TSTP Solution File: SET677+3 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET677+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_uns --cores 0 -t %d %s
% Computer : n026.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 18:21:51 EDT 2022
% Result : Theorem 0.18s 0.50s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 7 unt; 0 def)
% Number of atoms : 182 ( 38 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 214 ( 85 ~; 78 |; 28 &)
% ( 5 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 62 ( 54 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f179,plain,
$false,
inference(avatar_sat_refutation,[],[f102,f147,f160,f178]) ).
fof(f178,plain,
( spl6_2
| ~ spl6_5 ),
inference(avatar_contradiction_clause,[],[f177]) ).
fof(f177,plain,
( $false
| spl6_2
| ~ spl6_5 ),
inference(subsumption_resolution,[],[f176,f151]) ).
fof(f151,plain,
( ilf_type(sK4,relation_type(sK3,sK3))
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f150,plain,
( spl6_5
<=> ilf_type(sK4,relation_type(sK3,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).
fof(f176,plain,
( ~ ilf_type(sK4,relation_type(sK3,sK3))
| spl6_2 ),
inference(subsumption_resolution,[],[f174,f75]) ).
fof(f75,plain,
subset(identity_relation_of(sK3),sK4),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
( ilf_type(sK3,set_type)
& ilf_type(sK4,identity_relation_of_type(sK3))
& ( sK3 != domain(sK3,sK3,sK4)
| sK3 != range(sK3,sK3,sK4) )
& subset(identity_relation_of(sK3),sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f40,f60,f59]) ).
fof(f59,plain,
( ? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,identity_relation_of_type(X0))
& ( domain(X0,X0,X1) != X0
| range(X0,X0,X1) != X0 )
& subset(identity_relation_of(X0),X1) ) )
=> ( ilf_type(sK3,set_type)
& ? [X1] :
( ilf_type(X1,identity_relation_of_type(sK3))
& ( sK3 != domain(sK3,sK3,X1)
| sK3 != range(sK3,sK3,X1) )
& subset(identity_relation_of(sK3),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
( ? [X1] :
( ilf_type(X1,identity_relation_of_type(sK3))
& ( sK3 != domain(sK3,sK3,X1)
| sK3 != range(sK3,sK3,X1) )
& subset(identity_relation_of(sK3),X1) )
=> ( ilf_type(sK4,identity_relation_of_type(sK3))
& ( sK3 != domain(sK3,sK3,sK4)
| sK3 != range(sK3,sK3,sK4) )
& subset(identity_relation_of(sK3),sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,identity_relation_of_type(X0))
& ( domain(X0,X0,X1) != X0
| range(X0,X0,X1) != X0 )
& subset(identity_relation_of(X0),X1) ) ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
? [X0] :
( ? [X1] :
( ( domain(X0,X0,X1) != X0
| range(X0,X0,X1) != X0 )
& subset(identity_relation_of(X0),X1)
& ilf_type(X1,identity_relation_of_type(X0)) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,identity_relation_of_type(X0))
=> ( subset(identity_relation_of(X0),X1)
=> ( range(X0,X0,X1) = X0
& domain(X0,X0,X1) = X0 ) ) ) ),
inference(negated_conjecture,[],[f35]) ).
fof(f35,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,identity_relation_of_type(X0))
=> ( subset(identity_relation_of(X0),X1)
=> ( range(X0,X0,X1) = X0
& domain(X0,X0,X1) = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_44) ).
fof(f174,plain,
( ~ subset(identity_relation_of(sK3),sK4)
| ~ ilf_type(sK4,relation_type(sK3,sK3))
| spl6_2 ),
inference(trivial_inequality_removal,[],[f172]) ).
fof(f172,plain,
( ~ subset(identity_relation_of(sK3),sK4)
| sK3 != sK3
| ~ ilf_type(sK4,relation_type(sK3,sK3))
| spl6_2 ),
inference(superposition,[],[f101,f169]) ).
fof(f169,plain,
! [X2,X0,X1] :
( domain(X1,X0,X2) = X1
| ~ subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,relation_type(X1,X0)) ),
inference(subsumption_resolution,[],[f168,f81]) ).
fof(f81,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p34) ).
fof(f168,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,set_type)
| domain(X1,X0,X2) = X1
| ~ ilf_type(X2,relation_type(X1,X0))
| ~ subset(identity_relation_of(X1),X2) ),
inference(subsumption_resolution,[],[f88,f81]) ).
fof(f88,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ subset(identity_relation_of(X1),X2)
| domain(X1,X0,X2) = X1
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X1,X0)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X1,X0))
| ( subset(X1,range(X1,X0,X2))
& domain(X1,X0,X2) = X1 )
| ~ subset(identity_relation_of(X1),X2) ) ) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( subset(X1,range(X1,X0,X2))
& domain(X1,X0,X2) = X1 )
| ~ subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,relation_type(X1,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)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( subset(identity_relation_of(X1),X2)
=> ( subset(X1,range(X1,X0,X2))
& domain(X1,X0,X2) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f101,plain,
( sK3 != domain(sK3,sK3,sK4)
| spl6_2 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f99,plain,
( spl6_2
<=> sK3 = domain(sK3,sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
fof(f160,plain,
spl6_5,
inference(avatar_contradiction_clause,[],[f159]) ).
fof(f159,plain,
( $false
| spl6_5 ),
inference(subsumption_resolution,[],[f158,f77]) ).
fof(f77,plain,
ilf_type(sK4,identity_relation_of_type(sK3)),
inference(cnf_transformation,[],[f61]) ).
fof(f158,plain,
( ~ ilf_type(sK4,identity_relation_of_type(sK3))
| spl6_5 ),
inference(resolution,[],[f152,f112]) ).
fof(f112,plain,
! [X0,X1] :
( ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X1,identity_relation_of_type(X0)) ),
inference(subsumption_resolution,[],[f111,f81]) ).
fof(f111,plain,
! [X0,X1] :
( ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f82,f81]) ).
fof(f82,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,identity_relation_of_type(X0)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X1,relation_type(X0,X0)) )
& ( ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X1,identity_relation_of_type(X0)) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5) ).
fof(f152,plain,
( ~ ilf_type(sK4,relation_type(sK3,sK3))
| spl6_5 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f147,plain,
spl6_1,
inference(avatar_contradiction_clause,[],[f146]) ).
fof(f146,plain,
( $false
| spl6_1 ),
inference(subsumption_resolution,[],[f145,f77]) ).
fof(f145,plain,
( ~ ilf_type(sK4,identity_relation_of_type(sK3))
| spl6_1 ),
inference(resolution,[],[f144,f112]) ).
fof(f144,plain,
( ~ ilf_type(sK4,relation_type(sK3,sK3))
| spl6_1 ),
inference(subsumption_resolution,[],[f142,f75]) ).
fof(f142,plain,
( ~ ilf_type(sK4,relation_type(sK3,sK3))
| ~ subset(identity_relation_of(sK3),sK4)
| spl6_1 ),
inference(trivial_inequality_removal,[],[f140]) ).
fof(f140,plain,
( sK3 != sK3
| ~ subset(identity_relation_of(sK3),sK4)
| ~ ilf_type(sK4,relation_type(sK3,sK3))
| spl6_1 ),
inference(superposition,[],[f97,f139]) ).
fof(f139,plain,
! [X2,X0,X1] :
( range(X0,X1,X2) = X1
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ subset(identity_relation_of(X1),X2) ),
inference(subsumption_resolution,[],[f138,f81]) ).
fof(f138,plain,
! [X2,X0,X1] :
( range(X0,X1,X2) = X1
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ subset(identity_relation_of(X1),X2)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f73,f81]) ).
fof(f73,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ subset(identity_relation_of(X1),X2)
| range(X0,X1,X2) = X1
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ( range(X0,X1,X2) = X1
& subset(X1,domain(X0,X1,X2)) )
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ subset(identity_relation_of(X1),X2) ) ) ),
inference(flattening,[],[f45]) ).
fof(f45,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,[],[f2]) ).
fof(f2,axiom,
! [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)
=> ( range(X0,X1,X2) = X1
& subset(X1,domain(X0,X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f97,plain,
( sK3 != range(sK3,sK3,sK4)
| spl6_1 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f95,plain,
( spl6_1
<=> sK3 = range(sK3,sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
fof(f102,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f76,f99,f95]) ).
fof(f76,plain,
( sK3 != domain(sK3,sK3,sK4)
| sK3 != range(sK3,sK3,sK4) ),
inference(cnf_transformation,[],[f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET677+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 30 14:27:36 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.49 % (26920)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.18/0.49 % (26922)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.18/0.50 % (26928)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.50 % (26920)First to succeed.
% 0.18/0.50 % (26920)Refutation found. Thanks to Tanya!
% 0.18/0.50 % SZS status Theorem for theBenchmark
% 0.18/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.50 % (26920)------------------------------
% 0.18/0.50 % (26920)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.50 % (26920)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50 % (26920)Termination reason: Refutation
% 0.18/0.50
% 0.18/0.50 % (26920)Memory used [KB]: 6012
% 0.18/0.50 % (26920)Time elapsed: 0.104 s
% 0.18/0.50 % (26920)Instructions burned: 4 (million)
% 0.18/0.50 % (26920)------------------------------
% 0.18/0.50 % (26920)------------------------------
% 0.18/0.50 % (26913)Success in time 0.162 s
%------------------------------------------------------------------------------