TSTP Solution File: NUN066+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUN066+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.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 : Tue Apr 30 14:40:19 EDT 2024
% Result : Theorem 0.22s 0.41s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 12
% Syntax : Number of formulae : 77 ( 13 unt; 0 def)
% Number of atoms : 221 ( 89 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 238 ( 94 ~; 85 |; 53 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 163 ( 131 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1249,plain,
$false,
inference(resolution,[],[f1209,f1187]) ).
fof(f1187,plain,
! [X2,X1] : r2(X2,X1),
inference(superposition,[],[f943,f1169]) ).
fof(f1169,plain,
! [X0,X1] : X0 = X1,
inference(resolution,[],[f1128,f943]) ).
fof(f1128,plain,
! [X2,X0,X1] :
( ~ r2(X2,sK13(X1))
| X0 = X2 ),
inference(resolution,[],[f112,f943]) ).
fof(f112,plain,
! [X3,X0,X1] :
( ~ r2(X1,X3)
| ~ r2(X0,X3)
| X0 = X1 ),
inference(equality_resolution,[],[f86]) ).
fof(f86,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/sandbox2/benchmark/theBenchmark.p',axiom_3a) ).
fof(f943,plain,
! [X0,X1] : r2(X0,sK13(X1)),
inference(superposition,[],[f110,f916]) ).
fof(f916,plain,
! [X0,X1] : sK13(X0) = sK13(X1),
inference(superposition,[],[f903,f903]) ).
fof(f903,plain,
! [X0] : sK13(X0) = sK13(sK13(sK24)),
inference(resolution,[],[f899,f110]) ).
fof(f899,plain,
! [X0,X1] :
( ~ r2(X1,sK13(X0))
| sK13(X0) = sK13(sK13(sK24)) ),
inference(duplicate_literal_removal,[],[f887]) ).
fof(f887,plain,
! [X0,X1] :
( ~ r2(X1,sK13(X0))
| sK13(X0) = sK13(sK13(sK24))
| sK13(X0) = sK13(sK13(sK24)) ),
inference(superposition,[],[f816,f818]) ).
fof(f818,plain,
! [X0] :
( sK13(X0) = sK4(sK13(X0))
| sK13(X0) = sK13(sK13(sK24)) ),
inference(backward_demodulation,[],[f338,f802]) ).
fof(f802,plain,
! [X0] : sK2(sK13(X0)) = sK13(sK24),
inference(resolution,[],[f798,f110]) ).
fof(f798,plain,
! [X0,X1] :
( ~ r2(X1,sK13(X0))
| sK2(sK13(X0)) = sK13(sK24) ),
inference(duplicate_literal_removal,[],[f786]) ).
fof(f786,plain,
! [X0,X1] :
( ~ r2(X1,sK13(X0))
| sK2(sK13(X0)) = sK13(sK24)
| sK2(sK13(X0)) = sK13(sK24) ),
inference(superposition,[],[f317,f319]) ).
fof(f319,plain,
! [X0] :
( sK13(X0) = sK4(sK13(X0))
| sK2(sK13(X0)) = sK13(sK24) ),
inference(resolution,[],[f294,f69]) ).
fof(f69,plain,
! [X0] :
( sP0(X0)
| sK4(X0) = X0 ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0] :
( ( sK4(X0) = X0
& r1(sK4(X0)) )
| sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f27,f34]) ).
fof(f34,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& r1(X1) )
=> ( sK4(X0) = X0
& r1(sK4(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& r1(X1) )
| sP0(X0) ),
inference(definition_folding,[],[f25,f26]) ).
fof(f26,plain,
! [X0] :
( ? [X2] :
( X0 = X2
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) ) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
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/sandbox2/benchmark/theBenchmark.p',nonzerononetwoexist) ).
fof(f294,plain,
! [X0] :
( ~ sP0(sK13(X0))
| sK2(sK13(X0)) = sK13(sK24) ),
inference(resolution,[],[f83,f188]) ).
fof(f188,plain,
! [X0] :
( r2(sK24,sK2(sK13(X0)))
| ~ sP0(sK13(X0)) ),
inference(superposition,[],[f65,f180]) ).
fof(f180,plain,
! [X0] : sK24 = sK3(sK13(X0)),
inference(resolution,[],[f178,f110]) ).
fof(f178,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| sK3(X0) = sK24 ),
inference(duplicate_literal_removal,[],[f175]) ).
fof(f175,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| sK3(X0) = sK24
| sK3(X0) = sK24 ),
inference(superposition,[],[f159,f161]) ).
fof(f161,plain,
! [X0] :
( sK4(X0) = X0
| sK3(X0) = sK24 ),
inference(resolution,[],[f123,f69]) ).
fof(f123,plain,
! [X0] :
( ~ sP0(X0)
| sK3(X0) = sK24 ),
inference(resolution,[],[f107,f64]) ).
fof(f64,plain,
! [X0] :
( r1(sK3(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0] :
( ( sK1(X0) = X0
& r2(sK2(X0),sK1(X0))
& r2(sK3(X0),sK2(X0))
& r1(sK3(X0)) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f29,f32,f31,f30]) ).
fof(f30,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r2(X3,X2)
& r1(X3) ) ) )
=> ( sK1(X0) = X0
& ? [X2] :
( r2(X2,sK1(X0))
& ? [X3] :
( r2(X3,X2)
& r1(X3) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0] :
( ? [X2] :
( r2(X2,sK1(X0))
& ? [X3] :
( r2(X3,X2)
& r1(X3) ) )
=> ( r2(sK2(X0),sK1(X0))
& ? [X3] :
( r2(X3,sK2(X0))
& r1(X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
! [X0] :
( ? [X3] :
( r2(X3,sK2(X0))
& r1(X3) )
=> ( r2(sK3(X0),sK2(X0))
& r1(sK3(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r2(X3,X2)
& r1(X3) ) ) )
| ~ sP0(X0) ),
inference(rectify,[],[f28]) ).
fof(f28,plain,
! [X0] :
( ? [X2] :
( X0 = X2
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) ) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f26]) ).
fof(f107,plain,
! [X1] :
( ~ r1(X1)
| sK24 = X1 ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X1] :
( ( sK24 = X1
& r1(X1) )
| ( sK24 != X1
& ~ r1(X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f1,f62]) ).
fof(f62,plain,
( ? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| ( X0 != X1
& ~ r1(X1) ) )
=> ! [X1] :
( ( sK24 = X1
& r1(X1) )
| ( sK24 != X1
& ~ r1(X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1,axiom,
? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| ( X0 != X1
& ~ r1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f159,plain,
! [X0,X1] :
( ~ r2(X1,sK4(X0))
| sK3(X0) = sK24 ),
inference(resolution,[],[f123,f137]) ).
fof(f137,plain,
! [X0,X1] :
( sP0(X1)
| ~ r2(X0,sK4(X1)) ),
inference(resolution,[],[f111,f68]) ).
fof(f68,plain,
! [X0] :
( r1(sK4(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f111,plain,
! [X2,X0] :
( ~ r1(X2)
| ~ r2(X0,X2) ),
inference(equality_resolution,[],[f85]) ).
fof(f85,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/sandbox2/benchmark/theBenchmark.p',axiom_7a) ).
fof(f65,plain,
! [X0] :
( r2(sK3(X0),sK2(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f83,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| sK13(X0) = X2 ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X2] :
( ( sK13(X0) = X2
& r2(X0,X2) )
| ( sK13(X0) != X2
& ~ r2(X0,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f18,f46]) ).
fof(f46,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( X1 = X2
& r2(X0,X2) )
| ( X1 != X2
& ~ r2(X0,X2) ) )
=> ! [X2] :
( ( sK13(X0) = X2
& r2(X0,X2) )
| ( sK13(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/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f317,plain,
! [X0,X1] :
( ~ r2(X1,sK4(sK13(X0)))
| sK2(sK13(X0)) = sK13(sK24) ),
inference(resolution,[],[f294,f137]) ).
fof(f338,plain,
! [X0] :
( sK13(X0) = sK13(sK2(sK13(X0)))
| sK13(X0) = sK4(sK13(X0)) ),
inference(resolution,[],[f291,f69]) ).
fof(f291,plain,
! [X0] :
( ~ sP0(sK13(X0))
| sK13(X0) = sK13(sK2(sK13(X0))) ),
inference(resolution,[],[f83,f216]) ).
fof(f216,plain,
! [X0] :
( r2(sK2(sK13(X0)),sK13(X0))
| ~ sP0(sK13(X0)) ),
inference(superposition,[],[f66,f145]) ).
fof(f145,plain,
! [X0] : sK13(X0) = sK1(sK13(X0)),
inference(resolution,[],[f144,f110]) ).
fof(f144,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| sK1(X0) = X0 ),
inference(duplicate_literal_removal,[],[f143]) ).
fof(f143,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| sK1(X0) = X0
| sK1(X0) = X0 ),
inference(superposition,[],[f139,f141]) ).
fof(f141,plain,
! [X0] :
( sK4(X0) = X0
| sK1(X0) = X0 ),
inference(resolution,[],[f67,f69]) ).
fof(f67,plain,
! [X0] :
( ~ sP0(X0)
| sK1(X0) = X0 ),
inference(cnf_transformation,[],[f33]) ).
fof(f139,plain,
! [X0,X1] :
( ~ r2(X1,sK4(X0))
| sK1(X0) = X0 ),
inference(resolution,[],[f67,f137]) ).
fof(f66,plain,
! [X0] :
( r2(sK2(X0),sK1(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f816,plain,
! [X0,X1] :
( ~ r2(X1,sK4(sK13(X0)))
| sK13(X0) = sK13(sK13(sK24)) ),
inference(backward_demodulation,[],[f336,f802]) ).
fof(f336,plain,
! [X0,X1] :
( sK13(X0) = sK13(sK2(sK13(X0)))
| ~ r2(X1,sK4(sK13(X0))) ),
inference(resolution,[],[f291,f137]) ).
fof(f110,plain,
! [X0] : r2(X0,sK13(X0)),
inference(equality_resolution,[],[f82]) ).
fof(f82,plain,
! [X2,X0] :
( r2(X0,X2)
| sK13(X0) != X2 ),
inference(cnf_transformation,[],[f47]) ).
fof(f1209,plain,
! [X0,X1] : ~ r2(X1,X0),
inference(superposition,[],[f138,f1169]) ).
fof(f138,plain,
! [X0] : ~ r2(X0,sK24),
inference(resolution,[],[f111,f118]) ).
fof(f118,plain,
r1(sK24),
inference(equality_resolution,[],[f106]) ).
fof(f106,plain,
! [X1] :
( r1(X1)
| sK24 != X1 ),
inference(cnf_transformation,[],[f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUN066+2 : TPTP v8.1.2. Released v7.3.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n023.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 : Tue Apr 30 02:45:10 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (15452)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (15456)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (15455)WARNING: value z3 for option sas not known
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.14/0.37 % (15453)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (15457)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 % (15455)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 % (15459)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 % (15458)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 % (15454)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 TRYING [3]
% 0.14/0.38 TRYING [4]
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [2]
% 0.22/0.39 TRYING [5]
% 0.22/0.39 TRYING [3]
% 0.22/0.40 TRYING [6]
% 0.22/0.41 % (15458)First to succeed.
% 0.22/0.41 % (15458)Refutation found. Thanks to Tanya!
% 0.22/0.41 % SZS status Theorem for theBenchmark
% 0.22/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.41 % (15458)------------------------------
% 0.22/0.41 % (15458)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.41 % (15458)Termination reason: Refutation
% 0.22/0.41
% 0.22/0.41 % (15458)Memory used [KB]: 1108
% 0.22/0.41 % (15458)Time elapsed: 0.036 s
% 0.22/0.41 % (15458)Instructions burned: 60 (million)
% 0.22/0.41 % (15458)------------------------------
% 0.22/0.41 % (15458)------------------------------
% 0.22/0.41 % (15452)Success in time 0.053 s
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