TSTP Solution File: SET025-7 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET025-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.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 : Sun May 5 09:10:32 EDT 2024
% Result : Unsatisfiable 0.13s 0.38s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 36
% Syntax : Number of formulae : 61 ( 36 unt; 0 def)
% Number of atoms : 91 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 17 ~; 13 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 18 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f331,plain,
$false,
inference(avatar_sat_refutation,[],[f257,f262,f267,f271,f276,f280,f284,f288,f293,f297,f301,f305,f310,f315,f319,f323,f328,f330]) ).
fof(f330,plain,
( spl0_3
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f329]) ).
fof(f329,plain,
( $false
| spl0_3
| ~ spl0_12 ),
inference(resolution,[],[f304,f266]) ).
fof(f266,plain,
( ~ member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),universal_class)
| spl0_3 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f264,plain,
( spl0_3
<=> member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f304,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f303,plain,
( spl0_12
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f328,plain,
spl0_17,
inference(avatar_split_clause,[],[f158,f325]) ).
fof(f325,plain,
( spl0_17
<=> member(null_class,unordered_pair(null_class,null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f158,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(f323,plain,
spl0_16,
inference(avatar_split_clause,[],[f51,f321]) ).
fof(f321,plain,
( spl0_16
<=> ! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f51,axiom,
! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive2) ).
fof(f319,plain,
spl0_15,
inference(avatar_split_clause,[],[f47,f317]) ).
fof(f317,plain,
( spl0_15
<=> ! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).
fof(f315,plain,
spl0_14,
inference(avatar_split_clause,[],[f44,f312]) ).
fof(f312,plain,
( spl0_14
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation1) ).
fof(f310,plain,
spl0_13,
inference(avatar_split_clause,[],[f18,f307]) ).
fof(f307,plain,
( spl0_13
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).
fof(f305,plain,
spl0_12,
inference(avatar_split_clause,[],[f11,f303]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f301,plain,
spl0_11,
inference(avatar_split_clause,[],[f78,f299]) ).
fof(f299,plain,
( spl0_11
<=> ! [X8] :
( ~ operation(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f78,axiom,
! [X8] :
( ~ operation(X8)
| function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation1) ).
fof(f297,plain,
spl0_10,
inference(avatar_split_clause,[],[f71,f295]) ).
fof(f295,plain,
( spl0_10
<=> ! [X8] :
( ~ one_to_one(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f71,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one1) ).
fof(f293,plain,
spl0_9,
inference(avatar_split_clause,[],[f107,f290]) ).
fof(f290,plain,
( spl0_9
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f107,axiom,
member(null_class,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_a_set) ).
fof(f288,plain,
spl0_8,
inference(avatar_split_clause,[],[f104,f286]) ).
fof(f286,plain,
( spl0_8
<=> ! [X0] : subclass(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f104,axiom,
! [X0] : subclass(null_class,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_subclass) ).
fof(f284,plain,
spl0_7,
inference(avatar_split_clause,[],[f103,f282]) ).
fof(f282,plain,
( spl0_7
<=> ! [X4] : ~ member(X4,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f103,axiom,
! [X4] : ~ member(X4,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f280,plain,
spl0_6,
inference(avatar_split_clause,[],[f96,f278]) ).
fof(f278,plain,
( spl0_6
<=> ! [X0] : subclass(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f96,axiom,
! [X0] : subclass(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_is_reflexive) ).
fof(f276,plain,
spl0_5,
inference(avatar_split_clause,[],[f52,f273]) ).
fof(f273,plain,
( spl0_5
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f271,plain,
spl0_4,
inference(avatar_split_clause,[],[f4,f269]) ).
fof(f269,plain,
( spl0_4
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f267,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f157,f264]) ).
fof(f157,plain,
~ member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),universal_class),
inference(definition_unfolding,[],[f145,f150]) ).
fof(f150,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f145,axiom,
~ member(ordered_pair(x,y),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_is_set_1) ).
fof(f262,plain,
spl0_2,
inference(avatar_split_clause,[],[f69,f259]) ).
fof(f259,plain,
( spl0_2
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).
fof(f257,plain,
spl0_1,
inference(avatar_split_clause,[],[f50,f254]) ).
fof(f254,plain,
( spl0_1
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET025-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n002.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 : Fri May 3 16:30:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (4887)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (4891)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37 % (4890)WARNING: value z3 for option sas not known
% 0.13/0.37 % (4888)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 % (4889)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 % (4892)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 % (4890)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 % (4893)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)
% 0.13/0.37 % (4894)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)
% 0.13/0.38 % (4892)First to succeed.
% 0.13/0.38 % (4892)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4887"
% 0.13/0.38 % (4892)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 % (4892)------------------------------
% 0.13/0.38 % (4892)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.38 % (4892)Termination reason: Refutation
% 0.13/0.38
% 0.13/0.38 % (4892)Memory used [KB]: 1038
% 0.13/0.38 % (4892)Time elapsed: 0.012 s
% 0.13/0.38 % (4892)Instructions burned: 19 (million)
% 0.13/0.38 % (4887)Success in time 0.032 s
%------------------------------------------------------------------------------