TSTP Solution File: SET669+3 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET669+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n012.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 : Wed Aug 31 18:25:17 EDT 2022
% Result : Theorem 1.81s 0.62s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 19
% Syntax : Number of formulae : 110 ( 21 unt; 0 def)
% Number of atoms : 455 ( 27 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 573 ( 228 ~; 224 |; 72 &)
% ( 13 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-3 aty)
% Number of variables : 187 ( 166 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f669,plain,
$false,
inference(subsumption_resolution,[],[f665,f146]) ).
fof(f146,plain,
ilf_type(sK4,set_type),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
( ilf_type(sK3,set_type)
& ( range(sK3,sK4,sK5) != sK4
| ~ subset(sK4,domain(sK3,sK4,sK5)) )
& subset(identity_relation_of(sK4),sK5)
& ilf_type(sK5,relation_type(sK3,sK4))
& ilf_type(sK4,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f50,f94,f93,f92]) ).
fof(f92,plain,
( ? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ? [X2] :
( ( range(X0,X1,X2) != X1
| ~ subset(X1,domain(X0,X1,X2)) )
& subset(identity_relation_of(X1),X2)
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) ) )
=> ( ilf_type(sK3,set_type)
& ? [X1] :
( ? [X2] :
( ( range(sK3,X1,X2) != X1
| ~ subset(X1,domain(sK3,X1,X2)) )
& subset(identity_relation_of(X1),X2)
& ilf_type(X2,relation_type(sK3,X1)) )
& ilf_type(X1,set_type) ) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
( ? [X1] :
( ? [X2] :
( ( range(sK3,X1,X2) != X1
| ~ subset(X1,domain(sK3,X1,X2)) )
& subset(identity_relation_of(X1),X2)
& ilf_type(X2,relation_type(sK3,X1)) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ( range(sK3,sK4,X2) != sK4
| ~ subset(sK4,domain(sK3,sK4,X2)) )
& subset(identity_relation_of(sK4),X2)
& ilf_type(X2,relation_type(sK3,sK4)) )
& ilf_type(sK4,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
( ? [X2] :
( ( range(sK3,sK4,X2) != sK4
| ~ subset(sK4,domain(sK3,sK4,X2)) )
& subset(identity_relation_of(sK4),X2)
& ilf_type(X2,relation_type(sK3,sK4)) )
=> ( ( range(sK3,sK4,sK5) != sK4
| ~ subset(sK4,domain(sK3,sK4,sK5)) )
& subset(identity_relation_of(sK4),sK5)
& ilf_type(sK5,relation_type(sK3,sK4)) ) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ? [X2] :
( ( range(X0,X1,X2) != X1
| ~ subset(X1,domain(X0,X1,X2)) )
& subset(identity_relation_of(X1),X2)
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) ) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( range(X0,X1,X2) != X1
| ~ subset(X1,domain(X0,X1,X2)) )
& subset(identity_relation_of(X1),X2)
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(identity_relation_of(X1),X2)
=> ( subset(X1,domain(X0,X1,X2))
& range(X0,X1,X2) = X1 ) ) ) ) ),
inference(negated_conjecture,[],[f33]) ).
fof(f33,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(identity_relation_of(X1),X2)
=> ( subset(X1,domain(X0,X1,X2))
& range(X0,X1,X2) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_32) ).
fof(f665,plain,
~ ilf_type(sK4,set_type),
inference(resolution,[],[f647,f157]) ).
fof(f157,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
fof(f647,plain,
empty(power_set(sK4)),
inference(subsumption_resolution,[],[f645,f531]) ).
fof(f531,plain,
~ subset(sF15,sK4),
inference(subsumption_resolution,[],[f530,f146]) ).
fof(f530,plain,
( ~ subset(sF15,sK4)
| ~ ilf_type(sK4,set_type) ),
inference(subsumption_resolution,[],[f529,f318]) ).
fof(f318,plain,
sF15 != sK4,
inference(resolution,[],[f309,f191]) ).
fof(f191,plain,
( ~ subset(sK4,sF16)
| sF15 != sK4 ),
inference(definition_folding,[],[f149,f190,f189]) ).
fof(f189,plain,
sF15 = range(sK3,sK4,sK5),
introduced(function_definition,[]) ).
fof(f190,plain,
sF16 = domain(sK3,sK4,sK5),
introduced(function_definition,[]) ).
fof(f149,plain,
( range(sK3,sK4,sK5) != sK4
| ~ subset(sK4,domain(sK3,sK4,sK5)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f309,plain,
subset(sK4,sF16),
inference(subsumption_resolution,[],[f308,f193]) ).
fof(f193,plain,
subset(sF17,sK5),
inference(definition_folding,[],[f148,f192]) ).
fof(f192,plain,
sF17 = identity_relation_of(sK4),
introduced(function_definition,[]) ).
fof(f148,plain,
subset(identity_relation_of(sK4),sK5),
inference(cnf_transformation,[],[f95]) ).
fof(f308,plain,
( ~ subset(sF17,sK5)
| subset(sK4,sF16) ),
inference(superposition,[],[f305,f192]) ).
fof(f305,plain,
! [X0] :
( ~ subset(identity_relation_of(X0),sK5)
| subset(X0,sF16) ),
inference(subsumption_resolution,[],[f304,f195]) ).
fof(f195,plain,
ilf_type(sK5,sF18),
inference(definition_folding,[],[f147,f194]) ).
fof(f194,plain,
relation_type(sK3,sK4) = sF18,
introduced(function_definition,[]) ).
fof(f147,plain,
ilf_type(sK5,relation_type(sK3,sK4)),
inference(cnf_transformation,[],[f95]) ).
fof(f304,plain,
! [X0] :
( ~ ilf_type(sK5,sF18)
| ~ subset(identity_relation_of(X0),sK5)
| subset(X0,sF16) ),
inference(forward_demodulation,[],[f303,f194]) ).
fof(f303,plain,
! [X0] :
( ~ ilf_type(sK5,relation_type(sK3,sK4))
| subset(X0,sF16)
| ~ subset(identity_relation_of(X0),sK5) ),
inference(superposition,[],[f208,f190]) ).
fof(f208,plain,
! [X2,X3,X0,X1] :
( subset(X2,domain(X0,X1,X3))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3) ),
inference(subsumption_resolution,[],[f207,f175]) ).
fof(f175,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p32) ).
fof(f207,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X0,set_type)
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,domain(X0,X1,X3)) ),
inference(subsumption_resolution,[],[f206,f175]) ).
fof(f206,plain,
! [X2,X3,X0,X1] :
( subset(X2,domain(X0,X1,X3))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3) ),
inference(subsumption_resolution,[],[f182,f175]) ).
fof(f182,plain,
! [X2,X3,X0,X1] :
( subset(X2,domain(X0,X1,X3))
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ subset(identity_relation_of(X2),X3)
| ( subset(X2,domain(X0,X1,X3))
& subset(X2,range(X0,X1,X3)) )
| ~ ilf_type(X3,relation_type(X0,X1)) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( subset(X2,domain(X0,X1,X3))
& subset(X2,range(X0,X1,X3)) )
| ~ subset(identity_relation_of(X2),X3)
| ~ 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,[],[f2]) ).
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,relation_type(X0,X1))
=> ( subset(identity_relation_of(X2),X3)
=> ( subset(X2,domain(X0,X1,X3))
& subset(X2,range(X0,X1,X3)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f529,plain,
( sF15 = sK4
| ~ ilf_type(sK4,set_type)
| ~ subset(sF15,sK4) ),
inference(subsumption_resolution,[],[f528,f175]) ).
fof(f528,plain,
( ~ subset(sF15,sK4)
| ~ ilf_type(sF15,set_type)
| ~ ilf_type(sK4,set_type)
| sF15 = sK4 ),
inference(resolution,[],[f510,f137]) ).
fof(f137,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( ( ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f86]) ).
fof(f86,plain,
! [X0] :
( ! [X1] :
( ( ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X1,X0)
& subset(X0,X1) )
<=> X0 = X1 )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ( subset(X1,X0)
& subset(X0,X1) )
<=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).
fof(f510,plain,
subset(sK4,sF15),
inference(subsumption_resolution,[],[f509,f193]) ).
fof(f509,plain,
( ~ subset(sF17,sK5)
| subset(sK4,sF15) ),
inference(superposition,[],[f499,f192]) ).
fof(f499,plain,
! [X0] :
( ~ subset(identity_relation_of(X0),sK5)
| subset(X0,sF15) ),
inference(forward_demodulation,[],[f495,f189]) ).
fof(f495,plain,
! [X0] :
( subset(X0,range(sK3,sK4,sK5))
| ~ subset(identity_relation_of(X0),sK5) ),
inference(resolution,[],[f460,f195]) ).
fof(f460,plain,
! [X0,X1] :
( ~ ilf_type(X0,sF18)
| subset(X1,range(sK3,sK4,X0))
| ~ subset(identity_relation_of(X1),X0) ),
inference(subsumption_resolution,[],[f459,f150]) ).
fof(f150,plain,
ilf_type(sK3,set_type),
inference(cnf_transformation,[],[f95]) ).
fof(f459,plain,
! [X0,X1] :
( ~ subset(identity_relation_of(X1),X0)
| ~ ilf_type(X0,sF18)
| ~ ilf_type(sK3,set_type)
| subset(X1,range(sK3,sK4,X0)) ),
inference(subsumption_resolution,[],[f458,f175]) ).
fof(f458,plain,
! [X0,X1] :
( ~ subset(identity_relation_of(X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK3,set_type)
| subset(X1,range(sK3,sK4,X0))
| ~ ilf_type(X0,sF18) ),
inference(subsumption_resolution,[],[f456,f146]) ).
fof(f456,plain,
! [X0,X1] :
( ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK3,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,sF18)
| ~ subset(identity_relation_of(X1),X0)
| subset(X1,range(sK3,sK4,X0)) ),
inference(superposition,[],[f181,f194]) ).
fof(f181,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X1,set_type)
| subset(X2,range(X0,X1,X3)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f645,plain,
( subset(sF15,sK4)
| empty(power_set(sK4)) ),
inference(duplicate_literal_removal,[],[f643]) ).
fof(f643,plain,
( subset(sF15,sK4)
| subset(sF15,sK4)
| empty(power_set(sK4)) ),
inference(resolution,[],[f555,f210]) ).
fof(f210,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(subsumption_resolution,[],[f209,f175]) ).
fof(f209,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1)
| ~ ilf_type(X1,set_type) ),
inference(subsumption_resolution,[],[f142,f175]) ).
fof(f142,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| ~ ilf_type(X0,set_type)
| subset(X0,X1)
| ~ ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ! [X1] :
( ( ( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1)
| ~ ilf_type(X2,set_type) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ( member(sK2(X0,X1),X0)
& ~ member(sK2(X0,X1),X1)
& ilf_type(sK2(X0,X1),set_type) ) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f89,f90]) ).
fof(f90,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X0)
& ~ member(X3,X1)
& ilf_type(X3,set_type) )
=> ( member(sK2(X0,X1),X0)
& ~ member(sK2(X0,X1),X1)
& ilf_type(sK2(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( ( ( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1)
| ~ ilf_type(X2,set_type) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X3] :
( member(X3,X0)
& ~ member(X3,X1)
& ilf_type(X3,set_type) ) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ! [X1] :
( ( ( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1)
| ~ ilf_type(X2,set_type) )
| ~ subset(X0,X1) )
& ( subset(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(nnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1)
| ~ ilf_type(X2,set_type) )
<=> subset(X0,X1) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(f555,plain,
! [X1] :
( member(sK2(sF15,X1),sK4)
| empty(power_set(sK4))
| subset(sF15,X1) ),
inference(resolution,[],[f487,f214]) ).
fof(f214,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(subsumption_resolution,[],[f213,f175]) ).
fof(f213,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ilf_type(X0,set_type)
| member(sK2(X0,X1),X0) ),
inference(subsumption_resolution,[],[f143,f175]) ).
fof(f143,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ilf_type(X1,set_type)
| member(sK2(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f91]) ).
fof(f487,plain,
! [X0] :
( ~ member(X0,sF15)
| empty(power_set(sK4))
| member(X0,sK4) ),
inference(subsumption_resolution,[],[f486,f175]) ).
fof(f486,plain,
! [X0] :
( empty(power_set(sK4))
| ~ member(X0,sF15)
| ~ ilf_type(X0,set_type)
| member(X0,sK4) ),
inference(subsumption_resolution,[],[f485,f146]) ).
fof(f485,plain,
! [X0] :
( member(X0,sK4)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,sF15)
| empty(power_set(sK4)) ),
inference(subsumption_resolution,[],[f483,f175]) ).
fof(f483,plain,
! [X0] :
( ~ ilf_type(sF15,set_type)
| ~ member(X0,sF15)
| empty(power_set(sK4))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK4,set_type)
| member(X0,sK4) ),
inference(resolution,[],[f478,f170]) ).
fof(f170,plain,
! [X3,X0,X1] :
( ~ member(X0,power_set(X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK12(X0,X1),X1)
& member(sK12(X0,X1),X0)
& ilf_type(sK12(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f111,f112]) ).
fof(f112,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK12(X0,X1),X1)
& member(sK12(X0,X1),X0)
& ilf_type(sK12(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f111,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(rectify,[],[f110]) ).
fof(f110,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
fof(f478,plain,
( member(sF15,power_set(sK4))
| empty(power_set(sK4)) ),
inference(resolution,[],[f474,f268]) ).
fof(f268,plain,
! [X2,X1] :
( ~ ilf_type(X1,subset_type(X2))
| member(X1,power_set(X2))
| empty(power_set(X2)) ),
inference(subsumption_resolution,[],[f267,f175]) ).
fof(f267,plain,
! [X2,X1] :
( ~ ilf_type(X1,set_type)
| member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2))
| empty(power_set(X2)) ),
inference(subsumption_resolution,[],[f263,f175]) ).
fof(f263,plain,
! [X2,X1] :
( empty(power_set(X2))
| ~ ilf_type(power_set(X2),set_type)
| ~ ilf_type(X1,set_type)
| member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(resolution,[],[f121,f222]) ).
fof(f222,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ),
inference(subsumption_resolution,[],[f221,f175]) ).
fof(f221,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,subset_type(X0)) ),
inference(subsumption_resolution,[],[f165,f175]) ).
fof(f165,plain,
! [X0,X1] :
( ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) )
& ( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) )
| ~ 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(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p16) ).
fof(f121,plain,
! [X0,X1] :
( ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| empty(X1)
| member(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( empty(X1)
| ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( empty(X1)
| ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type) ) ),
inference(flattening,[],[f38]) ).
fof(f38,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,[],[f22]) ).
fof(f22,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',p22) ).
fof(f474,plain,
ilf_type(sF15,subset_type(sK4)),
inference(forward_demodulation,[],[f469,f189]) ).
fof(f469,plain,
ilf_type(range(sK3,sK4,sK5),subset_type(sK4)),
inference(resolution,[],[f349,f195]) ).
fof(f349,plain,
! [X0] :
( ~ ilf_type(X0,sF18)
| ilf_type(range(sK3,sK4,X0),subset_type(sK4)) ),
inference(subsumption_resolution,[],[f348,f150]) ).
fof(f348,plain,
! [X0] :
( ~ ilf_type(X0,sF18)
| ilf_type(range(sK3,sK4,X0),subset_type(sK4))
| ~ ilf_type(sK3,set_type) ),
inference(subsumption_resolution,[],[f346,f146]) ).
fof(f346,plain,
! [X0] :
( ~ ilf_type(X0,sF18)
| ilf_type(range(sK3,sK4,X0),subset_type(sK4))
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK3,set_type) ),
inference(superposition,[],[f136,f194]) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ilf_type(range(X0,X1,X2),subset_type(X1)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ! [X2] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(range(X0,X1,X2),subset_type(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p31) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET669+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 14:12:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.55 % (6979)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.55 TRYING [1]
% 0.19/0.56 % (6996)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.56 % (6988)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.56 % (6995)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.57 % (6980)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.57 TRYING [2]
% 0.19/0.58 % (6980)Instruction limit reached!
% 0.19/0.58 % (6980)------------------------------
% 0.19/0.58 % (6980)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.58 % (6980)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.58 % (6980)Termination reason: Unknown
% 0.19/0.58 % (6980)Termination phase: Saturation
% 0.19/0.58
% 0.19/0.58 % (6980)Memory used [KB]: 5500
% 0.19/0.58 % (6980)Time elapsed: 0.088 s
% 0.19/0.58 % (6980)Instructions burned: 7 (million)
% 0.19/0.58 % (6980)------------------------------
% 0.19/0.58 % (6980)------------------------------
% 0.19/0.59 TRYING [3]
% 0.19/0.59 % (6987)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.59 % (6981)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.59 % (6978)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.59 % (6981)Instruction limit reached!
% 0.19/0.59 % (6981)------------------------------
% 0.19/0.59 % (6981)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.59 % (6981)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.59 % (6981)Termination reason: Unknown
% 0.19/0.59 % (6981)Termination phase: Preprocessing 1
% 0.19/0.59
% 0.19/0.59 % (6981)Memory used [KB]: 895
% 0.19/0.59 % (6981)Time elapsed: 0.002 s
% 0.19/0.59 % (6981)Instructions burned: 2 (million)
% 0.19/0.59 % (6981)------------------------------
% 0.19/0.59 % (6981)------------------------------
% 0.19/0.59 % (6974)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.60 % (6976)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.60 % (6977)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.81/0.61 % (6988)First to succeed.
% 1.81/0.61 % (6973)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 1.81/0.61 % (6975)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.81/0.61 % (6998)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.81/0.61 % (7000)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 1.81/0.61 % (7002)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.81/0.62 % (6979)Instruction limit reached!
% 1.81/0.62 % (6979)------------------------------
% 1.81/0.62 % (6979)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.62 % (6990)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.81/0.62 % (7001)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.81/0.62 % (6988)Refutation found. Thanks to Tanya!
% 1.81/0.62 % SZS status Theorem for theBenchmark
% 1.81/0.62 % SZS output start Proof for theBenchmark
% See solution above
% 1.81/0.62 % (6988)------------------------------
% 1.81/0.62 % (6988)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.62 % (6988)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.62 % (6988)Termination reason: Refutation
% 1.81/0.62
% 1.81/0.62 % (6988)Memory used [KB]: 1407
% 1.81/0.62 % (6988)Time elapsed: 0.114 s
% 1.81/0.62 % (6988)Instructions burned: 25 (million)
% 1.81/0.62 % (6988)------------------------------
% 1.81/0.62 % (6988)------------------------------
% 1.81/0.62 % (6972)Success in time 0.267 s
%------------------------------------------------------------------------------