TSTP Solution File: NUN066+2 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : NUN066+2 : TPTP v8.2.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n020.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 : Mon Jun 24 13:32:46 EDT 2024
% Result : Theorem 0.21s 0.44s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 63 ( 5 unt; 0 def)
% Number of atoms : 205 ( 65 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 225 ( 83 ~; 93 |; 43 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 126 ( 104 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1020,plain,
$false,
inference(resolution,[],[f938,f118]) ).
fof(f118,plain,
r1(sK23),
inference(equality_resolution,[],[f103]) ).
fof(f103,plain,
! [X1] :
( r1(X1)
| sK23 != X1 ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X1] :
( ( sK23 = X1
& r1(X1) )
| ( sK23 != X1
& ~ r1(X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f1,f57]) ).
fof(f57,plain,
( ? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| ( X0 != X1
& ~ r1(X1) ) )
=> ! [X1] :
( ( sK23 = X1
& r1(X1) )
| ( sK23 != X1
& ~ r1(X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1,axiom,
? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| ( X0 != X1
& ~ r1(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f938,plain,
! [X0] : ~ r1(X0),
inference(resolution,[],[f902,f110]) ).
fof(f110,plain,
! [X0] : r2(X0,sK12(X0)),
inference(equality_resolution,[],[f79]) ).
fof(f79,plain,
! [X2,X0] :
( r2(X0,X2)
| sK12(X0) != X2 ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X2] :
( ( sK12(X0) = X2
& r2(X0,X2) )
| ( sK12(X0) != X2
& ~ r2(X0,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f18,f41]) ).
fof(f41,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( X1 = X2
& r2(X0,X2) )
| ( X1 != X2
& ~ r2(X0,X2) ) )
=> ! [X2] :
( ( sK12(X0) = X2
& r2(X0,X2) )
| ( sK12(X0) != X2
& ~ r2(X0,X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0] :
? [X1] :
! [X2] :
( ( X1 = X2
& r2(X0,X2) )
| ( X1 != X2
& ~ r2(X0,X2) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2] :
? [X3] :
! [X4] :
( ( X3 = X4
& r2(X2,X4) )
| ( X3 != X4
& ~ r2(X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f902,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| ~ r1(X1) ),
inference(subsumption_resolution,[],[f895,f111]) ).
fof(f111,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) ),
inference(equality_resolution,[],[f82]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| X1 != X2
| ~ r1(X2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( ~ r2(X0,X1)
| ! [X2] :
( X1 != X2
| ~ r1(X2) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X40,X41] :
( ~ r2(X40,X41)
| ! [X42] :
( X41 != X42
| ~ r1(X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f895,plain,
! [X0,X1] :
( r1(X0)
| ~ r1(X1)
| ~ r2(X1,X0) ),
inference(superposition,[],[f432,f468]) ).
fof(f468,plain,
! [X0,X1] :
( sK0(X0) = X0
| ~ r1(X1)
| ~ r2(X1,X0) ),
inference(subsumption_resolution,[],[f462,f142]) ).
fof(f142,plain,
! [X0] :
( sK0(X0) = X0
| ~ r1(X0) ),
inference(resolution,[],[f138,f111]) ).
fof(f138,plain,
! [X0] :
( r2(sK2(X0),X0)
| sK0(X0) = X0 ),
inference(duplicate_literal_removal,[],[f136]) ).
fof(f136,plain,
! [X0] :
( r2(sK2(X0),X0)
| sK0(X0) = X0
| sK0(X0) = X0 ),
inference(superposition,[],[f65,f66]) ).
fof(f66,plain,
! [X0] :
( sK1(X0) = X0
| sK0(X0) = X0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0] :
( ( sK0(X0) = X0
& r1(sK0(X0)) )
| ( sK1(X0) = X0
& r2(sK2(X0),sK1(X0))
& r2(sK3(X0),sK2(X0))
& r1(sK3(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f25,f29,f28,f27,f26]) ).
fof(f26,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& r1(X1) )
=> ( sK0(X0) = X0
& r1(sK0(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0] :
( ? [X2] :
( X0 = X2
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) ) )
=> ( sK1(X0) = X0
& ? [X3] :
( r2(X3,sK1(X0))
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
! [X0] :
( ? [X3] :
( r2(X3,sK1(X0))
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) )
=> ( r2(sK2(X0),sK1(X0))
& ? [X4] :
( r2(X4,sK2(X0))
& r1(X4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0] :
( ? [X4] :
( r2(X4,sK2(X0))
& r1(X4) )
=> ( r2(sK3(X0),sK2(X0))
& r1(sK3(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& r1(X1) )
| ? [X2] :
( X0 = X2
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) ) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
~ ? [X0] :
( ! [X1] :
( X0 != X1
| ~ r1(X1) )
& ! [X2] :
( X0 != X2
| ! [X3] :
( ~ r2(X3,X2)
| ! [X4] :
( ~ r2(X4,X3)
| ~ r1(X4) ) ) ) ),
inference(rectify,[],[f13]) ).
fof(f13,negated_conjecture,
~ ? [X38] :
( ! [X16] :
( X16 != X38
| ~ r1(X16) )
& ! [X21] :
( X21 != X38
| ! [X22] :
( ~ r2(X22,X21)
| ! [X15] :
( ~ r2(X15,X22)
| ~ r1(X15) ) ) ) ),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
? [X38] :
( ! [X16] :
( X16 != X38
| ~ r1(X16) )
& ! [X21] :
( X21 != X38
| ! [X22] :
( ~ r2(X22,X21)
| ! [X15] :
( ~ r2(X15,X22)
| ~ r1(X15) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f65,plain,
! [X0] :
( r2(sK2(X0),sK1(X0))
| sK0(X0) = X0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f462,plain,
! [X0,X1] :
( ~ r1(X1)
| r1(X0)
| sK0(X0) = X0
| ~ r2(X1,X0) ),
inference(superposition,[],[f435,f141]) ).
fof(f141,plain,
! [X0,X1] :
( sK2(X0) = X1
| sK0(X0) = X0
| ~ r2(X1,X0) ),
inference(resolution,[],[f138,f112]) ).
fof(f112,plain,
! [X3,X0,X1] :
( ~ r2(X1,X3)
| X0 = X1
| ~ r2(X0,X3) ),
inference(equality_resolution,[],[f83]) ).
fof(f83,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ r2(X1,X2)
| X2 != X3
| ~ r2(X0,X3) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( X0 = X1
| ! [X2] :
( ~ r2(X1,X2)
| ! [X3] :
( X2 != X3
| ~ r2(X0,X3) ) ) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X25,X26] :
( X25 = X26
| ! [X27] :
( ~ r2(X26,X27)
| ! [X28] :
( X27 != X28
| ~ r2(X25,X28) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f435,plain,
! [X0] :
( ~ r1(sK2(X0))
| r1(X0) ),
inference(superposition,[],[f432,f131]) ).
fof(f131,plain,
! [X0] :
( sK0(X0) = X0
| ~ r1(sK2(X0)) ),
inference(resolution,[],[f64,f111]) ).
fof(f64,plain,
! [X0] :
( r2(sK3(X0),sK2(X0))
| sK0(X0) = X0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f432,plain,
! [X0] : r1(sK0(X0)),
inference(subsumption_resolution,[],[f427,f120]) ).
fof(f120,plain,
! [X0] :
( ~ r1(sK2(X0))
| r1(sK0(X0)) ),
inference(resolution,[],[f60,f111]) ).
fof(f60,plain,
! [X0] :
( r2(sK3(X0),sK2(X0))
| r1(sK0(X0)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f427,plain,
! [X0] :
( r1(sK2(X0))
| r1(sK0(X0)) ),
inference(duplicate_literal_removal,[],[f425]) ).
fof(f425,plain,
! [X0] :
( r1(sK2(X0))
| r1(sK0(X0))
| r1(sK0(X0)) ),
inference(superposition,[],[f193,f318]) ).
fof(f318,plain,
! [X0] :
( sK2(X0) = sK0(sK2(X0))
| r1(sK0(X0)) ),
inference(subsumption_resolution,[],[f316,f131]) ).
fof(f316,plain,
! [X0] :
( r1(sK2(sK2(X0)))
| r1(sK0(X0))
| sK2(X0) = sK0(sK2(X0)) ),
inference(duplicate_literal_removal,[],[f315]) ).
fof(f315,plain,
! [X0] :
( r1(sK2(sK2(X0)))
| r1(sK0(X0))
| r1(sK0(X0))
| sK2(X0) = sK0(sK2(X0)) ),
inference(superposition,[],[f59,f143]) ).
fof(f143,plain,
! [X0] :
( sK3(X0) = sK2(sK2(X0))
| r1(sK0(X0))
| sK2(X0) = sK0(sK2(X0)) ),
inference(resolution,[],[f119,f138]) ).
fof(f119,plain,
! [X0,X1] :
( ~ r2(X1,sK2(X0))
| sK3(X0) = X1
| r1(sK0(X0)) ),
inference(resolution,[],[f60,f112]) ).
fof(f59,plain,
! [X0] :
( r1(sK3(X0))
| r1(sK0(X0)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f193,plain,
! [X0] :
( r1(sK0(sK2(X0)))
| r1(sK0(X0)) ),
inference(subsumption_resolution,[],[f187,f59]) ).
fof(f187,plain,
! [X0] :
( r1(sK0(sK2(X0)))
| ~ r1(sK3(X0))
| r1(sK0(X0)) ),
inference(resolution,[],[f168,f60]) ).
fof(f168,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| r1(sK0(X0))
| ~ r1(X1) ),
inference(duplicate_literal_removal,[],[f164]) ).
fof(f164,plain,
! [X0,X1] :
( ~ r1(X1)
| r1(sK0(X0))
| r1(sK0(X0))
| ~ r2(X1,X0) ),
inference(superposition,[],[f120,f132]) ).
fof(f132,plain,
! [X0,X1] :
( sK2(X0) = X1
| r1(sK0(X0))
| ~ r2(X1,X0) ),
inference(resolution,[],[f124,f112]) ).
fof(f124,plain,
! [X0] :
( r2(sK2(X0),X0)
| r1(sK0(X0)) ),
inference(duplicate_literal_removal,[],[f123]) ).
fof(f123,plain,
! [X0] :
( r2(sK2(X0),X0)
| r1(sK0(X0))
| r1(sK0(X0)) ),
inference(superposition,[],[f61,f62]) ).
fof(f62,plain,
! [X0] :
( sK1(X0) = X0
| r1(sK0(X0)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f61,plain,
! [X0] :
( r2(sK2(X0),sK1(X0))
| r1(sK0(X0)) ),
inference(cnf_transformation,[],[f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUN066+2 : TPTP v8.2.0. Released v7.3.0.
% 0.03/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Jun 18 21:26:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.12/0.35 Running first-order theorem proving
% 0.12/0.36 Running /export/starexec/sandbox/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.42 % (2259)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (2263)lrs+21_2461:262144_anc=none:drc=off:sil=2000:sp=occurrence:nwc=6.0:updr=off:st=3.0:i=109:sd=2:afp=4000:erml=3:nm=14:afq=2.0:uhcvi=on:ss=included:er=filter:abs=on:nicw=on:ile=on:sims=off:s2a=on:s2agt=50:s2at=-1.0:plsq=on:plsql=on:plsqc=2:plsqr=1,32:newcnf=on:bd=off:to=lpo_0 on theBenchmark for (2999ds/109Mi)
% 0.21/0.42 % (2259)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (2264)lrs-1011_37821:262144_bsr=unit_only:sil=2000:fde=none:plsq=on:plsqr=43543,131072:bce=on:rnwc=on:plsql=on:rp=on:nwc=10.0:newcnf=on:i=109:awrs=decay:awrsf=10:ep=R:mep=off:amm=sco_0 on theBenchmark for (2999ds/109Mi)
% 0.21/0.42 % (2259)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (2260)ott+4_40_av=off:bce=on:fsd=off:fde=unused:nm=4:nwc=1.1:sos=all:sp=frequency:i=69040_0 on theBenchmark for (2999ds/69040Mi)
% 0.21/0.42 % (2259)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (2265)ott-1011_16:1_sil=2000:sp=const_max:urr=on:lsd=20:st=3.0:i=117:ss=axioms:gsp=on:rp=on:sos=on:fd=off:aac=none_0 on theBenchmark for (2999ds/117Mi)
% 0.21/0.42 % (2259)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (2262)dis+1011_1:99_anc=none:fde=unused:plsqc=2:bsd=on:plsq=on:plsqr=109,504:sp=reverse_frequency:spb=intro:rp=on:alpa=random:s2a=on:i=257151:s2at=-1.0:aac=none:nm=16:rawr=on:sil=256000:acc=model_0 on theBenchmark for (2999ds/257151Mi)
% 0.21/0.42 % (2259)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (2261)lrs+1011_8:1_sil=128000:tgt=ground:fde=unused:sp=frequency:nwc=5.0:lwlo=on:i=105338:awrs=converge:awrsf=1385:av=off_0 on theBenchmark for (2999ds/105338Mi)
% 0.21/0.42 % (2259)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (2266)lrs+1010_1:1_to=lpo:sil=2000:sos=on:fd=off:i=117:bd=off_0 on theBenchmark for (2999ds/117Mi)
% 0.21/0.42 % (2264)Refutation not found, incomplete strategy% (2264)------------------------------
% 0.21/0.42 % (2264)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.21/0.42 % (2264)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.21/0.42 % (2264)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.42
% 0.21/0.42 % (2264)Memory used [KB]: 1165
% 0.21/0.42 % (2264)Time elapsed: 0.004 s
% 0.21/0.42 % (2264)Instructions burned: 3 (million)
% 0.21/0.42 % (2264)------------------------------
% 0.21/0.42 % (2264)------------------------------
% 0.21/0.44 % (2266)First to succeed.
% 0.21/0.44 % (2266)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2259"
% 0.21/0.44 % (2259)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.44 % (2266)Refutation found. Thanks to Tanya!
% 0.21/0.44 % SZS status Theorem for theBenchmark
% 0.21/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.44 % (2266)------------------------------
% 0.21/0.44 % (2266)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.21/0.44 % (2266)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.21/0.44 % (2266)Termination reason: Refutation
% 0.21/0.44
% 0.21/0.44 % (2266)Memory used [KB]: 1213
% 0.21/0.44 % (2266)Time elapsed: 0.019 s
% 0.21/0.44 % (2266)Instructions burned: 31 (million)
% 0.21/0.44 % (2266)------------------------------
% 0.21/0.44 % (2266)------------------------------
% 0.21/0.44 % (2259)Success in time 0.08 s
%------------------------------------------------------------------------------