TSTP Solution File: SEU212+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU212+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 : 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 18:27:28 EDT 2022
% Result : Theorem 0.18s 0.45s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 80 ( 7 unt; 0 def)
% Number of atoms : 237 ( 37 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 261 ( 104 ~; 110 |; 18 &)
% ( 16 <=>; 11 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 94 ( 86 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f246,plain,
$false,
inference(avatar_sat_refutation,[],[f136,f139,f142,f165,f169,f245]) ).
fof(f245,plain,
( ~ spl13_1
| spl13_2 ),
inference(avatar_contradiction_clause,[],[f244]) ).
fof(f244,plain,
( $false
| ~ spl13_1
| spl13_2 ),
inference(subsumption_resolution,[],[f236,f186]) ).
fof(f186,plain,
( ~ empty(sK8)
| ~ spl13_1 ),
inference(unit_resulting_resolution,[],[f126,f97]) ).
fof(f97,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X1,X0] :
( ~ empty(X0)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,plain,
! [X1,X0] :
~ ( empty(X0)
& in(X1,X0) ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X1,X0] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f126,plain,
( in(unordered_pair(singleton(sK7),unordered_pair(sK6,sK7)),sK8)
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f125,plain,
( spl13_1
<=> in(unordered_pair(singleton(sK7),unordered_pair(sK6,sK7)),sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).
fof(f236,plain,
( empty(sK8)
| ~ spl13_1
| spl13_2 ),
inference(unit_resulting_resolution,[],[f185,f200,f106]) ).
fof(f106,plain,
! [X0,X1] :
( ~ element(X1,X0)
| empty(X0)
| in(X1,X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X1,X0] :
( in(X1,X0)
| empty(X0)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,plain,
! [X1,X0] :
( element(X1,X0)
=> ( in(X1,X0)
| empty(X0) ) ),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X1,X0] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f200,plain,
( ! [X0] : ~ in(unordered_pair(singleton(sK7),unordered_pair(X0,sK7)),sK8)
| spl13_2 ),
inference(superposition,[],[f179,f103]) ).
fof(f103,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f179,plain,
( ! [X0] : ~ in(unordered_pair(singleton(sK7),unordered_pair(sK7,X0)),sK8)
| spl13_2 ),
inference(forward_demodulation,[],[f170,f103]) ).
fof(f170,plain,
( ! [X0] : ~ in(unordered_pair(unordered_pair(sK7,X0),singleton(sK7)),sK8)
| spl13_2 ),
inference(unit_resulting_resolution,[],[f89,f131,f120]) ).
fof(f120,plain,
! [X2,X3,X0] :
( ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0)
| ~ relation(X0)
| in(X2,relation_dom(X0)) ),
inference(equality_resolution,[],[f113]) ).
fof(f113,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| relation_dom(X0) != X1
| in(X2,X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0) ),
inference(definition_unfolding,[],[f94,f104]) ).
fof(f104,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f94,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| relation_dom(X0) != X1
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ? [X3] : in(ordered_pair(X2,X3),X0)
<=> in(X2,X1) )
<=> relation_dom(X0) = X1 )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( ! [X2] :
( ? [X3] : in(ordered_pair(X2,X3),X0)
<=> in(X2,X1) )
<=> relation_dom(X0) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f131,plain,
( ~ in(sK7,relation_dom(sK8))
| spl13_2 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f129,plain,
( spl13_2
<=> in(sK7,relation_dom(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).
fof(f89,plain,
relation(sK8),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
? [X2,X1,X0] :
( ( ( in(X1,relation_dom(X0))
& apply(X0,X1) = X2 )
<~> in(ordered_pair(X1,X2),X0) )
& function(X0)
& relation(X0) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
? [X2,X0,X1] :
( ( ( in(X1,relation_dom(X0))
& apply(X0,X1) = X2 )
<~> in(ordered_pair(X1,X2),X0) )
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,plain,
~ ! [X2,X0,X1] :
( ( relation(X0)
& function(X0) )
=> ( ( in(X1,relation_dom(X0))
& apply(X0,X1) = X2 )
<=> in(ordered_pair(X1,X2),X0) ) ),
inference(rectify,[],[f36]) ).
fof(f36,negated_conjecture,
~ ! [X2,X0,X1] :
( ( relation(X2)
& function(X2) )
=> ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
<=> in(ordered_pair(X0,X1),X2) ) ),
inference(negated_conjecture,[],[f35]) ).
fof(f35,conjecture,
! [X2,X0,X1] :
( ( relation(X2)
& function(X2) )
=> ( ( apply(X2,X0) = X1
& in(X0,relation_dom(X2)) )
<=> in(ordered_pair(X0,X1),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
fof(f185,plain,
( element(unordered_pair(singleton(sK7),unordered_pair(sK6,sK7)),sK8)
| ~ spl13_1 ),
inference(unit_resulting_resolution,[],[f126,f98]) ).
fof(f98,plain,
! [X0,X1] :
( ~ in(X1,X0)
| element(X1,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( element(X1,X0)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,plain,
! [X1,X0] :
( in(X1,X0)
=> element(X1,X0) ),
inference(rectify,[],[f30]) ).
fof(f30,axiom,
! [X1,X0] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f169,plain,
( ~ spl13_1
| ~ spl13_2
| spl13_3 ),
inference(avatar_split_clause,[],[f168,f133,f129,f125]) ).
fof(f133,plain,
( spl13_3
<=> sK6 = apply(sK8,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).
fof(f168,plain,
( ~ in(unordered_pair(singleton(sK7),unordered_pair(sK6,sK7)),sK8)
| ~ spl13_2
| spl13_3 ),
inference(forward_demodulation,[],[f167,f103]) ).
fof(f167,plain,
( ~ in(unordered_pair(singleton(sK7),unordered_pair(sK7,sK6)),sK8)
| ~ spl13_2
| spl13_3 ),
inference(forward_demodulation,[],[f166,f103]) ).
fof(f166,plain,
( ~ in(unordered_pair(unordered_pair(sK7,sK6),singleton(sK7)),sK8)
| ~ spl13_2
| spl13_3 ),
inference(unit_resulting_resolution,[],[f89,f90,f130,f135,f108]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) = X2
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f83,f104]) ).
fof(f83,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ~ relation(X0)
| ! [X2,X1] :
( ( ( in(ordered_pair(X1,X2),X0)
<=> apply(X0,X1) = X2 )
| ~ in(X1,relation_dom(X0)) )
& ( in(X1,relation_dom(X0))
| ( empty_set = X2
<=> apply(X0,X1) = X2 ) ) )
| ~ function(X0) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ! [X2,X1] :
( ( ( in(ordered_pair(X1,X2),X0)
<=> apply(X0,X1) = X2 )
| ~ in(X1,relation_dom(X0)) )
& ( in(X1,relation_dom(X0))
| ( empty_set = X2
<=> apply(X0,X1) = X2 ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X2,X1] :
( ( in(X1,relation_dom(X0))
=> ( in(ordered_pair(X1,X2),X0)
<=> apply(X0,X1) = X2 ) )
& ( ~ in(X1,relation_dom(X0))
=> ( empty_set = X2
<=> apply(X0,X1) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f135,plain,
( sK6 != apply(sK8,sK7)
| spl13_3 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f130,plain,
( in(sK7,relation_dom(sK8))
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f90,plain,
function(sK8),
inference(cnf_transformation,[],[f49]) ).
fof(f165,plain,
( spl13_1
| ~ spl13_2
| ~ spl13_3 ),
inference(avatar_split_clause,[],[f164,f133,f129,f125]) ).
fof(f164,plain,
( in(unordered_pair(singleton(sK7),unordered_pair(sK6,sK7)),sK8)
| ~ spl13_2
| ~ spl13_3 ),
inference(forward_demodulation,[],[f163,f103]) ).
fof(f163,plain,
( in(unordered_pair(singleton(sK7),unordered_pair(sK7,sK6)),sK8)
| ~ spl13_2
| ~ spl13_3 ),
inference(forward_demodulation,[],[f162,f103]) ).
fof(f162,plain,
( in(unordered_pair(unordered_pair(sK7,sK6),singleton(sK7)),sK8)
| ~ spl13_2
| ~ spl13_3 ),
inference(subsumption_resolution,[],[f161,f90]) ).
fof(f161,plain,
( in(unordered_pair(unordered_pair(sK7,sK6),singleton(sK7)),sK8)
| ~ function(sK8)
| ~ spl13_2
| ~ spl13_3 ),
inference(subsumption_resolution,[],[f160,f89]) ).
fof(f160,plain,
( in(unordered_pair(unordered_pair(sK7,sK6),singleton(sK7)),sK8)
| ~ relation(sK8)
| ~ function(sK8)
| ~ spl13_2
| ~ spl13_3 ),
inference(subsumption_resolution,[],[f159,f130]) ).
fof(f159,plain,
( ~ in(sK7,relation_dom(sK8))
| ~ function(sK8)
| in(unordered_pair(unordered_pair(sK7,sK6),singleton(sK7)),sK8)
| ~ relation(sK8)
| ~ spl13_3 ),
inference(superposition,[],[f119,f134]) ).
fof(f134,plain,
( sK6 = apply(sK8,sK7)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f119,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X1,apply(X0,X1)),singleton(X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f109]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) != X2
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f82,f104]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) != X2
| in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f142,plain,
( spl13_2
| spl13_1 ),
inference(avatar_split_clause,[],[f141,f125,f129]) ).
fof(f141,plain,
( in(unordered_pair(singleton(sK7),unordered_pair(sK6,sK7)),sK8)
| in(sK7,relation_dom(sK8)) ),
inference(forward_demodulation,[],[f140,f103]) ).
fof(f140,plain,
( in(unordered_pair(singleton(sK7),unordered_pair(sK7,sK6)),sK8)
| in(sK7,relation_dom(sK8)) ),
inference(forward_demodulation,[],[f110,f103]) ).
fof(f110,plain,
( in(unordered_pair(unordered_pair(sK7,sK6),singleton(sK7)),sK8)
| in(sK7,relation_dom(sK8)) ),
inference(definition_unfolding,[],[f88,f104]) ).
fof(f88,plain,
( in(ordered_pair(sK7,sK6),sK8)
| in(sK7,relation_dom(sK8)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f139,plain,
( spl13_3
| spl13_1 ),
inference(avatar_split_clause,[],[f138,f125,f133]) ).
fof(f138,plain,
( in(unordered_pair(singleton(sK7),unordered_pair(sK6,sK7)),sK8)
| sK6 = apply(sK8,sK7) ),
inference(forward_demodulation,[],[f137,f103]) ).
fof(f137,plain,
( in(unordered_pair(singleton(sK7),unordered_pair(sK7,sK6)),sK8)
| sK6 = apply(sK8,sK7) ),
inference(forward_demodulation,[],[f111,f103]) ).
fof(f111,plain,
( sK6 = apply(sK8,sK7)
| in(unordered_pair(unordered_pair(sK7,sK6),singleton(sK7)),sK8) ),
inference(definition_unfolding,[],[f87,f104]) ).
fof(f87,plain,
( in(ordered_pair(sK7,sK6),sK8)
| sK6 = apply(sK8,sK7) ),
inference(cnf_transformation,[],[f49]) ).
fof(f136,plain,
( ~ spl13_1
| ~ spl13_2
| ~ spl13_3 ),
inference(avatar_split_clause,[],[f123,f133,f129,f125]) ).
fof(f123,plain,
( sK6 != apply(sK8,sK7)
| ~ in(sK7,relation_dom(sK8))
| ~ in(unordered_pair(singleton(sK7),unordered_pair(sK6,sK7)),sK8) ),
inference(forward_demodulation,[],[f122,f103]) ).
fof(f122,plain,
( ~ in(sK7,relation_dom(sK8))
| sK6 != apply(sK8,sK7)
| ~ in(unordered_pair(singleton(sK7),unordered_pair(sK7,sK6)),sK8) ),
inference(forward_demodulation,[],[f112,f103]) ).
fof(f112,plain,
( ~ in(sK7,relation_dom(sK8))
| sK6 != apply(sK8,sK7)
| ~ in(unordered_pair(unordered_pair(sK7,sK6),singleton(sK7)),sK8) ),
inference(definition_unfolding,[],[f86,f104]) ).
fof(f86,plain,
( ~ in(ordered_pair(sK7,sK6),sK8)
| sK6 != apply(sK8,sK7)
| ~ in(sK7,relation_dom(sK8)) ),
inference(cnf_transformation,[],[f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU212+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % 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 : n012.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 14:48:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.44 % (30206)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.44 % (30211)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)
% 0.18/0.45 % (30211)First to succeed.
% 0.18/0.45 % (30211)Refutation found. Thanks to Tanya!
% 0.18/0.45 % SZS status Theorem for theBenchmark
% 0.18/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.45 % (30211)------------------------------
% 0.18/0.45 % (30211)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.45 % (30211)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.45 % (30211)Termination reason: Refutation
% 0.18/0.45
% 0.18/0.45 % (30211)Memory used [KB]: 6140
% 0.18/0.45 % (30211)Time elapsed: 0.056 s
% 0.18/0.45 % (30211)Instructions burned: 7 (million)
% 0.18/0.45 % (30211)------------------------------
% 0.18/0.45 % (30211)------------------------------
% 0.18/0.45 % (30202)Success in time 0.112 s
%------------------------------------------------------------------------------