TSTP Solution File: SET665+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET665+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:15:42 EDT 2024
% Result : Theorem 0.12s 0.36s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 15
% Syntax : Number of formulae : 95 ( 6 unt; 0 def)
% Number of atoms : 457 ( 21 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 659 ( 297 ~; 271 |; 48 &)
% ( 11 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 151 ( 141 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1269,plain,
$false,
inference(resolution,[],[f1268,f126]) ).
fof(f126,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(f1268,plain,
~ ilf_type(sK6,set_type),
inference(duplicate_literal_removal,[],[f1266]) ).
fof(f1266,plain,
( ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK6,set_type) ),
inference(resolution,[],[f1265,f137]) ).
fof(f137,plain,
! [X0] :
( ilf_type(identity_relation_of(X0),binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] :
( ilf_type(identity_relation_of(X0),binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(identity_relation_of(X0),binary_relation_type) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8) ).
fof(f1265,plain,
( ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(sK6,set_type) ),
inference(resolution,[],[f1264,f126]) ).
fof(f1264,plain,
( ~ ilf_type(cross_product(sK6,sK6),set_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type) ),
inference(duplicate_literal_removal,[],[f1263]) ).
fof(f1263,plain,
( ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(cross_product(sK6,sK6),set_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK6,set_type) ),
inference(resolution,[],[f1262,f157]) ).
fof(f157,plain,
! [X0,X1] :
( ilf_type(cross_product(X0,X1),relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( ilf_type(cross_product(X0,X1),relation_type(X0,X1))
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(cross_product(X0,X1),relation_type(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f1262,plain,
! [X0,X1] :
( ~ ilf_type(cross_product(sK6,sK6),relation_type(X1,X0))
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(cross_product(sK6,sK6),set_type) ),
inference(duplicate_literal_removal,[],[f1259]) ).
fof(f1259,plain,
! [X0,X1] :
( ~ ilf_type(cross_product(sK6,sK6),set_type)
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(cross_product(sK6,sK6),relation_type(X1,X0))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ),
inference(resolution,[],[f1222,f159]) ).
fof(f159,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( ( ! [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))) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [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)) ) ) ) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
fof(f1222,plain,
! [X0,X1] :
( ~ ilf_type(cross_product(sK6,sK6),subset_type(cross_product(X0,X1)))
| ~ ilf_type(cross_product(sK6,sK6),set_type)
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[],[f1221,f188]) ).
fof(f188,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,[],[f55]) ).
fof(f55,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,[],[f20]) ).
fof(f20,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',p20) ).
fof(f1221,plain,
( ~ relation_like(cross_product(sK6,sK6))
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(cross_product(sK6,sK6),set_type)
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type) ),
inference(resolution,[],[f1220,f201]) ).
fof(f201,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) ),
inference(duplicate_literal_removal,[],[f154]) ).
fof(f154,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f92]) ).
fof(f92,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11) ).
fof(f1220,plain,
( ~ ilf_type(cross_product(sK6,sK6),binary_relation_type)
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(sK6,set_type) ),
inference(resolution,[],[f1219,f126]) ).
fof(f1219,plain,
( ~ ilf_type(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(cross_product(sK6,sK6),binary_relation_type)
| ~ ilf_type(sK6,set_type) ),
inference(duplicate_literal_removal,[],[f1212]) ).
fof(f1212,plain,
( ~ ilf_type(sK6,set_type)
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(cross_product(sK6,sK6),binary_relation_type)
| ~ ilf_type(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(cross_product(sK6,sK6),binary_relation_type) ),
inference(resolution,[],[f1211,f203]) ).
fof(f203,plain,
( ~ sP0(cross_product(sK6,sK6),identity_relation_of(sK6))
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(cross_product(sK6,sK6),binary_relation_type) ),
inference(resolution,[],[f135,f202]) ).
fof(f202,plain,
( ~ sP1(identity_relation_of(sK6),cross_product(sK6,sK6))
| ~ sP0(cross_product(sK6,sK6),identity_relation_of(sK6)) ),
inference(resolution,[],[f129,f125]) ).
fof(f125,plain,
~ subset(identity_relation_of(sK6),cross_product(sK6,sK6)),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
( ~ subset(identity_relation_of(sK6),cross_product(sK6,sK6))
& ilf_type(sK6,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f31,f73]) ).
fof(f73,plain,
( ? [X0] :
( ~ subset(identity_relation_of(X0),cross_product(X0,X0))
& ilf_type(X0,set_type) )
=> ( ~ subset(identity_relation_of(sK6),cross_product(sK6,sK6))
& ilf_type(sK6,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
? [X0] :
( ~ subset(identity_relation_of(X0),cross_product(X0,X0))
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> subset(identity_relation_of(X0),cross_product(X0,X0)) ),
inference(negated_conjecture,[],[f28]) ).
fof(f28,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> subset(identity_relation_of(X0),cross_product(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_28) ).
fof(f129,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( ( ( subset(X0,X1)
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| ~ subset(X0,X1) ) )
| ~ sP1(X0,X1) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ( subset(X0,X1)
<=> sP0(X1,X0) )
| ~ sP1(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f135,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( sP1(X0,X1)
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(definition_folding,[],[f34,f65,f64]) ).
fof(f64,plain,
! [X1,X0] :
( sP0(X1,X0)
<=> ! [X2] :
( ! [X3] :
( member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f34,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( ! [X3] :
( member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( ! [X3] :
( member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(ordered_pair(X2,X3),X0)
=> member(ordered_pair(X2,X3),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f1211,plain,
( sP0(cross_product(sK6,sK6),identity_relation_of(sK6))
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(cross_product(sK6,sK6),binary_relation_type)
| ~ ilf_type(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type) ),
inference(duplicate_literal_removal,[],[f1202]) ).
fof(f1202,plain,
( ~ ilf_type(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(cross_product(sK6,sK6),binary_relation_type)
| sP0(cross_product(sK6,sK6),identity_relation_of(sK6))
| ~ ilf_type(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ ilf_type(sK6,set_type) ),
inference(resolution,[],[f1169,f1181]) ).
fof(f1181,plain,
( member(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),sK6)
| sP0(cross_product(sK6,sK6),identity_relation_of(sK6))
| ~ ilf_type(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ ilf_type(sK6,set_type) ),
inference(duplicate_literal_removal,[],[f1173]) ).
fof(f1173,plain,
( sP0(cross_product(sK6,sK6),identity_relation_of(sK6))
| member(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),sK6)
| ~ ilf_type(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ ilf_type(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ ilf_type(sK6,set_type) ),
inference(resolution,[],[f1171,f179]) ).
fof(f179,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| member(X1,X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(ordered_pair(X1,X2),identity_relation_of(X0))
| X1 != X2
| ~ member(X1,X0) )
& ( ( X1 = X2
& member(X1,X0) )
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0)) ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f109]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(ordered_pair(X1,X2),identity_relation_of(X0))
| X1 != X2
| ~ member(X1,X0) )
& ( ( X1 = X2
& member(X1,X0) )
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0)) ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(ordered_pair(X1,X2),identity_relation_of(X0))
<=> ( X1 = X2
& member(X1,X0) ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(ordered_pair(X1,X2),identity_relation_of(X0))
<=> ( X1 = X2
& member(X1,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(f1171,plain,
( member(ordered_pair(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),sK7(cross_product(sK6,sK6),identity_relation_of(sK6))),identity_relation_of(sK6))
| sP0(cross_product(sK6,sK6),identity_relation_of(sK6)) ),
inference(superposition,[],[f133,f1152]) ).
fof(f1152,plain,
sK7(cross_product(sK6,sK6),identity_relation_of(sK6)) = sK8(cross_product(sK6,sK6),identity_relation_of(sK6)),
inference(resolution,[],[f1151,f126]) ).
fof(f1151,plain,
( ~ ilf_type(sK6,set_type)
| sK7(cross_product(sK6,sK6),identity_relation_of(sK6)) = sK8(cross_product(sK6,sK6),identity_relation_of(sK6)) ),
inference(duplicate_literal_removal,[],[f1149]) ).
fof(f1149,plain,
( sK7(cross_product(sK6,sK6),identity_relation_of(sK6)) = sK8(cross_product(sK6,sK6),identity_relation_of(sK6))
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK6,set_type) ),
inference(resolution,[],[f1148,f137]) ).
fof(f1148,plain,
( ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| sK7(cross_product(sK6,sK6),identity_relation_of(sK6)) = sK8(cross_product(sK6,sK6),identity_relation_of(sK6))
| ~ ilf_type(sK6,set_type) ),
inference(resolution,[],[f1147,f126]) ).
fof(f1147,plain,
( ~ ilf_type(cross_product(sK6,sK6),set_type)
| sK7(cross_product(sK6,sK6),identity_relation_of(sK6)) = sK8(cross_product(sK6,sK6),identity_relation_of(sK6))
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(sK6,set_type) ),
inference(duplicate_literal_removal,[],[f1146]) ).
fof(f1146,plain,
( ~ ilf_type(cross_product(sK6,sK6),set_type)
| sK7(cross_product(sK6,sK6),identity_relation_of(sK6)) = sK8(cross_product(sK6,sK6),identity_relation_of(sK6))
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK6,set_type) ),
inference(resolution,[],[f1093,f157]) ).
fof(f1093,plain,
! [X0,X1] :
( ~ ilf_type(cross_product(sK6,sK6),relation_type(X1,X0))
| ~ ilf_type(cross_product(sK6,sK6),set_type)
| sK7(cross_product(sK6,sK6),identity_relation_of(sK6)) = sK8(cross_product(sK6,sK6),identity_relation_of(sK6))
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK6,set_type) ),
inference(duplicate_literal_removal,[],[f1090]) ).
fof(f1090,plain,
! [X0,X1] :
( ~ ilf_type(sK6,set_type)
| ~ ilf_type(cross_product(sK6,sK6),set_type)
| sK7(cross_product(sK6,sK6),identity_relation_of(sK6)) = sK8(cross_product(sK6,sK6),identity_relation_of(sK6))
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(cross_product(sK6,sK6),relation_type(X1,X0))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ),
inference(resolution,[],[f1055,f159]) ).
fof(f1055,plain,
! [X0,X1] :
( ~ ilf_type(cross_product(sK6,sK6),subset_type(cross_product(X0,X1)))
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(cross_product(sK6,sK6),set_type)
| sK7(cross_product(sK6,sK6),identity_relation_of(sK6)) = sK8(cross_product(sK6,sK6),identity_relation_of(sK6))
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[],[f1054,f188]) ).
fof(f1054,plain,
( ~ relation_like(cross_product(sK6,sK6))
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(cross_product(sK6,sK6),set_type)
| sK7(cross_product(sK6,sK6),identity_relation_of(sK6)) = sK8(cross_product(sK6,sK6),identity_relation_of(sK6)) ),
inference(resolution,[],[f1053,f201]) ).
fof(f1053,plain,
( ~ ilf_type(cross_product(sK6,sK6),binary_relation_type)
| sK7(cross_product(sK6,sK6),identity_relation_of(sK6)) = sK8(cross_product(sK6,sK6),identity_relation_of(sK6))
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(sK6,set_type) ),
inference(resolution,[],[f1052,f126]) ).
fof(f1052,plain,
( ~ ilf_type(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ ilf_type(sK6,set_type)
| sK7(cross_product(sK6,sK6),identity_relation_of(sK6)) = sK8(cross_product(sK6,sK6),identity_relation_of(sK6))
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(cross_product(sK6,sK6),binary_relation_type) ),
inference(resolution,[],[f1045,f126]) ).
fof(f1045,plain,
( ~ ilf_type(sK8(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ ilf_type(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ ilf_type(sK6,set_type)
| sK7(cross_product(sK6,sK6),identity_relation_of(sK6)) = sK8(cross_product(sK6,sK6),identity_relation_of(sK6))
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(cross_product(sK6,sK6),binary_relation_type) ),
inference(resolution,[],[f242,f203]) ).
fof(f242,plain,
! [X0,X1] :
( sP0(X0,identity_relation_of(X1))
| ~ ilf_type(sK8(X0,identity_relation_of(X1)),set_type)
| ~ ilf_type(sK7(X0,identity_relation_of(X1)),set_type)
| ~ ilf_type(X1,set_type)
| sK7(X0,identity_relation_of(X1)) = sK8(X0,identity_relation_of(X1)) ),
inference(resolution,[],[f180,f133]) ).
fof(f180,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| X1 = X2
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f110]) ).
fof(f133,plain,
! [X0,X1] :
( member(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ~ member(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0)
& member(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X1)
& ilf_type(sK8(X0,X1),set_type)
& ilf_type(sK7(X0,X1),set_type) ) )
& ( ! [X4] :
( ! [X5] :
( member(ordered_pair(X4,X5),X0)
| ~ member(ordered_pair(X4,X5),X1)
| ~ ilf_type(X5,set_type) )
| ~ ilf_type(X4,set_type) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f77,f79,f78]) ).
fof(f78,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( ~ member(ordered_pair(X2,X3),X0)
& member(ordered_pair(X2,X3),X1)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
=> ( ? [X3] :
( ~ member(ordered_pair(sK7(X0,X1),X3),X0)
& member(ordered_pair(sK7(X0,X1),X3),X1)
& ilf_type(X3,set_type) )
& ilf_type(sK7(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X0,X1] :
( ? [X3] :
( ~ member(ordered_pair(sK7(X0,X1),X3),X0)
& member(ordered_pair(sK7(X0,X1),X3),X1)
& ilf_type(X3,set_type) )
=> ( ~ member(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0)
& member(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X1)
& ilf_type(sK8(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ? [X3] :
( ~ member(ordered_pair(X2,X3),X0)
& member(ordered_pair(X2,X3),X1)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) )
& ( ! [X4] :
( ! [X5] :
( member(ordered_pair(X4,X5),X0)
| ~ member(ordered_pair(X4,X5),X1)
| ~ ilf_type(X5,set_type) )
| ~ ilf_type(X4,set_type) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f76]) ).
fof(f76,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ? [X2] :
( ? [X3] :
( ~ member(ordered_pair(X2,X3),X1)
& member(ordered_pair(X2,X3),X0)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ! [X3] :
( member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ sP0(X1,X0) ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f1169,plain,
( ~ member(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),sK6)
| ~ ilf_type(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(cross_product(sK6,sK6),binary_relation_type) ),
inference(duplicate_literal_removal,[],[f1168]) ).
fof(f1168,plain,
( ~ member(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),sK6)
| ~ ilf_type(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ member(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),sK6)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(cross_product(sK6,sK6),binary_relation_type) ),
inference(forward_demodulation,[],[f1161,f1152]) ).
fof(f1161,plain,
( ~ ilf_type(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ member(sK8(cross_product(sK6,sK6),identity_relation_of(sK6)),sK6)
| ~ member(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),sK6)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(cross_product(sK6,sK6),binary_relation_type) ),
inference(duplicate_literal_removal,[],[f1159]) ).
fof(f1159,plain,
( ~ ilf_type(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ member(sK8(cross_product(sK6,sK6),identity_relation_of(sK6)),sK6)
| ~ member(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),sK6)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(cross_product(sK6,sK6),binary_relation_type) ),
inference(backward_demodulation,[],[f382,f1152]) ).
fof(f382,plain,
( ~ member(sK8(cross_product(sK6,sK6),identity_relation_of(sK6)),sK6)
| ~ member(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),sK6)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK8(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ ilf_type(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(cross_product(sK6,sK6),binary_relation_type) ),
inference(duplicate_literal_removal,[],[f374]) ).
fof(f374,plain,
( ~ member(sK8(cross_product(sK6,sK6),identity_relation_of(sK6)),sK6)
| ~ member(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),sK6)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK8(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ ilf_type(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),set_type)
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(cross_product(sK6,sK6),binary_relation_type) ),
inference(resolution,[],[f187,f205]) ).
fof(f205,plain,
( ~ member(ordered_pair(sK7(cross_product(sK6,sK6),identity_relation_of(sK6)),sK8(cross_product(sK6,sK6),identity_relation_of(sK6))),cross_product(sK6,sK6))
| ~ ilf_type(identity_relation_of(sK6),binary_relation_type)
| ~ ilf_type(cross_product(sK6,sK6),binary_relation_type) ),
inference(resolution,[],[f134,f203]) ).
fof(f134,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ member(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f187,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) )
& ( ( member(X1,X3)
& member(X0,X2) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f113]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) )
& ( ( member(X1,X3)
& member(X0,X2) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X1,X3)
& member(X0,X2) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,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)
=> ( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X1,X3)
& member(X0,X2) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SET665+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.09 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Fri May 3 16:28:52 EDT 2024
% 0.08/0.27 % CPUTime :
% 0.12/0.28 % (14471)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.29 % (14474)WARNING: value z3 for option sas not known
% 0.12/0.29 % (14474)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.29 % (14473)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.29 % (14476)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.12/0.29 % (14478)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.12/0.29 % (14475)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.29 % (14477)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.12/0.29 % (14472)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.29 TRYING [1]
% 0.12/0.29 TRYING [2]
% 0.12/0.30 TRYING [3]
% 0.12/0.30 TRYING [1]
% 0.12/0.30 TRYING [2]
% 0.12/0.31 TRYING [4]
% 0.12/0.33 TRYING [3]
% 0.12/0.36 % (14477)First to succeed.
% 0.12/0.36 % (14477)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-14471"
% 0.12/0.36 % (14477)Refutation found. Thanks to Tanya!
% 0.12/0.36 % SZS status Theorem for theBenchmark
% 0.12/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.36 % (14477)------------------------------
% 0.12/0.36 % (14477)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.36 % (14477)Termination reason: Refutation
% 0.12/0.36
% 0.12/0.36 % (14477)Memory used [KB]: 2109
% 0.12/0.36 % (14477)Time elapsed: 0.075 s
% 0.12/0.36 % (14477)Instructions burned: 283 (million)
% 0.12/0.36 % (14471)Success in time 0.087 s
%------------------------------------------------------------------------------