TSTP Solution File: SET976+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET976+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 : n021.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 09:19:51 EDT 2024
% Result : Theorem 0.14s 0.37s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 6 unt; 0 def)
% Number of atoms : 143 ( 44 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 166 ( 61 ~; 64 |; 30 &)
% ( 8 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 86 ( 67 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f219,plain,
$false,
inference(unit_resulting_resolution,[],[f76,f52,f158,f45]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,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,[],[f24]) ).
fof(f24,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,[],[f6]) ).
fof(f6,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(f158,plain,
~ in(ordered_pair(sK1,sK2),cartesian_product2(sK3,singleton(sK2))),
inference(unit_resulting_resolution,[],[f93,f76,f50]) ).
fof(f50,plain,
( ~ in(ordered_pair(sK1,sK2),cartesian_product2(sK3,singleton(sK2)))
| ~ in(sK1,sK3)
| sK2 != sK4 ),
inference(inner_rewriting,[],[f32]) ).
fof(f32,plain,
( sK2 != sK4
| ~ in(sK1,sK3)
| ~ in(ordered_pair(sK1,sK2),cartesian_product2(sK3,singleton(sK4))) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
( ( sK2 != sK4
| ~ in(sK1,sK3)
| ~ in(ordered_pair(sK1,sK2),cartesian_product2(sK3,singleton(sK4))) )
& ( ( sK2 = sK4
& in(sK1,sK3) )
| in(ordered_pair(sK1,sK2),cartesian_product2(sK3,singleton(sK4))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f16,f17]) ).
fof(f17,plain,
( ? [X0,X1,X2,X3] :
( ( X1 != X3
| ~ in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) )
& ( ( X1 = X3
& in(X0,X2) )
| in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) ) )
=> ( ( sK2 != sK4
| ~ in(sK1,sK3)
| ~ in(ordered_pair(sK1,sK2),cartesian_product2(sK3,singleton(sK4))) )
& ( ( sK2 = sK4
& in(sK1,sK3) )
| in(ordered_pair(sK1,sK2),cartesian_product2(sK3,singleton(sK4))) ) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
? [X0,X1,X2,X3] :
( ( X1 != X3
| ~ in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) )
& ( ( X1 = X3
& in(X0,X2) )
| in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) ) ),
inference(flattening,[],[f15]) ).
fof(f15,plain,
? [X0,X1,X2,X3] :
( ( X1 != X3
| ~ in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) )
& ( ( X1 = X3
& in(X0,X2) )
| in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
<~> ( X1 = X3
& in(X0,X2) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
<=> ( X1 = X3
& in(X0,X2) ) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
<=> ( X1 = X3
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_zfmisc_1) ).
fof(f93,plain,
sK2 = sK4,
inference(subsumption_resolution,[],[f91,f61]) ).
fof(f61,plain,
! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(resolution,[],[f37,f49]) ).
fof(f49,plain,
! [X0] : sP0(X0,singleton(X0)),
inference(equality_resolution,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( sP0(X0,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( singleton(X0) = X1
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f3,f13]) ).
fof(f13,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f3,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f37,plain,
! [X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,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])],[f20,f21]) ).
fof(f21,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(f20,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,[],[f19]) ).
fof(f19,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,[],[f13]) ).
fof(f91,plain,
( in(sK2,singleton(sK4))
| sK2 = sK4 ),
inference(resolution,[],[f44,f31]) ).
fof(f31,plain,
( in(ordered_pair(sK1,sK2),cartesian_product2(sK3,singleton(sK4)))
| sK2 = sK4 ),
inference(cnf_transformation,[],[f18]) ).
fof(f44,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f25]) ).
fof(f52,plain,
! [X0] : in(X0,singleton(X0)),
inference(unit_resulting_resolution,[],[f49,f48]) ).
fof(f48,plain,
! [X3,X1] :
( ~ sP0(X3,X1)
| in(X3,X1) ),
inference(equality_resolution,[],[f38]) ).
fof(f38,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f76,plain,
in(sK1,sK3),
inference(duplicate_literal_removal,[],[f75]) ).
fof(f75,plain,
( in(sK1,sK3)
| in(sK1,sK3) ),
inference(resolution,[],[f43,f30]) ).
fof(f30,plain,
( in(ordered_pair(sK1,sK2),cartesian_product2(sK3,singleton(sK4)))
| in(sK1,sK3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f43,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET976+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 17:05:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (14553)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (14561)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)
% 0.14/0.37 % (14556)WARNING: value z3 for option sas not known
% 0.14/0.37 % (14561)First to succeed.
% 0.14/0.37 % (14554)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (14557)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (14556)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)
% 0.14/0.37 % (14555)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (14558)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 % (14561)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-14553"
% 0.14/0.37 % (14559)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)
% 0.14/0.37 % (14561)Refutation found. Thanks to Tanya!
% 0.14/0.37 % SZS status Theorem for theBenchmark
% 0.14/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.37 % (14561)------------------------------
% 0.14/0.37 % (14561)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.37 % (14561)Termination reason: Refutation
% 0.14/0.37
% 0.14/0.37 % (14561)Memory used [KB]: 855
% 0.14/0.37 % (14561)Time elapsed: 0.007 s
% 0.14/0.37 % (14561)Instructions burned: 15 (million)
% 0.14/0.37 % (14553)Success in time 0.018 s
%------------------------------------------------------------------------------