TSTP Solution File: SEU245+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU245+1 : TPTP v8.1.0. Released v3.3.0.
% 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 18:27:55 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 5 unt; 0 def)
% Number of atoms : 235 ( 20 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 275 ( 102 ~; 110 |; 48 &)
% ( 8 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 82 ( 63 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f483,plain,
$false,
inference(avatar_sat_refutation,[],[f127,f128,f129,f320,f338,f479]) ).
fof(f479,plain,
( ~ spl12_1
| ~ spl12_2
| spl12_3 ),
inference(avatar_contradiction_clause,[],[f478]) ).
fof(f478,plain,
( $false
| ~ spl12_1
| ~ spl12_2
| spl12_3 ),
inference(subsumption_resolution,[],[f477,f117]) ).
fof(f117,plain,
( in(sK8,sF10)
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f116,plain,
( spl12_1
<=> in(sK8,sF10) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).
fof(f477,plain,
( ~ in(sK8,sF10)
| ~ spl12_2
| spl12_3 ),
inference(subsumption_resolution,[],[f452,f121]) ).
fof(f121,plain,
( in(sK8,sK7)
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f120,plain,
( spl12_2
<=> in(sK8,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).
fof(f452,plain,
( ~ in(sK8,sK7)
| ~ in(sK8,sF10)
| spl12_3 ),
inference(resolution,[],[f440,f126]) ).
fof(f126,plain,
( ~ in(sK8,sF11)
| spl12_3 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f124,plain,
( spl12_3
<=> in(sK8,sF11) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).
fof(f440,plain,
! [X21] :
( in(X21,sF11)
| ~ in(X21,sF10)
| ~ in(X21,sK7) ),
inference(superposition,[],[f107,f289]) ).
fof(f289,plain,
sF11 = set_intersection2(sK7,sF10),
inference(subsumption_resolution,[],[f284,f102]) ).
fof(f102,plain,
relation(sK7),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
( relation(sK7)
& ( ~ in(sK8,sK7)
| ~ in(sK8,cartesian_product2(sK6,sK6))
| ~ in(sK8,relation_restriction(sK7,sK6)) )
& ( ( in(sK8,sK7)
& in(sK8,cartesian_product2(sK6,sK6)) )
| in(sK8,relation_restriction(sK7,sK6)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f67,f68]) ).
fof(f68,plain,
( ? [X0,X1,X2] :
( relation(X1)
& ( ~ in(X2,X1)
| ~ in(X2,cartesian_product2(X0,X0))
| ~ in(X2,relation_restriction(X1,X0)) )
& ( ( in(X2,X1)
& in(X2,cartesian_product2(X0,X0)) )
| in(X2,relation_restriction(X1,X0)) ) )
=> ( relation(sK7)
& ( ~ in(sK8,sK7)
| ~ in(sK8,cartesian_product2(sK6,sK6))
| ~ in(sK8,relation_restriction(sK7,sK6)) )
& ( ( in(sK8,sK7)
& in(sK8,cartesian_product2(sK6,sK6)) )
| in(sK8,relation_restriction(sK7,sK6)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
? [X0,X1,X2] :
( relation(X1)
& ( ~ in(X2,X1)
| ~ in(X2,cartesian_product2(X0,X0))
| ~ in(X2,relation_restriction(X1,X0)) )
& ( ( in(X2,X1)
& in(X2,cartesian_product2(X0,X0)) )
| in(X2,relation_restriction(X1,X0)) ) ),
inference(rectify,[],[f66]) ).
fof(f66,plain,
? [X2,X0,X1] :
( relation(X0)
& ( ~ in(X1,X0)
| ~ in(X1,cartesian_product2(X2,X2))
| ~ in(X1,relation_restriction(X0,X2)) )
& ( ( in(X1,X0)
& in(X1,cartesian_product2(X2,X2)) )
| in(X1,relation_restriction(X0,X2)) ) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
? [X2,X0,X1] :
( relation(X0)
& ( ~ in(X1,X0)
| ~ in(X1,cartesian_product2(X2,X2))
| ~ in(X1,relation_restriction(X0,X2)) )
& ( ( in(X1,X0)
& in(X1,cartesian_product2(X2,X2)) )
| in(X1,relation_restriction(X0,X2)) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f40,plain,
? [X2,X0,X1] :
( relation(X0)
& ( in(X1,relation_restriction(X0,X2))
<~> ( in(X1,X0)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,plain,
~ ! [X0,X1,X2] :
( relation(X0)
=> ( in(X1,relation_restriction(X0,X2))
<=> ( in(X1,X0)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
inference(rectify,[],[f26]) ).
fof(f26,negated_conjecture,
~ ! [X2,X0,X1] :
( relation(X2)
=> ( ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) )
<=> in(X0,relation_restriction(X2,X1)) ) ),
inference(negated_conjecture,[],[f25]) ).
fof(f25,conjecture,
! [X2,X0,X1] :
( relation(X2)
=> ( ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) )
<=> in(X0,relation_restriction(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f284,plain,
( sF11 = set_intersection2(sK7,sF10)
| ~ relation(sK7) ),
inference(superposition,[],[f111,f232]) ).
fof(f232,plain,
! [X0] :
( relation_restriction(X0,sK6) = set_intersection2(X0,sF10)
| ~ relation(X0) ),
inference(superposition,[],[f85,f110]) ).
fof(f110,plain,
cartesian_product2(sK6,sK6) = sF10,
introduced(function_definition,[]) ).
fof(f85,plain,
! [X0,X1] :
( relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( relation(X0)
=> ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_wellord1) ).
fof(f111,plain,
sF11 = relation_restriction(sK7,sK6),
introduced(function_definition,[]) ).
fof(f107,plain,
! [X2,X3,X1] :
( in(X3,set_intersection2(X1,X2))
| ~ in(X3,X1)
| ~ in(X3,X2) ),
inference(equality_resolution,[],[f80]) ).
fof(f80,plain,
! [X2,X3,X0,X1] :
( in(X3,X0)
| ~ in(X3,X2)
| ~ in(X3,X1)
| set_intersection2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ~ in(X3,X2)
| ~ in(X3,X1) )
& ( ( in(X3,X2)
& in(X3,X1) )
| ~ in(X3,X0) ) )
| set_intersection2(X1,X2) != X0 )
& ( set_intersection2(X1,X2) = X0
| ( ( ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0) )
& ( ( in(sK1(X0,X1,X2),X2)
& in(sK1(X0,X1,X2),X1) )
| in(sK1(X0,X1,X2),X0) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f51,f52]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X2)
& in(X4,X1) )
| in(X4,X0) ) )
=> ( ( ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0) )
& ( ( in(sK1(X0,X1,X2),X2)
& in(sK1(X0,X1,X2),X1) )
| in(sK1(X0,X1,X2),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ~ in(X3,X2)
| ~ in(X3,X1) )
& ( ( in(X3,X2)
& in(X3,X1) )
| ~ in(X3,X0) ) )
| set_intersection2(X1,X2) != X0 )
& ( set_intersection2(X1,X2) = X0
| ? [X4] :
( ( ~ in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X2)
& in(X4,X1) )
| in(X4,X0) ) ) ) ),
inference(rectify,[],[f50]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 )
& ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) ) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 )
& ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X2,X0,X1] :
( ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) )
<=> set_intersection2(X0,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f338,plain,
( spl12_2
| ~ spl12_3 ),
inference(avatar_contradiction_clause,[],[f337]) ).
fof(f337,plain,
( $false
| spl12_2
| ~ spl12_3 ),
inference(subsumption_resolution,[],[f333,f125]) ).
fof(f125,plain,
( in(sK8,sF11)
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f333,plain,
( ~ in(sK8,sF11)
| spl12_2 ),
inference(resolution,[],[f122,f293]) ).
fof(f293,plain,
! [X0] :
( in(X0,sK7)
| ~ in(X0,sF11) ),
inference(superposition,[],[f109,f289]) ).
fof(f109,plain,
! [X2,X3,X1] :
( ~ in(X3,set_intersection2(X1,X2))
| in(X3,X1) ),
inference(equality_resolution,[],[f78]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| set_intersection2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f53]) ).
fof(f122,plain,
( ~ in(sK8,sK7)
| spl12_2 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f320,plain,
( spl12_1
| ~ spl12_3 ),
inference(avatar_contradiction_clause,[],[f319]) ).
fof(f319,plain,
( $false
| spl12_1
| ~ spl12_3 ),
inference(subsumption_resolution,[],[f314,f125]) ).
fof(f314,plain,
( ~ in(sK8,sF11)
| spl12_1 ),
inference(resolution,[],[f294,f118]) ).
fof(f118,plain,
( ~ in(sK8,sF10)
| spl12_1 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f294,plain,
! [X1] :
( in(X1,sF10)
| ~ in(X1,sF11) ),
inference(superposition,[],[f108,f289]) ).
fof(f108,plain,
! [X2,X3,X1] :
( ~ in(X3,set_intersection2(X1,X2))
| in(X3,X2) ),
inference(equality_resolution,[],[f79]) ).
fof(f79,plain,
! [X2,X3,X0,X1] :
( in(X3,X2)
| ~ in(X3,X0)
| set_intersection2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f53]) ).
fof(f129,plain,
( spl12_3
| spl12_1 ),
inference(avatar_split_clause,[],[f114,f116,f124]) ).
fof(f114,plain,
( in(sK8,sF10)
| in(sK8,sF11) ),
inference(definition_folding,[],[f99,f111,f110]) ).
fof(f99,plain,
( in(sK8,cartesian_product2(sK6,sK6))
| in(sK8,relation_restriction(sK7,sK6)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f128,plain,
( spl12_2
| spl12_3 ),
inference(avatar_split_clause,[],[f113,f124,f120]) ).
fof(f113,plain,
( in(sK8,sF11)
| in(sK8,sK7) ),
inference(definition_folding,[],[f100,f111]) ).
fof(f100,plain,
( in(sK8,sK7)
| in(sK8,relation_restriction(sK7,sK6)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f127,plain,
( ~ spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(avatar_split_clause,[],[f112,f124,f120,f116]) ).
fof(f112,plain,
( ~ in(sK8,sF11)
| ~ in(sK8,sK7)
| ~ in(sK8,sF10) ),
inference(definition_folding,[],[f101,f111,f110]) ).
fof(f101,plain,
( ~ in(sK8,sK7)
| ~ in(sK8,cartesian_product2(sK6,sK6))
| ~ in(sK8,relation_restriction(sK7,sK6)) ),
inference(cnf_transformation,[],[f69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU245+1 : TPTP v8.1.0. Released v3.3.0.
% 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
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 30 15:11:06 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.41 % (776)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.43 % (776)First to succeed.
% 0.19/0.44 % (794)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.44 % (785)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)
% 0.19/0.44 % (776)Refutation found. Thanks to Tanya!
% 0.19/0.44 % SZS status Theorem for theBenchmark
% 0.19/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.44 % (776)------------------------------
% 0.19/0.44 % (776)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.44 % (776)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.44 % (776)Termination reason: Refutation
% 0.19/0.44
% 0.19/0.44 % (776)Memory used [KB]: 6140
% 0.19/0.44 % (776)Time elapsed: 0.063 s
% 0.19/0.44 % (776)Instructions burned: 12 (million)
% 0.19/0.44 % (776)------------------------------
% 0.19/0.44 % (776)------------------------------
% 0.19/0.44 % (769)Success in time 0.1 s
%------------------------------------------------------------------------------