TSTP Solution File: SET025+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET025+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n017.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 Apr 30 15:05:04 EDT 2024
% Result : Theorem 0.18s 0.37s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 27
% Syntax : Number of formulae : 74 ( 38 unt; 0 def)
% Number of atoms : 159 ( 18 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 126 ( 41 ~; 38 |; 27 &)
% ( 14 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 67 ( 55 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f324,plain,
$false,
inference(avatar_sat_refutation,[],[f271,f276,f281,f285,f289,f294,f298,f303,f308,f312,f316,f320,f323]) ).
fof(f323,plain,
( spl8_3
| ~ spl8_11 ),
inference(avatar_contradiction_clause,[],[f322]) ).
fof(f322,plain,
( $false
| spl8_3
| ~ spl8_11 ),
inference(resolution,[],[f315,f280]) ).
fof(f280,plain,
( ~ member(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))),universal_class)
| spl8_3 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f278,plain,
( spl8_3
<=> member(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
fof(f315,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f314,plain,
( spl8_11
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).
fof(f320,plain,
spl8_12,
inference(avatar_split_clause,[],[f222,f318]) ).
fof(f318,plain,
( spl8_12
<=> ! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).
fof(f222,plain,
! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
( ! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) )
& inductive(sK7)
& member(sK7,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f84,f133]) ).
fof(f133,plain,
( ? [X0] :
( ! [X1] :
( subclass(X0,X1)
| ~ inductive(X1) )
& inductive(X0)
& member(X0,universal_class) )
=> ( ! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) )
& inductive(sK7)
& member(sK7,universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
? [X0] :
( ! [X1] :
( subclass(X0,X1)
| ~ inductive(X1) )
& inductive(X0)
& member(X0,universal_class) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
? [X0] :
( ! [X1] :
( inductive(X1)
=> subclass(X0,X1) )
& inductive(X0)
& member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infinity) ).
fof(f316,plain,
spl8_11,
inference(avatar_split_clause,[],[f160,f314]) ).
fof(f160,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
fof(f312,plain,
spl8_10,
inference(avatar_split_clause,[],[f151,f310]) ).
fof(f310,plain,
( spl8_10
<=> ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).
fof(f151,plain,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) )
& ( ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) )
| ~ inductive(X0) ) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) )
& ( ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) )
| ~ inductive(X0) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( inductive(X0)
<=> ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive_defn) ).
fof(f308,plain,
spl8_9,
inference(avatar_split_clause,[],[f137,f305]) ).
fof(f305,plain,
( spl8_9
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).
fof(f137,plain,
subclass(successor_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation_defn1) ).
fof(f303,plain,
spl8_8,
inference(avatar_split_clause,[],[f136,f300]) ).
fof(f300,plain,
( spl8_8
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).
fof(f136,plain,
subclass(element_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation) ).
fof(f298,plain,
spl8_7,
inference(avatar_split_clause,[],[f262,f296]) ).
fof(f296,plain,
( spl8_7
<=> ! [X1] : subclass(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).
fof(f262,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f169]) ).
fof(f169,plain,
! [X0,X1] :
( subclass(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) )
& ( ( subclass(X1,X0)
& subclass(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) )
& ( ( subclass(X1,X0)
& subclass(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subclass(X1,X0)
& subclass(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality) ).
fof(f294,plain,
spl8_6,
inference(avatar_split_clause,[],[f220,f291]) ).
fof(f291,plain,
( spl8_6
<=> member(sK7,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
fof(f220,plain,
member(sK7,universal_class),
inference(cnf_transformation,[],[f134]) ).
fof(f289,plain,
spl8_5,
inference(avatar_split_clause,[],[f139,f287]) ).
fof(f287,plain,
( spl8_5
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
fof(f139,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f285,plain,
spl8_4,
inference(avatar_split_clause,[],[f138,f283]) ).
fof(f283,plain,
( spl8_4
<=> ! [X0] : ~ member(X0,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
fof(f138,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_defn) ).
fof(f281,plain,
~ spl8_3,
inference(avatar_split_clause,[],[f228,f278]) ).
fof(f228,plain,
~ member(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))),universal_class),
inference(definition_unfolding,[],[f135,f226]) ).
fof(f226,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f164,f141,f141]) ).
fof(f141,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f164,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_defn) ).
fof(f135,plain,
~ member(ordered_pair(sK0,sK1),universal_class),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
~ member(ordered_pair(sK0,sK1),universal_class),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f71,f85]) ).
fof(f85,plain,
( ? [X0,X1] : ~ member(ordered_pair(X0,X1),universal_class)
=> ~ member(ordered_pair(sK0,sK1),universal_class) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
? [X0,X1] : ~ member(ordered_pair(X0,X1),universal_class),
inference(ennf_transformation,[],[f45]) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] : member(ordered_pair(X0,X1),universal_class),
inference(negated_conjecture,[],[f44]) ).
fof(f44,conjecture,
! [X0,X1] : member(ordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_is_set) ).
fof(f276,plain,
spl8_2,
inference(avatar_split_clause,[],[f221,f273]) ).
fof(f273,plain,
( spl8_2
<=> inductive(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
fof(f221,plain,
inductive(sK7),
inference(cnf_transformation,[],[f134]) ).
fof(f271,plain,
spl8_1,
inference(avatar_split_clause,[],[f218,f268]) ).
fof(f268,plain,
( spl8_1
<=> function(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
fof(f218,plain,
function(sK6),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
( ! [X1] :
( member(apply(sK6,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f83,f131]) ).
fof(f131,plain,
( ? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) )
=> ( ! [X1] :
( member(apply(sK6,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) ),
inference(flattening,[],[f82]) ).
fof(f82,plain,
? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,plain,
? [X0] :
( ! [X1] :
( member(X1,universal_class)
=> ( member(apply(X0,X1),X1)
| null_class = X1 ) )
& function(X0) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
? [X8] :
( ! [X1] :
( member(X1,universal_class)
=> ( member(apply(X8,X1),X1)
| null_class = X1 ) )
& function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET025+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n017.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 Apr 30 01:14:33 EDT 2024
% 0.18/0.35 % CPUTime :
% 0.18/0.35 % (17791)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.36 % (17797)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)
% 0.18/0.36 % (17795)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.18/0.36 % (17794)WARNING: value z3 for option sas not known
% 0.18/0.36 % (17798)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.18/0.37 % (17796)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)
% 0.18/0.37 % (17794)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)
% 0.18/0.37 % (17793)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.18/0.37 % (17792)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.18/0.37 % (17796)First to succeed.
% 0.18/0.37 % (17796)Refutation found. Thanks to Tanya!
% 0.18/0.37 % SZS status Theorem for theBenchmark
% 0.18/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.37 % (17796)------------------------------
% 0.18/0.37 % (17796)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.18/0.37 % (17796)Termination reason: Refutation
% 0.18/0.37
% 0.18/0.37 % (17796)Memory used [KB]: 969
% 0.18/0.37 % (17796)Time elapsed: 0.007 s
% 0.18/0.37 % (17796)Instructions burned: 10 (million)
% 0.18/0.37 % (17796)------------------------------
% 0.18/0.37 % (17796)------------------------------
% 0.18/0.37 % (17791)Success in time 0.009 s
%------------------------------------------------------------------------------