TSTP Solution File: SET872+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET872+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n027.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 : Wed Aug 31 18:25:58 EDT 2022
% Result : Theorem 1.55s 0.58s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 14 unt; 0 def)
% Number of atoms : 184 ( 91 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 223 ( 82 ~; 83 |; 43 &)
% ( 10 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 101 ( 85 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f123,plain,
$false,
inference(subsumption_resolution,[],[f122,f68]) ).
fof(f68,plain,
~ subset(sF7,sF8),
inference(definition_folding,[],[f57,f67,f66]) ).
fof(f66,plain,
singleton(sK6) = sF7,
introduced(function_definition,[]) ).
fof(f67,plain,
sF8 = unordered_pair(sK6,sK5),
introduced(function_definition,[]) ).
fof(f57,plain,
~ subset(singleton(sK6),unordered_pair(sK6,sK5)),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
~ subset(singleton(sK6),unordered_pair(sK6,sK5)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f36,f37]) ).
fof(f37,plain,
( ? [X0,X1] : ~ subset(singleton(X1),unordered_pair(X1,X0))
=> ~ subset(singleton(sK6),unordered_pair(sK6,sK5)) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
? [X0,X1] : ~ subset(singleton(X1),unordered_pair(X1,X0)),
inference(rectify,[],[f16]) ).
fof(f16,plain,
? [X1,X0] : ~ subset(singleton(X0),unordered_pair(X0,X1)),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X1,X0] : subset(singleton(X0),unordered_pair(X0,X1)),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X1,X0] : subset(singleton(X0),unordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_zfmisc_1) ).
fof(f122,plain,
subset(sF7,sF8),
inference(subsumption_resolution,[],[f121,f71]) ).
fof(f71,plain,
in(sK6,sF8),
inference(superposition,[],[f62,f67]) ).
fof(f62,plain,
! [X3,X1] : in(X3,unordered_pair(X3,X1)),
inference(equality_resolution,[],[f61]) ).
fof(f61,plain,
! [X3,X0,X1] :
( in(X3,X0)
| unordered_pair(X3,X1) != X0 ),
inference(equality_resolution,[],[f50]) ).
fof(f50,plain,
! [X2,X3,X0,X1] :
( in(X3,X0)
| X2 != X3
| unordered_pair(X2,X1) != X0 ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ( X2 != X3
& X1 != X3 ) )
& ( X2 = X3
| X1 = X3
| ~ in(X3,X0) ) )
| unordered_pair(X2,X1) != X0 )
& ( unordered_pair(X2,X1) = X0
| ( ( ( sK2(X0,X1,X2) != X2
& sK2(X0,X1,X2) != X1 )
| ~ in(sK2(X0,X1,X2),X0) )
& ( sK2(X0,X1,X2) = X2
| sK2(X0,X1,X2) = X1
| in(sK2(X0,X1,X2),X0) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f27,f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ( X2 != X4
& X1 != X4 )
| ~ in(X4,X0) )
& ( X2 = X4
| X1 = X4
| in(X4,X0) ) )
=> ( ( ( sK2(X0,X1,X2) != X2
& sK2(X0,X1,X2) != X1 )
| ~ in(sK2(X0,X1,X2),X0) )
& ( sK2(X0,X1,X2) = X2
| sK2(X0,X1,X2) = X1
| in(sK2(X0,X1,X2),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ( X2 != X3
& X1 != X3 ) )
& ( X2 = X3
| X1 = X3
| ~ in(X3,X0) ) )
| unordered_pair(X2,X1) != X0 )
& ( unordered_pair(X2,X1) = X0
| ? [X4] :
( ( ( X2 != X4
& X1 != X4 )
| ~ in(X4,X0) )
& ( X2 = X4
| X1 = X4
| in(X4,X0) ) ) ) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X1,X0) != X2 )
& ( unordered_pair(X1,X0) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) ) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X1,X0) != X2 )
& ( unordered_pair(X1,X0) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X2,X0,X1] :
( ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) )
<=> unordered_pair(X1,X0) = X2 ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0,X2] :
( ! [X3] :
( in(X3,X2)
<=> ( X0 = X3
| X1 = X3 ) )
<=> unordered_pair(X0,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f121,plain,
( ~ in(sK6,sF8)
| subset(sF7,sF8) ),
inference(superposition,[],[f53,f117]) ).
fof(f117,plain,
sK6 = sK4(sF8,sF7),
inference(resolution,[],[f103,f68]) ).
fof(f103,plain,
! [X0] :
( subset(sF7,X0)
| sK6 = sK4(X0,sF7) ),
inference(resolution,[],[f98,f54]) ).
fof(f54,plain,
! [X0,X1] :
( in(sK4(X0,X1),X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ( in(sK4(X0,X1),X1)
& ~ in(sK4(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f33,f34]) ).
fof(f34,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X1)
& ~ in(X3,X0) )
=> ( in(sK4(X0,X1),X1)
& ~ in(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X3] :
( in(X3,X1)
& ~ in(X3,X0) ) ) ),
inference(rectify,[],[f32]) ).
fof(f32,plain,
! [X1,X0] :
( ( ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) ) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X1,X0] :
( ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) )
<=> subset(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f98,plain,
! [X0] :
( ~ in(X0,sF7)
| sK6 = X0 ),
inference(superposition,[],[f60,f66]) ).
fof(f60,plain,
! [X2,X0] :
( ~ in(X2,singleton(X0))
| X0 = X2 ),
inference(equality_resolution,[],[f42]) ).
fof(f42,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ( ( sK1(X0,X1) != X0
| ~ in(sK1(X0,X1),X1) )
& ( sK1(X0,X1) = X0
| in(sK1(X0,X1),X1) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f21,f22]) ).
fof(f22,plain,
! [X0,X1] :
( ? [X3] :
( ( X0 != X3
| ~ in(X3,X1) )
& ( X0 = X3
| in(X3,X1) ) )
=> ( ( sK1(X0,X1) != X0
| ~ in(sK1(X0,X1),X1) )
& ( sK1(X0,X1) = X0
| in(sK1(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ? [X3] :
( ( X0 != X3
| ~ in(X3,X1) )
& ( X0 = X3
| in(X3,X1) ) ) ) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
! [X1,X0] :
( ( ! [X2] :
( ( in(X2,X0)
| X1 != X2 )
& ( X1 = X2
| ~ in(X2,X0) ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ? [X2] :
( ( X1 != X2
| ~ in(X2,X0) )
& ( X1 = X2
| in(X2,X0) ) ) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X1,X0] :
( ! [X2] :
( in(X2,X0)
<=> X1 = X2 )
<=> singleton(X1) = X0 ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] :
( singleton(X0) = X1
<=> ! [X2] :
( X0 = X2
<=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f53,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X0)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET872+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 14:42:46 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.55 % (6640)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/100Mi)
% 0.20/0.56 % (6641)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/100Mi)
% 0.20/0.56 % (6632)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.20/0.56 % (6633)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/100Mi)
% 0.20/0.56 % (6649)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/177Mi)
% 0.20/0.56 % (6640)First to succeed.
% 0.20/0.56 % (6626)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.20/0.57 % (6648)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/68Mi)
% 1.55/0.57 % (6649)Also succeeded, but the first one will report.
% 1.55/0.58 % (6640)Refutation found. Thanks to Tanya!
% 1.55/0.58 % SZS status Theorem for theBenchmark
% 1.55/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 1.55/0.58 % (6640)------------------------------
% 1.55/0.58 % (6640)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.55/0.58 % (6640)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.55/0.58 % (6640)Termination reason: Refutation
% 1.55/0.58
% 1.55/0.58 % (6640)Memory used [KB]: 5500
% 1.55/0.58 % (6640)Time elapsed: 0.146 s
% 1.55/0.58 % (6640)Instructions burned: 4 (million)
% 1.55/0.58 % (6640)------------------------------
% 1.55/0.58 % (6640)------------------------------
% 1.55/0.58 % (6621)Success in time 0.225 s
%------------------------------------------------------------------------------