TSTP Solution File: SET679+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET679+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n003.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 : Tue May 21 03:21:53 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 24
% Syntax : Number of formulae : 123 ( 19 unt; 0 def)
% Number of atoms : 463 ( 32 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 563 ( 223 ~; 207 |; 85 &)
% ( 20 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 227 ( 198 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f232,plain,
$false,
inference(subsumption_resolution,[],[f231,f96]) ).
fof(f96,plain,
~ empty(sK4),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
( ~ not_equal(identity_relation_of(sK4),empty_set)
& ilf_type(sK4,set_type)
& ~ empty(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f28,f59]) ).
fof(f59,plain,
( ? [X0] :
( ~ not_equal(identity_relation_of(X0),empty_set)
& ilf_type(X0,set_type)
& ~ empty(X0) )
=> ( ~ not_equal(identity_relation_of(sK4),empty_set)
& ilf_type(sK4,set_type)
& ~ empty(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
? [X0] :
( ~ not_equal(identity_relation_of(X0),empty_set)
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
? [X0] :
( ~ not_equal(identity_relation_of(X0),empty_set)
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,negated_conjecture,
~ ! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> not_equal(identity_relation_of(X0),empty_set) ),
inference(negated_conjecture,[],[f24]) ).
fof(f24,conjecture,
! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> not_equal(identity_relation_of(X0),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_46) ).
fof(f231,plain,
empty(sK4),
inference(resolution,[],[f229,f160]) ).
fof(f160,plain,
! [X0] :
( member(sK8(X0),X0)
| empty(X0) ),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116]) ).
fof(f116,plain,
! [X0] :
( empty(X0)
| member(sK8(X0),X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK8(X0),X0)
& ilf_type(sK8(X0),set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f69,f70]) ).
fof(f70,plain,
! [X0] :
( ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) )
=> ( member(sK8(X0),X0)
& ilf_type(sK8(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f69,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,[],[f68]) ).
fof(f68,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,[],[f34]) ).
fof(f34,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,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',p8) ).
fof(f159,plain,
! [X0] : sP1(X0),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113]) ).
fof(f113,plain,
! [X0] :
( sP1(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( sP1(X0)
| ~ ilf_type(X0,set_type) ),
inference(definition_folding,[],[f33,f54,f53]) ).
fof(f53,plain,
! [X0] :
( sP0(X0)
<=> ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f54,plain,
! [X0] :
( ( relation_like(X0)
<=> sP0(X0) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f33,plain,
! [X0] :
( ( relation_like(X0)
<=> ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f32]) ).
fof(f32,plain,
! [X0] :
( ( relation_like(X0)
<=> ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( relation_like(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,X0)
=> ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(f107,plain,
! [X0,X4] :
( ilf_type(sK6(X4),set_type)
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ( sP0(X0)
| ( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != sK5(X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(sK5(X0),X0)
& ilf_type(sK5(X0),set_type) ) )
& ( ! [X4] :
( ( ordered_pair(sK6(X4),sK7(X4)) = X4
& ilf_type(sK7(X4),set_type)
& ilf_type(sK6(X4),set_type) )
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f63,f66,f65,f64]) ).
fof(f64,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(X1,X0)
& ilf_type(X1,set_type) )
=> ( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != sK5(X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(sK5(X0),X0)
& ilf_type(sK5(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X4] :
( ? [X5] :
( ? [X6] :
( ordered_pair(X5,X6) = X4
& ilf_type(X6,set_type) )
& ilf_type(X5,set_type) )
=> ( ? [X6] :
( ordered_pair(sK6(X4),X6) = X4
& ilf_type(X6,set_type) )
& ilf_type(sK6(X4),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
! [X4] :
( ? [X6] :
( ordered_pair(sK6(X4),X6) = X4
& ilf_type(X6,set_type) )
=> ( ordered_pair(sK6(X4),sK7(X4)) = X4
& ilf_type(sK7(X4),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
! [X0] :
( ( sP0(X0)
| ? [X1] :
( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X4] :
( ? [X5] :
( ? [X6] :
( ordered_pair(X5,X6) = X4
& ilf_type(X6,set_type) )
& ilf_type(X5,set_type) )
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ( sP0(X0)
| ? [X1] :
( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f108,plain,
! [X0,X4] :
( ilf_type(sK7(X4),set_type)
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f109,plain,
! [X0,X4] :
( ordered_pair(sK6(X4),sK7(X4)) = X4
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f110,plain,
! [X0] :
( sP0(X0)
| ilf_type(sK5(X0),set_type) ),
inference(cnf_transformation,[],[f67]) ).
fof(f111,plain,
! [X0] :
( member(sK5(X0),X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f112,plain,
! [X2,X3,X0] :
( sP0(X0)
| ordered_pair(X2,X3) != sK5(X0)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(cnf_transformation,[],[f67]) ).
fof(f105,plain,
! [X0] :
( sP0(X0)
| ~ relation_like(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ( ( relation_like(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ relation_like(X0) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f54]) ).
fof(f106,plain,
! [X0] :
( relation_like(X0)
| ~ sP0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f158,plain,
! [X0] : ~ empty(power_set(X0)),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103]) ).
fof(f103,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
fof(f157,plain,
! [X0] : ilf_type(power_set(X0),set_type),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104]) ).
fof(f104,plain,
! [X0] :
( ilf_type(power_set(X0),set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f31]) ).
fof(f156,plain,
! [X0] : ilf_type(identity_relation_of(X0),binary_relation_type),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102]) ).
fof(f102,plain,
! [X0] :
( ilf_type(identity_relation_of(X0),binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0] :
( ilf_type(identity_relation_of(X0),binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(identity_relation_of(X0),binary_relation_type) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(f155,plain,
! [X0] : ~ member(X0,empty_set),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101]) ).
fof(f101,plain,
! [X0] :
( ~ member(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0] :
( ~ member(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ~ member(X0,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f100,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(f99,plain,
empty(empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3a) ).
fof(f97,plain,
ilf_type(sK4,set_type),
inference(cnf_transformation,[],[f60]) ).
fof(f98,plain,
~ not_equal(identity_relation_of(sK4),empty_set),
inference(cnf_transformation,[],[f60]) ).
fof(f229,plain,
! [X0] : ~ member(X0,sK4),
inference(subsumption_resolution,[],[f228,f155]) ).
fof(f228,plain,
! [X0] :
( member(ordered_pair(X0,X0),empty_set)
| ~ member(X0,sK4) ),
inference(superposition,[],[f178,f214]) ).
fof(f214,plain,
empty_set = identity_relation_of(sK4),
inference(resolution,[],[f174,f98]) ).
fof(f174,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1 ),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116,f160,f115,f161,f114,f162,f154,f163,f117,f164,f120,f165,f166,f121,f167,f168,f123,f128,f127,f126,f125,f169,f124,f170,f129,f171,f172,f131,f173]) ).
fof(f173,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116,f160,f115,f161,f114,f162,f154,f163,f117,f164,f120,f165,f166,f121,f167,f168,f123,f128,f127,f126,f125,f169,f124,f170,f129,f171,f172,f131]) ).
fof(f131,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ( ( not_equal(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ not_equal(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ( not_equal(X0,X1)
<=> X0 != X1 )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( not_equal(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(f172,plain,
! [X0,X1] : sP3(X0,X1),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116,f160,f115,f161,f114,f162,f154,f163,f117,f164,f120,f165,f166,f121,f167,f168,f123,f128,f127,f126,f125,f169,f124,f170,f129,f171]) ).
fof(f171,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116,f160,f115,f161,f114,f162,f154,f163,f117,f164,f120,f165,f166,f121,f167,f168,f123,f128,f127,f126,f125,f169,f124,f170,f129]) ).
fof(f129,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( sP3(X0,X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(definition_folding,[],[f38,f57,f56]) ).
fof(f56,plain,
! [X1,X0] :
( sP2(X1,X0)
<=> ! [X2] :
( ( member(X2,X0)
<=> member(X2,X1) )
| ~ ilf_type(X2,set_type) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f57,plain,
! [X0,X1] :
( ( X0 = X1
<=> sP2(X1,X0) )
| ~ sP3(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1
<=> ! [X2] :
( ( member(X2,X0)
<=> member(X2,X1) )
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( X0 = X1
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
<=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(f170,plain,
! [X3,X0,X1] :
( ~ sP2(X0,X1)
| ~ member(X3,X1)
| member(X3,X0) ),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116,f160,f115,f161,f114,f162,f154,f163,f117,f164,f120,f165,f166,f121,f167,f168,f123,f128,f127,f126,f125,f169,f124]) ).
fof(f124,plain,
! [X3,X0,X1] :
( member(X3,X0)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ( ~ member(sK9(X0,X1),X0)
| ~ member(sK9(X0,X1),X1) )
& ( member(sK9(X0,X1),X0)
| member(sK9(X0,X1),X1) )
& ilf_type(sK9(X0,X1),set_type) ) )
& ( ! [X3] :
( ( ( member(X3,X1)
| ~ member(X3,X0) )
& ( member(X3,X0)
| ~ member(X3,X1) ) )
| ~ ilf_type(X3,set_type) )
| ~ sP2(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f77,f78]) ).
fof(f78,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X0)
| member(X2,X1) )
& ilf_type(X2,set_type) )
=> ( ( ~ member(sK9(X0,X1),X0)
| ~ member(sK9(X0,X1),X1) )
& ( member(sK9(X0,X1),X0)
| member(sK9(X0,X1),X1) )
& ilf_type(sK9(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ? [X2] :
( ( ~ member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X0)
| member(X2,X1) )
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( ( ( member(X3,X1)
| ~ member(X3,X0) )
& ( member(X3,X0)
| ~ member(X3,X1) ) )
| ~ ilf_type(X3,set_type) )
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f76]) ).
fof(f76,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| ~ ilf_type(X2,set_type) )
| ~ sP2(X1,X0) ) ),
inference(flattening,[],[f75]) ).
fof(f75,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| ~ ilf_type(X2,set_type) )
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f169,plain,
! [X3,X0,X1] :
( ~ sP2(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116,f160,f115,f161,f114,f162,f154,f163,f117,f164,f120,f165,f166,f121,f167,f168,f123,f128,f127,f126,f125]) ).
fof(f125,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f126,plain,
! [X0,X1] :
( sP2(X0,X1)
| ilf_type(sK9(X0,X1),set_type) ),
inference(cnf_transformation,[],[f79]) ).
fof(f127,plain,
! [X0,X1] :
( sP2(X0,X1)
| member(sK9(X0,X1),X0)
| member(sK9(X0,X1),X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f128,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ member(sK9(X0,X1),X0)
| ~ member(sK9(X0,X1),X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f123,plain,
! [X0,X1] :
( X0 = X1
| ~ sP2(X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( ( ( X0 = X1
| ~ sP2(X1,X0) )
& ( sP2(X1,X0)
| X0 != X1 ) )
| ~ sP3(X0,X1) ),
inference(nnf_transformation,[],[f57]) ).
fof(f168,plain,
! [X0,X1] : ilf_type(ordered_pair(X0,X1),set_type),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116,f160,f115,f161,f114,f162,f154,f163,f117,f164,f120,f165,f166,f121,f167]) ).
fof(f167,plain,
! [X0,X1] :
( ilf_type(ordered_pair(X0,X1),set_type)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116,f160,f115,f161,f114,f162,f154,f163,f117,f164,f120,f165,f166,f121]) ).
fof(f121,plain,
! [X0,X1] :
( ilf_type(ordered_pair(X0,X1),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ilf_type(ordered_pair(X0,X1),set_type)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(ordered_pair(X0,X1),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).
fof(f166,plain,
! [X0,X1] : ilf_type(cross_product(X0,X1),set_type),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116,f160,f115,f161,f114,f162,f154,f163,f117,f164,f120,f165]) ).
fof(f165,plain,
! [X0,X1] :
( ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116,f160,f115,f161,f114,f162,f154,f163,f117,f164,f120]) ).
fof(f120,plain,
! [X0,X1] :
( ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] :
( ! [X1] :
( ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(cross_product(X0,X1),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
fof(f164,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| relation_like(X0) ),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116,f160,f115,f161,f114,f162,f154,f163,f117]) ).
fof(f117,plain,
! [X0] :
( relation_like(X0)
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,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,[],[f72]) ).
fof(f72,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,[],[f35]) ).
fof(f35,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',p10) ).
fof(f163,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116,f160,f115,f161,f114,f162,f154]) ).
fof(f154,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) ),
inference(duplicate_literal_removal,[],[f119]) ).
fof(f119,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f73]) ).
fof(f162,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0) ),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116,f160,f115,f161,f114]) ).
fof(f114,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f71]) ).
fof(f161,plain,
! [X0] :
( empty(X0)
| ilf_type(sK8(X0),set_type) ),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116,f160,f115]) ).
fof(f115,plain,
! [X0] :
( empty(X0)
| ilf_type(sK8(X0),set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f71]) ).
fof(f178,plain,
! [X0,X1] :
( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0) ),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116,f160,f115,f161,f114,f162,f154,f163,f117,f164,f120,f165,f166,f121,f167,f168,f123,f128,f127,f126,f125,f169,f124,f170,f129,f171,f172,f131,f173,f174,f133,f175,f176,f132,f177]) ).
fof(f177,plain,
! [X0,X1] :
( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116,f160,f115,f161,f114,f162,f154,f163,f117,f164,f120,f165,f166,f121,f167,f168,f123,f128,f127,f126,f125,f169,f124,f170,f129,f171,f172,f131,f173,f174,f133,f175,f176,f132]) ).
fof(f132,plain,
! [X0,X1] :
( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,X0)
| ~ member(ordered_pair(X1,X1),identity_relation_of(X0)) )
& ( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ( member(X1,X0)
<=> member(ordered_pair(X1,X1),identity_relation_of(X0)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,X0)
<=> member(ordered_pair(X1,X1),identity_relation_of(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f176,plain,
! [X0,X1] :
( ~ member(ordered_pair(X1,X1),identity_relation_of(X0))
| member(X1,X0) ),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116,f160,f115,f161,f114,f162,f154,f163,f117,f164,f120,f165,f166,f121,f167,f168,f123,f128,f127,f126,f125,f169,f124,f170,f129,f171,f172,f131,f173,f174,f133,f175]) ).
fof(f175,plain,
! [X0,X1] :
( member(X1,X0)
| ~ member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f98,f97,f96,f99,f100,f101,f155,f102,f156,f104,f157,f103,f158,f106,f105,f112,f111,f110,f109,f108,f107,f113,f159,f116,f160,f115,f161,f114,f162,f154,f163,f117,f164,f120,f165,f166,f121,f167,f168,f123,f128,f127,f126,f125,f169,f124,f170,f129,f171,f172,f131,f173,f174,f133]) ).
fof(f133,plain,
! [X0,X1] :
( member(X1,X0)
| ~ member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET679+3 : TPTP v8.2.0. Released v2.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 20 12:32:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (3226)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (3229)WARNING: value z3 for option sas not known
% 0.13/0.37 % (3229)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)
% 0.13/0.37 % (3232)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)
% 0.13/0.38 % (3229)First to succeed.
% 0.13/0.38 % (3231)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)
% 0.13/0.38 % (3230)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.38 % (3229)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3226"
% 0.13/0.38 % (3232)Also succeeded, but the first one will report.
% 0.13/0.38 % (3229)Refutation found. Thanks to Tanya!
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.38 % (3229)------------------------------
% 0.13/0.38 % (3229)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.38 % (3229)Termination reason: Refutation
% 0.13/0.38
% 0.13/0.38 % (3229)Memory used [KB]: 934
% 0.13/0.38 % (3229)Time elapsed: 0.011 s
% 0.13/0.38 % (3229)Instructions burned: 14 (million)
% 0.13/0.38 % (3226)Success in time 0.027 s
%------------------------------------------------------------------------------