TSTP Solution File: SET890+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET890+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n015.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 09:19:37 EDT 2024
% Result : Theorem 0.16s 0.51s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 15 unt; 0 def)
% Number of atoms : 172 ( 38 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 196 ( 73 ~; 74 |; 34 &)
% ( 11 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 97 ( 84 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7799,plain,
$false,
inference(subsumption_resolution,[],[f7730,f6284]) ).
fof(f6284,plain,
~ in(sK6(singleton(sK3),sK3),sK3),
inference(unit_resulting_resolution,[],[f92,f4170,f67]) ).
fof(f67,plain,
! [X0,X1] :
( ~ sP1(X0,sK6(X0,X1))
| sP2(X0,X1)
| ~ in(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ( ~ sP1(X0,sK6(X0,X1))
| ~ in(sK6(X0,X1),X1) )
& ( sP1(X0,sK6(X0,X1))
| in(sK6(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ sP1(X0,X3) )
& ( sP1(X0,X3)
| ~ in(X3,X1) ) )
| ~ sP2(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f36,f37]) ).
fof(f37,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ sP1(X0,X2)
| ~ in(X2,X1) )
& ( sP1(X0,X2)
| in(X2,X1) ) )
=> ( ( ~ sP1(X0,sK6(X0,X1))
| ~ in(sK6(X0,X1),X1) )
& ( sP1(X0,sK6(X0,X1))
| in(sK6(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ? [X2] :
( ( ~ sP1(X0,X2)
| ~ in(X2,X1) )
& ( sP1(X0,X2)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ sP1(X0,X3) )
& ( sP1(X0,X3)
| ~ in(X3,X1) ) )
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ? [X2] :
( ( ~ sP1(X0,X2)
| ~ in(X2,X1) )
& ( sP1(X0,X2)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ sP1(X0,X2) )
& ( sP1(X0,X2)
| ~ in(X2,X1) ) )
| ~ sP2(X0,X1) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( sP2(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> sP1(X0,X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f4170,plain,
sP1(singleton(sK3),sK6(singleton(sK3),sK3)),
inference(subsumption_resolution,[],[f4157,f644]) ).
fof(f644,plain,
! [X0,X1] :
( ~ in(X1,X0)
| sP1(singleton(X0),X1) ),
inference(resolution,[],[f70,f81]) ).
fof(f81,plain,
! [X0] : in(X0,singleton(X0)),
inference(unit_resulting_resolution,[],[f78,f77]) ).
fof(f77,plain,
! [X3,X1] :
( ~ sP0(X3,X1)
| in(X3,X1) ),
inference(equality_resolution,[],[f59]) ).
fof(f59,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( sK5(X0,X1) != X0
| ~ in(sK5(X0,X1),X1) )
& ( sK5(X0,X1) = X0
| in(sK5(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f31,f32]) ).
fof(f32,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK5(X0,X1) != X0
| ~ in(sK5(X0,X1),X1) )
& ( sK5(X0,X1) = X0
| in(sK5(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f78,plain,
! [X0] : sP0(X0,singleton(X0)),
inference(equality_resolution,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( sP0(X0,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( singleton(X0) = X1
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f3,f17]) ).
fof(f3,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ in(X2,X0)
| sP1(X0,X1)
| ~ in(X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| ~ in(X1,X2) ) )
& ( ( in(sK7(X0,X1),X0)
& in(X1,sK7(X0,X1)) )
| ~ sP1(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f40,f41]) ).
fof(f41,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X0)
& in(X1,X3) )
=> ( in(sK7(X0,X1),X0)
& in(X1,sK7(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| ~ in(X1,X2) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X1,X3) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f39]) ).
fof(f39,plain,
! [X0,X2] :
( ( sP1(X0,X2)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| ~ sP1(X0,X2) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X2] :
( sP1(X0,X2)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f4157,plain,
( sP1(singleton(sK3),sK6(singleton(sK3),sK3))
| in(sK6(singleton(sK3),sK3),sK3) ),
inference(resolution,[],[f66,f92]) ).
fof(f66,plain,
! [X0,X1] :
( sP2(X0,X1)
| sP1(X0,sK6(X0,X1))
| in(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f92,plain,
~ sP2(singleton(sK3),sK3),
inference(unit_resulting_resolution,[],[f48,f72]) ).
fof(f72,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1] :
( ( union(X0) = X1
| ~ sP2(X0,X1) )
& ( sP2(X0,X1)
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( union(X0) = X1
<=> sP2(X0,X1) ),
inference(definition_folding,[],[f5,f20,f19]) ).
fof(f5,axiom,
! [X0,X1] :
( union(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f48,plain,
sK3 != union(singleton(sK3)),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
sK3 != union(singleton(sK3)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f13,f22]) ).
fof(f22,plain,
( ? [X0] : union(singleton(X0)) != X0
=> sK3 != union(singleton(sK3)) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
? [X0] : union(singleton(X0)) != X0,
inference(ennf_transformation,[],[f11]) ).
fof(f11,negated_conjecture,
~ ! [X0] : union(singleton(X0)) = X0,
inference(negated_conjecture,[],[f10]) ).
fof(f10,conjecture,
! [X0] : union(singleton(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
fof(f7730,plain,
in(sK6(singleton(sK3),sK3),sK3),
inference(superposition,[],[f4174,f4335]) ).
fof(f4335,plain,
sK3 = sK7(singleton(sK3),sK6(singleton(sK3),sK3)),
inference(unit_resulting_resolution,[],[f78,f4173,f58]) ).
fof(f58,plain,
! [X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f33]) ).
fof(f4173,plain,
in(sK7(singleton(sK3),sK6(singleton(sK3),sK3)),singleton(sK3)),
inference(unit_resulting_resolution,[],[f4170,f69]) ).
fof(f69,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| in(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f4174,plain,
in(sK6(singleton(sK3),sK3),sK7(singleton(sK3),sK6(singleton(sK3),sK3))),
inference(unit_resulting_resolution,[],[f4170,f68]) ).
fof(f68,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| in(X1,sK7(X0,X1)) ),
inference(cnf_transformation,[],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET890+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31 % Computer : n015.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri May 3 17:05:08 EDT 2024
% 0.16/0.31 % CPUTime :
% 0.16/0.31 % (23969)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.33 % (23972)WARNING: value z3 for option sas not known
% 0.16/0.33 % (23975)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)
% 0.16/0.33 % (23973)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.33 % (23970)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.33 % (23971)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.33 % (23974)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)
% 0.16/0.33 % (23976)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)
% 0.16/0.33 % (23972)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)
% 0.16/0.33 TRYING [1]
% 0.16/0.33 TRYING [2]
% 0.16/0.33 TRYING [3]
% 0.16/0.34 TRYING [1]
% 0.16/0.34 TRYING [4]
% 0.16/0.34 TRYING [2]
% 0.16/0.34 TRYING [3]
% 0.16/0.34 TRYING [5]
% 0.16/0.36 TRYING [6]
% 0.16/0.36 TRYING [1]
% 0.16/0.36 TRYING [4]
% 0.16/0.36 TRYING [2]
% 0.16/0.36 TRYING [3]
% 0.16/0.37 TRYING [4]
% 0.16/0.37 TRYING [7]
% 0.16/0.38 TRYING [5]
% 0.16/0.40 TRYING [6]
% 0.16/0.40 TRYING [5]
% 0.16/0.42 TRYING [8]
% 0.16/0.43 TRYING [7]
% 0.16/0.48 TRYING [9]
% 0.16/0.49 TRYING [8]
% 0.16/0.50 TRYING [6]
% 0.16/0.50 % (23976)First to succeed.
% 0.16/0.50 % (23976)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-23969"
% 0.16/0.51 % (23976)Refutation found. Thanks to Tanya!
% 0.16/0.51 % SZS status Theorem for theBenchmark
% 0.16/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.51 % (23976)------------------------------
% 0.16/0.51 % (23976)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.51 % (23976)Termination reason: Refutation
% 0.16/0.51
% 0.16/0.51 % (23976)Memory used [KB]: 3135
% 0.16/0.51 % (23976)Time elapsed: 0.175 s
% 0.16/0.51 % (23976)Instructions burned: 377 (million)
% 0.16/0.51 % (23969)Success in time 0.177 s
%------------------------------------------------------------------------------