TSTP Solution File: SET962+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET962+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n007.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 09:19:49 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 50 ( 3 unt; 0 def)
% Number of atoms : 147 ( 26 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 173 ( 76 ~; 72 |; 13 &)
% ( 6 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 66 ( 59 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f152,plain,
$false,
inference(avatar_sat_refutation,[],[f91,f107,f111,f133,f139,f151]) ).
fof(f151,plain,
( ~ spl5_1
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f150]) ).
fof(f150,plain,
( $false
| ~ spl5_1
| ~ spl5_3 ),
inference(subsumption_resolution,[],[f148,f26]) ).
fof(f26,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
( sK0 != sK1
& cartesian_product2(sK0,sK0) = cartesian_product2(sK1,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f14]) ).
fof(f14,plain,
( ? [X0,X1] :
( X0 != X1
& cartesian_product2(X0,X0) = cartesian_product2(X1,X1) )
=> ( sK0 != sK1
& cartesian_product2(sK0,sK0) = cartesian_product2(sK1,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f11,plain,
? [X0,X1] :
( X0 != X1
& cartesian_product2(X0,X0) = cartesian_product2(X1,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] :
( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
=> X0 = X1 ),
inference(negated_conjecture,[],[f8]) ).
fof(f8,conjecture,
! [X0,X1] :
( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
fof(f148,plain,
( sK0 = sK1
| ~ spl5_1
| ~ spl5_3 ),
inference(resolution,[],[f134,f103]) ).
fof(f103,plain,
( ! [X1] : ~ in(X1,sK1)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f102,plain,
( spl5_3
<=> ! [X1] : ~ in(X1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f134,plain,
( ! [X0] :
( in(sK2(X0,sK0),X0)
| sK0 = X0 )
| ~ spl5_1 ),
inference(resolution,[],[f87,f31]) ).
fof(f31,plain,
! [X0,X1] :
( in(sK2(X0,X1),X1)
| in(sK2(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK2(X0,X1),X1)
| ~ in(sK2(X0,X1),X0) )
& ( in(sK2(X0,X1),X1)
| in(sK2(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f16,f17]) ).
fof(f17,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK2(X0,X1),X1)
| ~ in(sK2(X0,X1),X0) )
& ( in(sK2(X0,X1),X1)
| in(sK2(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f87,plain,
( ! [X1] : ~ in(X1,sK0)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f86,plain,
( spl5_1
<=> ! [X1] : ~ in(X1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f139,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f138]) ).
fof(f138,plain,
( $false
| ~ spl5_1
| ~ spl5_4 ),
inference(resolution,[],[f87,f128]) ).
fof(f128,plain,
( in(sK2(sK0,sK1),sK0)
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f123,f26]) ).
fof(f123,plain,
( in(sK2(sK0,sK1),sK0)
| sK0 = sK1
| ~ spl5_4 ),
inference(factoring,[],[f112]) ).
fof(f112,plain,
( ! [X0] :
( in(sK2(X0,sK1),sK0)
| in(sK2(X0,sK1),X0)
| sK1 = X0 )
| ~ spl5_4 ),
inference(resolution,[],[f106,f31]) ).
fof(f106,plain,
( ! [X0] :
( ~ in(X0,sK1)
| in(X0,sK0) )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f105,plain,
( spl5_4
<=> ! [X0] :
( ~ in(X0,sK1)
| in(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f133,plain,
( ~ spl5_2
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f132]) ).
fof(f132,plain,
( $false
| ~ spl5_2
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f131,f128]) ).
fof(f131,plain,
( ~ in(sK2(sK0,sK1),sK0)
| ~ spl5_2
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f129,f26]) ).
fof(f129,plain,
( sK0 = sK1
| ~ in(sK2(sK0,sK1),sK0)
| ~ spl5_2
| ~ spl5_4 ),
inference(resolution,[],[f128,f93]) ).
fof(f93,plain,
( ! [X0] :
( ~ in(sK2(X0,sK1),sK0)
| sK1 = X0
| ~ in(sK2(X0,sK1),X0) )
| ~ spl5_2 ),
inference(resolution,[],[f90,f32]) ).
fof(f32,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| X0 = X1
| ~ in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f90,plain,
( ! [X0] :
( in(X0,sK1)
| ~ in(X0,sK0) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f89,plain,
( spl5_2
<=> ! [X0] :
( ~ in(X0,sK0)
| in(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f111,plain,
( spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f110,f102,f89,f86]) ).
fof(f110,plain,
( ! [X0] : ~ in(X0,sK0)
| ~ spl5_2
| ~ spl5_3 ),
inference(resolution,[],[f103,f90]) ).
fof(f107,plain,
( spl5_3
| spl5_4 ),
inference(avatar_split_clause,[],[f98,f105,f102]) ).
fof(f98,plain,
! [X0,X1] :
( ~ in(X0,sK1)
| ~ in(X1,sK1)
| in(X0,sK0) ),
inference(resolution,[],[f84,f34]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f19]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f84,plain,
! [X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(sK0,sK0))
| ~ in(X1,sK1)
| ~ in(X0,sK1) ),
inference(superposition,[],[f35,f25]) ).
fof(f25,plain,
cartesian_product2(sK0,sK0) = cartesian_product2(sK1,sK1),
inference(cnf_transformation,[],[f15]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f91,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f81,f89,f86]) ).
fof(f81,plain,
! [X0,X1] :
( ~ in(X0,sK0)
| ~ in(X1,sK0)
| in(X0,sK1) ),
inference(resolution,[],[f35,f46]) ).
fof(f46,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(sK0,sK0))
| in(X1,sK1) ),
inference(superposition,[],[f34,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET962+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.08/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 16:20:53 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (3486)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (3491)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)
% 0.14/0.37 % (3489)WARNING: value z3 for option sas not known
% 0.14/0.38 % (3488)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (3490)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (3493)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)
% 0.14/0.38 % (3489)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)
% 0.14/0.38 % (3492)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)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 % (3487)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (3489)First to succeed.
% 0.14/0.38 % (3489)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3486"
% 0.14/0.38 % (3491)Also succeeded, but the first one will report.
% 0.14/0.38 TRYING [1]
% 0.14/0.38 % (3489)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38 % (3489)------------------------------
% 0.14/0.38 % (3489)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (3489)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (3489)Memory used [KB]: 865
% 0.14/0.38 % (3489)Time elapsed: 0.008 s
% 0.14/0.38 % (3489)Instructions burned: 9 (million)
% 0.14/0.38 % (3486)Success in time 0.022 s
%------------------------------------------------------------------------------