TSTP Solution File: SET093-7 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET093-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.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 May 21 03:16:02 EDT 2024
% Result : Unsatisfiable 0.13s 0.38s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 37
% Syntax : Number of formulae : 62 ( 36 unt; 0 def)
% Number of atoms : 94 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 18 ~; 14 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 19 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 23 ( 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f322,plain,
$false,
inference(avatar_sat_refutation,[],[f242,f247,f252,f257,f261,f266,f270,f274,f278,f283,f287,f291,f295,f300,f305,f309,f313,f318,f321]) ).
fof(f321,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f319,f293,f244,f239]) ).
fof(f239,plain,
( spl0_1
<=> member(x,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f244,plain,
( spl0_2
<=> x = unordered_pair(member_of(x),member_of(x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f293,plain,
( spl0_13
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f319,plain,
( member(x,universal_class)
| ~ spl0_2
| ~ spl0_13 ),
inference(superposition,[],[f294,f246]) ).
fof(f246,plain,
( x = unordered_pair(member_of(x),member_of(x))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f294,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f318,plain,
spl0_18,
inference(avatar_split_clause,[],[f150,f315]) ).
fof(f315,plain,
( spl0_18
<=> member(null_class,unordered_pair(null_class,null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f150,plain,
member(null_class,unordered_pair(null_class,null_class)),
inference(definition_unfolding,[],[f124,f12]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f124,axiom,
member(null_class,singleton(null_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_in_its_singleton) ).
fof(f313,plain,
spl0_17,
inference(avatar_split_clause,[],[f51,f311]) ).
fof(f311,plain,
( spl0_17
<=> ! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f51,axiom,
! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive2) ).
fof(f309,plain,
spl0_16,
inference(avatar_split_clause,[],[f47,f307]) ).
fof(f307,plain,
( spl0_16
<=> ! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).
fof(f305,plain,
spl0_15,
inference(avatar_split_clause,[],[f44,f302]) ).
fof(f302,plain,
( spl0_15
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation1) ).
fof(f300,plain,
spl0_14,
inference(avatar_split_clause,[],[f18,f297]) ).
fof(f297,plain,
( spl0_14
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).
fof(f295,plain,
spl0_13,
inference(avatar_split_clause,[],[f11,f293]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f291,plain,
spl0_12,
inference(avatar_split_clause,[],[f78,f289]) ).
fof(f289,plain,
( spl0_12
<=> ! [X8] :
( ~ operation(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f78,axiom,
! [X8] :
( ~ operation(X8)
| function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation1) ).
fof(f287,plain,
spl0_11,
inference(avatar_split_clause,[],[f71,f285]) ).
fof(f285,plain,
( spl0_11
<=> ! [X8] :
( ~ one_to_one(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f71,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one1) ).
fof(f283,plain,
spl0_10,
inference(avatar_split_clause,[],[f107,f280]) ).
fof(f280,plain,
( spl0_10
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f107,axiom,
member(null_class,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_a_set) ).
fof(f278,plain,
spl0_9,
inference(avatar_split_clause,[],[f104,f276]) ).
fof(f276,plain,
( spl0_9
<=> ! [X0] : subclass(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f104,axiom,
! [X0] : subclass(null_class,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_subclass) ).
fof(f274,plain,
spl0_8,
inference(avatar_split_clause,[],[f103,f272]) ).
fof(f272,plain,
( spl0_8
<=> ! [X4] : ~ member(X4,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f103,axiom,
! [X4] : ~ member(X4,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f270,plain,
spl0_7,
inference(avatar_split_clause,[],[f96,f268]) ).
fof(f268,plain,
( spl0_7
<=> ! [X0] : subclass(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f96,axiom,
! [X0] : subclass(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_is_reflexive) ).
fof(f266,plain,
spl0_6,
inference(avatar_split_clause,[],[f52,f263]) ).
fof(f263,plain,
( spl0_6
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f261,plain,
spl0_5,
inference(avatar_split_clause,[],[f4,f259]) ).
fof(f259,plain,
( spl0_5
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f257,plain,
spl0_4,
inference(avatar_split_clause,[],[f69,f254]) ).
fof(f254,plain,
( spl0_4
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).
fof(f252,plain,
spl0_3,
inference(avatar_split_clause,[],[f50,f249]) ).
fof(f249,plain,
( spl0_3
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f247,plain,
spl0_2,
inference(avatar_split_clause,[],[f149,f244]) ).
fof(f149,plain,
x = unordered_pair(member_of(x),member_of(x)),
inference(definition_unfolding,[],[f137,f12]) ).
fof(f137,axiom,
x = singleton(member_of(x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_singletons_are_sets_1) ).
fof(f242,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f138,f239]) ).
fof(f138,axiom,
~ member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_singletons_are_sets_2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET093-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.10/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.33 % Computer : n019.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 : Mon May 20 13:05:38 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % (22609)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (22614)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)
% 0.13/0.37 % (22610)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 % (22612)WARNING: value z3 for option sas not known
% 0.13/0.37 % (22612)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)
% 0.13/0.37 % (22611)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37 % (22614)First to succeed.
% 0.13/0.37 % (22614)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22609"
% 0.13/0.37 % (22612)Also succeeded, but the first one will report.
% 0.13/0.38 % (22614)Refutation found. Thanks to Tanya!
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.38 % (22614)------------------------------
% 0.13/0.38 % (22614)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.38 % (22614)Termination reason: Refutation
% 0.13/0.38
% 0.13/0.38 % (22614)Memory used [KB]: 1029
% 0.13/0.38 % (22614)Time elapsed: 0.014 s
% 0.13/0.38 % (22614)Instructions burned: 19 (million)
% 0.13/0.38 % (22609)Success in time 0.038 s
%------------------------------------------------------------------------------