_type(X0)) )
& ilf_type(X4,relation_type(X1,X2)) )
& ilf_type(X3,relation_type(X0,X1)) )
& ~ empty(X2)
& ilf_type(X2,set_type) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(rectify,[],[f94]) ).
fof(f96,plain,
( ( ! [X7] :
( ~ ilf_type(X7,member_type(sK12))
| ~ member(ordered_pair(sK16,X7),sK14)
| ~ member(ordered_pair(X7,sK17),sK15) )
| ~ member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15)) )
& ( ( ilf_type(sK18,member_type(sK12))
& member(ordered_pair(sK16,sK18),sK14)
& member(ordered_pair(sK18,sK17),sK15) )
| member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15)) )
& ilf_type(sK17,member_type(sK13))
& ilf_type(sK16,member_type(sK11))
& ilf_type(sK15,relation_type(sK12,sK13))
& ilf_type(sK14,relation_type(sK11,sK12))
& ~ empty(sK13)
& ilf_type(sK13,set_type)
& ~ empty(sK12)
& ilf_type(sK12,set_type)
& ~ empty(sK11)
& ilf_type(sK11,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14,sK15,sK16,sK17,sK18]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13),skolemize(X3,sK14),skolemize(X4,sK15),skolemize(X5,sK16),skolemize(X6,sK17),skolemize(X8,sK18)],[f95]) ).
fof(f97,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(sK0(X0,X1,X2,X3),X1),X3)
| ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f70]) ).
fof(f98,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,sK0(X0,X1,X2,X3)),X2)
| ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f70]) ).
fof(f100,plain,
! [X2,X3,X0,X1,X4] :
( member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X0,X4),X2)
| ~ member(ordered_pair(X4,X1),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f70]) ).
fof(f102,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f34]) ).
fof(f106,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,[],[f37]) ).
fof(f110,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,[],[f73]) ).
fof(f112,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f77]) ).
fof(f122,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f79]) ).
fof(f147,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,[],[f63]) ).
fof(f148,plain,
! [X2,X3,X0,X1,X4] :
( compose5(X0,X1,X2,X3,X4) = compose(X3,X4)
| ~ ilf_type(X4,relation_type(X1,X2))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f64]) ).
fof(f150,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f29]) ).
fof(f157,plain,
ilf_type(sK14,relation_type(sK11,sK12)),
inference(cnf_transformation,[],[f96]) ).
fof(f158,plain,
ilf_type(sK15,relation_type(sK12,sK13)),
inference(cnf_transformation,[],[f96]) ).
fof(f161,plain,
( member(ordered_pair(sK18,sK17),sK15)
| member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15)) ),
inference(cnf_transformation,[],[f96]) ).
fof(f162,plain,
( member(ordered_pair(sK16,sK18),sK14)
| member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15)) ),
inference(cnf_transformation,[],[f96]) ).
fof(f164,plain,
! [X7] :
( ~ ilf_type(X7,member_type(sK12))
| ~ member(ordered_pair(sK16,X7),sK14)
| ~ member(ordered_pair(X7,sK17),sK15)
| ~ member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15)) ),
inference(cnf_transformation,[],[f96]) ).
fof(f173,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f122]) ).
fof(f175,definition,
( spl19_1
<=> member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15)) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
fof(f176,plain,
( ~ member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15))
| spl19_1 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f177,plain,
( member(ordered_pair(sK16,sK17),compose5(sK11,sK12,sK13,sK14,sK15))
| ~ spl19_1 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f179,definition,
( spl19_2
<=> member(ordered_pair(sK18,sK17),sK15) ),
introduced(definition,[new_symbols(definition,[spl19_2])],[avatar_definition]) ).
fof(f181,plain,
( member(ordered_pair(sK18,sK17),sK15)
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f182,plain,
( spl19_1
| spl19_2 ),
inference(avatar_split_clause,[],[f161,f179,f175]) ).
fof(f184,definition,
( spl19_3
<=> member(ordered_pair(sK16,sK18),sK14) ),
introduced(definition,[new_symbols(definition,[spl19_3])],[avatar_definition]) ).
fof(f186,plain,
( member(ordered_pair(sK16,sK18),sK14)
| ~ spl19_3 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f187,plain,
( spl19_1
| spl19_3 ),
inference(avatar_split_clause,[],[f162,f184,f175]) ).
fof(f194,definition,
( spl19_5
<=> ! [X7] :
( ~ ilf_type(X7,member_type(sK12))
| ~ member(ordered_pair(X7,sK17),sK15)
| ~ member(ordered_pair(sK16,X7),sK14) ) ),
introduced(definition,[new_symbols(definition,[spl19_5])],[avatar_definition]) ).
fof(f195,plain,
( ! [X7] :
( ~ member(ordered_pair(sK16,X7),sK14)
| ~ member(ordered_pair(X7,sK17),sK15)
| ~ ilf_type(X7,member_type(sK12)) )
| ~ spl19_5 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f196,plain,
( ~ spl19_1
| spl19_5 ),
inference(avatar_split_clause,[],[f164,f194,f175]) ).
fof(f221,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f173,f150]) ).
fof(f227,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f112,f150]) ).
fof(f228,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[],[f227,f150]) ).
fof(f253,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,[],[f147,f150]) ).
fof(f254,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(forward_subsumption_resolution,[],[f253,f150]) ).
fof(f267,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,[],[f110,f228]) ).
fof(f268,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f267,f150]) ).
fof(f269,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[],[f268,f150]) ).
fof(f310,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,[],[f106,f150]) ).
fof(f311,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f310,f150]) ).
fof(f314,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(resolution,[],[f311,f254]) ).
fof(f331,plain,
relation_like(sK14),
inference(resolution,[],[f314,f157]) ).
fof(f332,plain,
relation_like(sK15),
inference(resolution,[],[f314,f158]) ).
fof(f431,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(forward_subsumption_resolution,[],[f102,f150]) ).
fof(f432,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(forward_subsumption_resolution,[],[f431,f150]) ).
fof(f433,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type) ),
inference(forward_subsumption_resolution,[],[f432,f150]) ).
fof(f434,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X2,X3),X4)
| member(X2,X0)
| ~ ilf_type(X4,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f433,f150]) ).
fof(f444,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(sK0(X0,X1,X2,X3),X1),X3)
| ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f97,f150]) ).
fof(f445,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(sK0(X0,X1,X2,X3),X1),X3)
| ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f444,f150]) ).
fof(f457,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| member(sK0(X0,X1,X2,X3),X4)
| ~ ilf_type(X3,relation_type(X4,X5)) ),
inference(resolution,[],[f445,f434]) ).
fof(f464,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,sK0(X0,X1,X2,X3)),X2)
| ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ),
inference(forward_subsumption_resolution,[],[f98,f150]) ).
fof(f465,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,sK0(X0,X1,X2,X3)),X2)
| ~ member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f464,f150]) ).
fof(f476,plain,
! [X2,X3,X0,X1,X4] :
( compose5(X0,X1,X2,X3,X4) = compose(X3,X4)
| ~ ilf_type(X4,relation_type(X1,X2))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f148,f150]) ).
fof(f477,plain,
! [X2,X3,X0,X1,X4] :
( compose5(X0,X1,X2,X3,X4) = compose(X3,X4)
| ~ ilf_type(X4,relation_type(X1,X2))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f476,f150]) ).
fof(f478,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X4,relation_type(X1,X2))
| compose5(X0,X1,X2,X3,X4) = compose(X3,X4)
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f477,f150]) ).
fof(f482,plain,
! [X0,X1] :
( ~ ilf_type(X1,relation_type(X0,sK12))
| compose5(X0,sK12,sK13,X1,sK15) = compose(X1,sK15) ),
inference(resolution,[],[f478,f158]) ).
fof(f496,plain,
! [X2,X3,X0,X1,X4] :
( member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X0,X4),X2)
| ~ member(ordered_pair(X4,X1),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ),
inference(forward_subsumption_resolution,[],[f100,f150]) ).
fof(f497,plain,
! [X2,X3,X0,X1,X4] :
( member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X0,X4),X2)
| ~ member(ordered_pair(X4,X1),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f496,f150]) ).
fof(f498,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X4,X1),X3)
| ~ member(ordered_pair(X0,X4),X2)
| member(ordered_pair(X0,X1),compose(X2,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f497,f150]) ).
fof(f502,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(X0,sK18),X1)
| member(ordered_pair(X0,sK17),compose(X1,sK15))
| ~ ilf_type(sK15,binary_relation_type)
| ~ ilf_type(X1,binary_relation_type) )
| ~ spl19_2 ),
inference(resolution,[],[f498,f181]) ).
fof(f510,definition,
( spl19_19
<=> ilf_type(sK15,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl19_19])],[avatar_definition]) ).
fof(f511,plain,
( ilf_type(sK15,binary_relation_type)
| ~ spl19_19 ),
inference(avatar_component_clause,[],[f510]) ).
fof(f512,plain,
( ~ ilf_type(sK15,binary_relation_type)
| spl19_19 ),
inference(avatar_component_clause,[],[f510]) ).
fof(f514,definition,
( spl19_20
<=> ! [X0,X1] :
( ~ member(ordered_pair(X0,sK18),X1)
| ~ ilf_type(X1,binary_relation_type)
| member(ordered_pair(X0,sK17),compose(X1,sK15)) ) ),
introduced(definition,[new_symbols(definition,[spl19_20])],[avatar_definition]) ).
fof(f515,plain,
( ! [X0,X1] :
( member(ordered_pair(X0,sK17),compose(X1,sK15))
| ~ ilf_type(X1,binary_relation_type)
| ~ member(ordered_pair(X0,sK18),X1) )
| ~ spl19_20 ),
inference(avatar_component_clause,[],[f514]) ).
fof(f516,plain,
( ~ spl19_19
| spl19_20
| ~ spl19_2 ),
inference(avatar_split_clause,[],[f502,f179,f514,f510]) ).
fof(f518,definition,
( spl19_21
<=> ilf_type(sK14,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl19_21])],[avatar_definition]) ).
fof(f519,plain,
( ilf_type(sK14,binary_relation_type)
| ~ spl19_21 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f520,plain,
( ~ ilf_type(sK14,binary_relation_type)
| spl19_21 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f525,plain,
( ~ relation_like(sK15)
| spl19_19 ),
inference(resolution,[],[f512,f221]) ).
fof(f526,plain,
( $false
| spl19_19 ),
inference(forward_subsumption_resolution,[],[f525,f332]) ).
fof(f527,plain,
spl19_19,
inference(avatar_contradiction_clause,[],[f526]) ).
fof(f529,plain,
( ~ relation_like(sK14)
| spl19_21 ),
inference(resolution,[],[f520,f221]) ).
fof(f530,plain,
( $false
| spl19_21 ),
inference(forward_subsumption_resolution,[],[f529,f331]) ).
fof(f531,plain,
spl19_21,
inference(avatar_contradiction_clause,[],[f530]) ).
fof(f540,plain,
compose5(sK11,sK12,sK13,sK14,sK15) = compose(sK14,sK15),
inference(resolution,[],[f482,f157]) ).
fof(f555,plain,
( ~ member(ordered_pair(sK16,sK17),compose(sK14,sK15))
| spl19_1 ),
inference(superposition,[],[f176,f540]) ).
fof(f563,plain,
( ~ ilf_type(sK14,binary_relation_type)
| ~ member(ordered_pair(sK16,sK18),sK14)
| spl19_1
| ~ spl19_20 ),
inference(resolution,[],[f555,f515]) ).
fof(f564,plain,
( ~ member(ordered_pair(sK16,sK18),sK14)
| spl19_1
| ~ spl19_20
| ~ spl19_21 ),
inference(forward_subsumption_resolution,[],[f563,f519]) ).
fof(f565,plain,
( $false
| spl19_1
| ~ spl19_3
| ~ spl19_20
| ~ spl19_21 ),
inference(forward_subsumption_resolution,[],[f564,f186]) ).
fof(f566,plain,
( spl19_1
| ~ spl19_3
| ~ spl19_20
| ~ spl19_21 ),
inference(avatar_contradiction_clause,[],[f565]) ).
fof(f567,plain,
( member(ordered_pair(sK16,sK17),compose(sK14,sK15))
| ~ spl19_1 ),
inference(forward_demodulation,[],[f177,f540]) ).
fof(f591,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(sK0(sK16,X0,sK14,X1),sK17),sK15)
| ~ ilf_type(sK0(sK16,X0,sK14,X1),member_type(sK12))
| ~ member(ordered_pair(sK16,X0),compose(sK14,X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(sK14,binary_relation_type) )
| ~ spl19_5 ),
inference(resolution,[],[f195,f465]) ).
fof(f592,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(sK0(sK16,X0,sK14,X1),sK17),sK15)
| ~ ilf_type(sK0(sK16,X0,sK14,X1),member_type(sK12))
| ~ member(ordered_pair(sK16,X0),compose(sK14,X1))
| ~ ilf_type(X1,binary_relation_type) )
| ~ spl19_5
| ~ spl19_21 ),
inference(forward_subsumption_resolution,[],[f591,f519]) ).
fof(f641,plain,
( ~ ilf_type(sK0(sK16,sK17,sK14,sK15),member_type(sK12))
| ~ member(ordered_pair(sK16,sK17),compose(sK14,sK15))
| ~ ilf_type(sK15,binary_relation_type)
| ~ member(ordered_pair(sK16,sK17),compose(sK14,sK15))
| ~ ilf_type(sK15,binary_relation_type)
| ~ ilf_type(sK14,binary_relation_type)
| ~ spl19_5
| ~ spl19_21 ),
inference(resolution,[],[f592,f445]) ).
fof(f642,plain,
( ~ ilf_type(sK0(sK16,sK17,sK14,sK15),member_type(sK12))
| ~ member(ordered_pair(sK16,sK17),compose(sK14,sK15))
| ~ ilf_type(sK15,binary_relation_type)
| ~ ilf_type(sK14,binary_relation_type)
| ~ spl19_5
| ~ spl19_21 ),
inference(duplicate_literal_removal,[],[f641]) ).
fof(f643,plain,
( ~ ilf_type(sK0(sK16,sK17,sK14,sK15),member_type(sK12))
| ~ ilf_type(sK15,binary_relation_type)
| ~ ilf_type(sK14,binary_relation_type)
| ~ spl19_1
| ~ spl19_5
| ~ spl19_21 ),
inference(forward_subsumption_resolution,[],[f642,f567]) ).
fof(f644,plain,
( ~ ilf_type(sK0(sK16,sK17,sK14,sK15),member_type(sK12))
| ~ ilf_type(sK14,binary_relation_type)
| ~ spl19_1
| ~ spl19_5
| ~ spl19_19
| ~ spl19_21 ),
inference(forward_subsumption_resolution,[],[f643,f511]) ).
fof(f645,plain,
( ~ ilf_type(sK0(sK16,sK17,sK14,sK15),member_type(sK12))
| ~ spl19_1
| ~ spl19_5
| ~ spl19_19
| ~ spl19_21 ),
inference(forward_subsumption_resolution,[],[f644,f519]) ).
fof(f646,plain,
( ~ member(sK0(sK16,sK17,sK14,sK15),sK12)
| ~ spl19_1
| ~ spl19_5
| ~ spl19_19
| ~ spl19_21 ),
inference(resolution,[],[f645,f269]) ).
fof(f932,plain,
( ! [X0,X1] :
( ~ ilf_type(sK15,binary_relation_type)
| ~ ilf_type(sK14,binary_relation_type)
| member(sK0(sK16,sK17,sK14,sK15),X0)
| ~ ilf_type(sK15,relation_type(X0,X1)) )
| ~ spl19_1 ),
inference(resolution,[],[f457,f567]) ).
fof(f944,plain,
( ! [X0,X1] :
( ~ ilf_type(sK14,binary_relation_type)
| member(sK0(sK16,sK17,sK14,sK15),X0)
| ~ ilf_type(sK15,relation_type(X0,X1)) )
| ~ spl19_1
| ~ spl19_19 ),
inference(forward_subsumption_resolution,[],[f932,f511]) ).
fof(f948,plain,
( ! [X0,X1] :
( ~ ilf_type(sK15,relation_type(X0,X1))
| member(sK0(sK16,sK17,sK14,sK15),X0) )
| ~ spl19_1
| ~ spl19_19
| ~ spl19_21 ),
inference(forward_subsumption_resolution,[],[f944,f519]) ).
fof(f949,plain,
( member(sK0(sK16,sK17,sK14,sK15),sK12)
| ~ spl19_1
| ~ spl19_19
| ~ spl19_21 ),
inference(resolution,[],[f948,f158]) ).
fof(f950,plain,
( $false
| ~ spl19_1
| ~ spl19_5
| ~ spl19_19
| ~ spl19_21 ),
inference(forward_subsumption_resolution,[],[f949,f646]) ).
fof(f951,plain,
( ~ spl19_1
| ~ spl19_5
| ~ spl19_19
| ~ spl19_21 ),
inference(avatar_contradiction_clause,[],[f950]) ).
cnf(s1,plain,
( spl19_1
| spl19_2 ),
inference(sat_conversion,[],[f182]) ).
cnf(s2,plain,
( spl19_1
| spl19_3 ),
inference(sat_conversion,[],[f187]) ).
cnf(s4,plain,
( ~ spl19_1
| spl19_5 ),
inference(sat_conversion,[],[f196]) ).
cnf(s15,plain,
( ~ spl19_2
| ~ spl19_19
| spl19_20 ),
inference(sat_conversion,[],[f516]) ).
cnf(s17,plain,
spl19_19,
inference(sat_conversion,[],[f527]) ).
cnf(s18,plain,
spl19_21,
inference(sat_conversion,[],[f531]) ).
cnf(s19,plain,
( spl19_1
| ~ spl19_3
| ~ spl19_20
| ~ spl19_21 ),
inference(sat_conversion,[],[f566]) ).
cnf(s34,plain,
( ~ spl19_1
| ~ spl19_5
| ~ spl19_19
| ~ spl19_21 ),
inference(sat_conversion,[],[f951]) ).
cnf(s38,plain,
( ~ spl19_2
| spl19_20 ),
inference(rat,[],[s15,s17]) ).
cnf(s41,plain,
spl19_1,
inference(rat,[],[s38,s19,s1,s2,s18]) ).
cnf(s42,plain,
~ spl19_5,
inference(rat,[],[s34,s18,s17,s41]) ).
cnf(s45,plain,
$false,
inference(rat,[],[s4,s42,s41]) ).
fof(f952,plain,
$false,
inference(avatar_sat_refutation,[],[s45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET684+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n026.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
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 02:35:12 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.47 % (3420583)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (3420591)dis+10_1_sil=32000:sp=arity:random_seed=3648084145:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (3420589)% WARNING: option uhcvi not known.
% 0.16/0.47 % (3420589)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2421291469:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (3420588)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1310196997_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % (3420590)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2594852347:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (3420592)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2894963704:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (3420594)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3990394337:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % (3420593)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2605599480:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (3420591) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3420583-3420591"...
% 0.16/0.47 % (3420591)...printing done.
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % (3420591)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (3420591)------------------------------
% 0.16/0.47 % (3420591)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (3420591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (3420591)CaDiCaL version: 2.1.3
% 0.16/0.47 % (3420591)Termination reason: Refutation
% 0.16/0.47 % (3420591)Time elapsed: 0.016 s
% 0.16/0.47 % (3420591)Peak memory usage: 13 MB
% 0.16/0.47 % (3420591)Instructions burned: 40 (million)
% 0.16/0.47 % (3420583)Success in time 0.042 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------