TSTP Solution File: NUN068+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUN068+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 : n019.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 08:45:02 EDT 2024
% Result : Theorem 0.16s 0.36s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 8 unt; 0 def)
% Number of atoms : 185 ( 76 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 197 ( 76 ~; 74 |; 42 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 117 ( 94 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f950,plain,
$false,
inference(subsumption_resolution,[],[f852,f116]) ).
fof(f116,plain,
r1(sK23),
inference(equality_resolution,[],[f104]) ).
fof(f104,plain,
! [X1] :
( r1(X1)
| sK23 != X1 ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X1] :
( ( sK23 = X1
& r1(X1) )
| ( sK23 != X1
& ~ r1(X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f1,f61]) ).
fof(f61,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/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f852,plain,
~ r1(sK23),
inference(superposition,[],[f131,f766]) ).
fof(f766,plain,
! [X0] : sK23 = X0,
inference(subsumption_resolution,[],[f765,f729]) ).
fof(f729,plain,
! [X0] :
( ~ sP0(sK12(X0))
| sK23 = X0 ),
inference(resolution,[],[f697,f177]) ).
fof(f177,plain,
! [X0] :
( r2(sK23,sK12(X0))
| ~ sP0(sK12(X0)) ),
inference(forward_demodulation,[],[f175,f145]) ).
fof(f145,plain,
! [X0] : sK12(X0) = sK1(sK12(X0)),
inference(resolution,[],[f143,f131]) ).
fof(f143,plain,
! [X0] :
( r1(X0)
| sK1(X0) = X0 ),
inference(subsumption_resolution,[],[f142,f65]) ).
fof(f65,plain,
! [X0] :
( ~ sP0(X0)
| sK1(X0) = X0 ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0] :
( ( sK1(X0) = X0
& r2(sK2(X0),sK1(X0))
& r1(sK2(X0)) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f29,f31,f30]) ).
fof(f30,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r2(X2,X1)
& r1(X2) ) )
=> ( sK1(X0) = X0
& ? [X2] :
( r2(X2,sK1(X0))
& r1(X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0] :
( ? [X2] :
( r2(X2,sK1(X0))
& r1(X2) )
=> ( r2(sK2(X0),sK1(X0))
& r1(sK2(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r2(X2,X1)
& r1(X2) ) )
| ~ sP0(X0) ),
inference(rectify,[],[f28]) ).
fof(f28,plain,
! [X0] :
( ? [X2] :
( X0 = X2
& ? [X3] :
( r2(X3,X2)
& r1(X3) ) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0] :
( ? [X2] :
( X0 = X2
& ? [X3] :
( r2(X3,X2)
& r1(X3) ) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f142,plain,
! [X0] :
( r1(X0)
| sP0(X0)
| sK1(X0) = X0 ),
inference(superposition,[],[f66,f135]) ).
fof(f135,plain,
! [X0] :
( sK3(X0) = X0
| sK1(X0) = X0 ),
inference(resolution,[],[f65,f67]) ).
fof(f67,plain,
! [X0] :
( sP0(X0)
| sK3(X0) = X0 ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0] :
( ( sK3(X0) = X0
& r1(sK3(X0)) )
| sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f27,f33]) ).
fof(f33,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& r1(X1) )
=> ( sK3(X0) = X0
& r1(sK3(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& r1(X1) )
| sP0(X0) ),
inference(definition_folding,[],[f25,f26]) ).
fof(f25,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& r1(X1) )
| ? [X2] :
( X0 = X2
& ? [X3] :
( r2(X3,X2)
& r1(X3) ) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
~ ? [X0] :
( ! [X1] :
( X0 != X1
| ~ r1(X1) )
& ! [X2] :
( X0 != X2
| ! [X3] :
( ~ r2(X3,X2)
| ~ r1(X3) ) ) ),
inference(rectify,[],[f13]) ).
fof(f13,negated_conjecture,
~ ? [X38] :
( ! [X15] :
( X15 != X38
| ~ r1(X15) )
& ! [X21] :
( X21 != X38
| ! [X22] :
( ~ r2(X22,X21)
| ~ r1(X22) ) ) ),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
? [X38] :
( ! [X15] :
( X15 != X38
| ~ r1(X15) )
& ! [X21] :
( X21 != X38
| ! [X22] :
( ~ r2(X22,X21)
| ~ r1(X22) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonzerosnononesexist) ).
fof(f66,plain,
! [X0] :
( r1(sK3(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f175,plain,
! [X0] :
( r2(sK23,sK1(sK12(X0)))
| ~ sP0(sK12(X0)) ),
inference(superposition,[],[f64,f172]) ).
fof(f172,plain,
! [X0] : sK23 = sK2(sK12(X0)),
inference(resolution,[],[f169,f131]) ).
fof(f169,plain,
! [X0] :
( r1(X0)
| sK2(X0) = sK23 ),
inference(subsumption_resolution,[],[f166,f118]) ).
fof(f118,plain,
! [X0] :
( ~ sP0(X0)
| sK2(X0) = sK23 ),
inference(resolution,[],[f105,f63]) ).
fof(f63,plain,
! [X0] :
( r1(sK2(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f105,plain,
! [X1] :
( ~ r1(X1)
| sK23 = X1 ),
inference(cnf_transformation,[],[f62]) ).
fof(f166,plain,
! [X0] :
( r1(X0)
| sP0(X0)
| sK2(X0) = sK23 ),
inference(superposition,[],[f66,f141]) ).
fof(f141,plain,
! [X0] :
( sK3(X0) = X0
| sK2(X0) = sK23 ),
inference(resolution,[],[f118,f67]) ).
fof(f64,plain,
! [X0] :
( r2(sK2(X0),sK1(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f697,plain,
! [X0,X1] :
( ~ r2(X0,sK12(X1))
| X0 = X1 ),
inference(resolution,[],[f110,f108]) ).
fof(f108,plain,
! [X0] : r2(X0,sK12(X0)),
inference(equality_resolution,[],[f80]) ).
fof(f80,plain,
! [X2,X0] :
( r2(X0,X2)
| sK12(X0) != X2 ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X2] :
( ( sK12(X0) = X2
& r2(X0,X2) )
| ( sK12(X0) != X2
& ~ r2(X0,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f18,f45]) ).
fof(f45,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/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f110,plain,
! [X3,X0,X1] :
( ~ r2(X1,X3)
| X0 = X1
| ~ r2(X0,X3) ),
inference(equality_resolution,[],[f84]) ).
fof(f84,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(f765,plain,
! [X0] :
( sP0(sK12(X0))
| sK23 = X0 ),
inference(subsumption_resolution,[],[f760,f131]) ).
fof(f760,plain,
! [X0] :
( r1(sK12(X0))
| sP0(sK12(X0))
| sK23 = X0 ),
inference(superposition,[],[f66,f727]) ).
fof(f727,plain,
! [X0] :
( sK12(X0) = sK3(sK12(X0))
| sK23 = X0 ),
inference(resolution,[],[f697,f576]) ).
fof(f576,plain,
! [X0] :
( r2(sK23,sK12(X0))
| sK12(X0) = sK3(sK12(X0)) ),
inference(forward_demodulation,[],[f564,f172]) ).
fof(f564,plain,
! [X0] :
( r2(sK2(sK12(X0)),sK12(X0))
| sK12(X0) = sK3(sK12(X0)) ),
inference(superposition,[],[f530,f145]) ).
fof(f530,plain,
! [X0] :
( r2(sK2(X0),sK1(X0))
| sK3(X0) = X0 ),
inference(superposition,[],[f108,f429]) ).
fof(f429,plain,
! [X0] :
( sK1(X0) = sK12(sK2(X0))
| sK3(X0) = X0 ),
inference(resolution,[],[f215,f67]) ).
fof(f215,plain,
! [X0] :
( ~ sP0(X0)
| sK1(X0) = sK12(sK2(X0)) ),
inference(resolution,[],[f81,f64]) ).
fof(f81,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| sK12(X0) = X2 ),
inference(cnf_transformation,[],[f46]) ).
fof(f131,plain,
! [X0] : ~ r1(sK12(X0)),
inference(resolution,[],[f109,f108]) ).
fof(f109,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) ),
inference(equality_resolution,[],[f83]) ).
fof(f83,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) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUN068+2 : TPTP v8.1.2. Released v7.3.0.
% 0.10/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n019.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri May 3 18:53:53 EDT 2024
% 0.16/0.32 % CPUTime :
% 0.16/0.32 % (413)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.33 % (416)WARNING: value z3 for option sas not known
% 0.16/0.33 % (420)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)
% 0.16/0.33 % (416)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)
% 0.16/0.34 % (417)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.34 % (414)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.34 % (418)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)
% 0.16/0.34 % (415)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.34 % (419)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)
% 0.16/0.34 TRYING [1]
% 0.16/0.34 TRYING [2]
% 0.16/0.34 TRYING [3]
% 0.16/0.34 TRYING [1]
% 0.16/0.34 TRYING [4]
% 0.16/0.34 TRYING [2]
% 0.16/0.35 TRYING [3]
% 0.16/0.35 TRYING [5]
% 0.16/0.36 % (416)First to succeed.
% 0.16/0.36 % (420)Also succeeded, but the first one will report.
% 0.16/0.36 % (416)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-413"
% 0.16/0.36 % (416)Refutation found. Thanks to Tanya!
% 0.16/0.36 % SZS status Theorem for theBenchmark
% 0.16/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.36 % (416)------------------------------
% 0.16/0.36 % (416)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.36 % (416)Termination reason: Refutation
% 0.16/0.36
% 0.16/0.36 % (416)Memory used [KB]: 1115
% 0.16/0.36 % (416)Time elapsed: 0.025 s
% 0.16/0.36 % (416)Instructions burned: 43 (million)
% 0.16/0.36 % (413)Success in time 0.04 s
%------------------------------------------------------------------------------