TSTP Solution File: SEU160+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU160+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n028.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 15:22:41 EDT 2024
% Result : Theorem 0.13s 0.37s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of formulae : 64 ( 19 unt; 0 def)
% Number of atoms : 156 ( 53 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 150 ( 58 ~; 60 |; 14 &)
% ( 14 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 12 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 39 ( 27 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,plain,
$false,
inference(avatar_sat_refutation,[],[f44,f53,f58,f63,f68,f73,f79,f81,f85,f87,f91,f95]) ).
fof(f95,plain,
( spl4_2
| spl4_4
| ~ spl4_8
| ~ spl4_11 ),
inference(avatar_split_clause,[],[f94,f89,f70,f50,f41]) ).
fof(f41,plain,
( spl4_2
<=> sK0 = singleton(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f50,plain,
( spl4_4
<=> empty_set = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).
fof(f70,plain,
( spl4_8
<=> subset(sK0,singleton(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
fof(f89,plain,
( spl4_11
<=> ! [X0,X1] :
( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).
fof(f94,plain,
( empty_set = sK0
| sK0 = singleton(sK1)
| ~ spl4_8
| ~ spl4_11 ),
inference(resolution,[],[f90,f72]) ).
fof(f72,plain,
( subset(sK0,singleton(sK1))
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f90,plain,
( ! [X0,X1] :
( ~ subset(X0,singleton(X1))
| empty_set = X0
| singleton(X1) = X0 )
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f91,plain,
spl4_11,
inference(avatar_split_clause,[],[f27,f89]) ).
fof(f27,plain,
! [X0,X1] :
( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) )
& ( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) )
& ( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( singleton(X1) = X0
| empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f87,plain,
( spl4_3
| ~ spl4_10 ),
inference(avatar_contradiction_clause,[],[f86]) ).
fof(f86,plain,
( $false
| spl4_3
| ~ spl4_10 ),
inference(resolution,[],[f84,f48]) ).
fof(f48,plain,
( ~ subset(empty_set,singleton(sK1))
| spl4_3 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f46,plain,
( spl4_3
<=> subset(empty_set,singleton(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
fof(f84,plain,
( ! [X1] : subset(empty_set,singleton(X1))
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f83,plain,
( spl4_10
<=> ! [X1] : subset(empty_set,singleton(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
fof(f85,plain,
spl4_10,
inference(avatar_split_clause,[],[f33,f83]) ).
fof(f33,plain,
! [X1] : subset(empty_set,singleton(X1)),
inference(equality_resolution,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( subset(X0,singleton(X1))
| empty_set != X0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f81,plain,
( spl4_1
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f80]) ).
fof(f80,plain,
( $false
| spl4_1
| ~ spl4_9 ),
inference(resolution,[],[f78,f39]) ).
fof(f39,plain,
( ~ subset(sK0,sK0)
| spl4_1 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f37,plain,
( spl4_1
<=> subset(sK0,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f78,plain,
( ! [X0] : subset(X0,X0)
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f77,plain,
( spl4_9
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
fof(f79,plain,
spl4_9,
inference(avatar_split_clause,[],[f26,f77]) ).
fof(f26,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f10,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f73,plain,
( spl4_8
| spl4_4
| spl4_2 ),
inference(avatar_split_clause,[],[f22,f41,f50,f70]) ).
fof(f22,plain,
( sK0 = singleton(sK1)
| empty_set = sK0
| subset(sK0,singleton(sK1)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
( ( ( sK0 != singleton(sK1)
& empty_set != sK0 )
| ~ subset(sK0,singleton(sK1)) )
& ( sK0 = singleton(sK1)
| empty_set = sK0
| subset(sK0,singleton(sK1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14]) ).
fof(f14,plain,
( ? [X0,X1] :
( ( ( singleton(X1) != X0
& empty_set != X0 )
| ~ subset(X0,singleton(X1)) )
& ( singleton(X1) = X0
| empty_set = X0
| subset(X0,singleton(X1)) ) )
=> ( ( ( sK0 != singleton(sK1)
& empty_set != sK0 )
| ~ subset(sK0,singleton(sK1)) )
& ( sK0 = singleton(sK1)
| empty_set = sK0
| subset(sK0,singleton(sK1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
? [X0,X1] :
( ( ( singleton(X1) != X0
& empty_set != X0 )
| ~ subset(X0,singleton(X1)) )
& ( singleton(X1) = X0
| empty_set = X0
| subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f12]) ).
fof(f12,plain,
? [X0,X1] :
( ( ( singleton(X1) != X0
& empty_set != X0 )
| ~ subset(X0,singleton(X1)) )
& ( singleton(X1) = X0
| empty_set = X0
| subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
? [X0,X1] :
( subset(X0,singleton(X1))
<~> ( singleton(X1) = X0
| empty_set = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( singleton(X1) = X0
| empty_set = X0 ) ),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( singleton(X1) = X0
| empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f68,plain,
spl4_7,
inference(avatar_split_clause,[],[f31,f65]) ).
fof(f65,plain,
( spl4_7
<=> empty(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
fof(f31,plain,
empty(sK3),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
empty(sK3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f1,f20]) ).
fof(f20,plain,
( ? [X0] : empty(X0)
=> empty(sK3) ),
introduced(choice_axiom,[]) ).
fof(f1,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f63,plain,
~ spl4_6,
inference(avatar_split_clause,[],[f30,f60]) ).
fof(f60,plain,
( spl4_6
<=> empty(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
fof(f30,plain,
~ empty(sK2),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
~ empty(sK2),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f2,f18]) ).
fof(f18,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK2) ),
introduced(choice_axiom,[]) ).
fof(f2,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f58,plain,
spl4_5,
inference(avatar_split_clause,[],[f25,f55]) ).
fof(f55,plain,
( spl4_5
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
fof(f25,plain,
empty(empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f53,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f35,f50,f46]) ).
fof(f35,plain,
( empty_set != sK0
| ~ subset(empty_set,singleton(sK1)) ),
inference(inner_rewriting,[],[f23]) ).
fof(f23,plain,
( empty_set != sK0
| ~ subset(sK0,singleton(sK1)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f44,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f34,f41,f37]) ).
fof(f34,plain,
( sK0 != singleton(sK1)
| ~ subset(sK0,sK0) ),
inference(inner_rewriting,[],[f24]) ).
fof(f24,plain,
( sK0 != singleton(sK1)
| ~ subset(sK0,singleton(sK1)) ),
inference(cnf_transformation,[],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU160+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n028.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 : Mon Apr 29 21:12:44 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (19662)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (19667)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 % (19667)First to succeed.
% 0.13/0.37 % (19667)Refutation found. Thanks to Tanya!
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.37 % (19667)------------------------------
% 0.13/0.37 % (19667)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.37 % (19667)Termination reason: Refutation
% 0.13/0.37
% 0.13/0.37 % (19667)Memory used [KB]: 763
% 0.13/0.37 % (19667)Time elapsed: 0.004 s
% 0.13/0.37 % (19667)Instructions burned: 4 (million)
% 0.13/0.37 % (19667)------------------------------
% 0.13/0.37 % (19667)------------------------------
% 0.13/0.37 % (19662)Success in time 0.019 s
%------------------------------------------------------------------------------