TSTP Solution File: NUM429+3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM429+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n008.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 08:26:55 EDT 2024
% Result : Theorem 0.18s 0.35s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 21
% Syntax : Number of formulae : 60 ( 25 unt; 0 def)
% Number of atoms : 162 ( 44 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 153 ( 51 ~; 34 |; 52 &)
% ( 13 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 40 ( 27 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f181,plain,
$false,
inference(avatar_sat_refutation,[],[f125,f130,f135,f140,f145,f150,f155,f160,f164,f169,f175,f179,f180]) ).
fof(f180,plain,
( ~ spl5_5
| ~ spl5_10 ),
inference(avatar_split_clause,[],[f170,f167,f142]) ).
fof(f142,plain,
( spl5_5
<=> aInteger0(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
fof(f167,plain,
( spl5_10
<=> ! [X0] :
( sdtasdt0(xq,X0) != sdtasdt0(xq,sK3)
| ~ aInteger0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).
fof(f170,plain,
( ~ aInteger0(sK3)
| ~ spl5_10 ),
inference(equality_resolution,[],[f168]) ).
fof(f168,plain,
( ! [X0] :
( sdtasdt0(xq,X0) != sdtasdt0(xq,sK3)
| ~ aInteger0(X0) )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f179,plain,
spl5_12,
inference(avatar_split_clause,[],[f120,f177]) ).
fof(f177,plain,
( spl5_12
<=> ! [X0] : ~ sP0(X0,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).
fof(f120,plain,
! [X0] : ~ sP0(X0,sz00),
inference(equality_resolution,[],[f101]) ).
fof(f101,plain,
! [X0,X1] :
( sz00 != X1
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) )
& ( ( sdtasdt0(X1,sK4(X0,X1)) = X0
& aInteger0(sK4(X0,X1))
& sz00 != X1
& aInteger0(X1) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f67,f68]) ).
fof(f68,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X1,X3) = X0
& aInteger0(X3) )
=> ( sdtasdt0(X1,sK4(X0,X1)) = X0
& aInteger0(sK4(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) )
& ( ( ? [X3] :
( sdtasdt0(X1,X3) = X0
& aInteger0(X3) )
& sz00 != X1
& aInteger0(X1) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) )
& ( ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) )
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) )
& ( ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f175,plain,
~ spl5_11,
inference(avatar_split_clause,[],[f75,f172]) ).
fof(f172,plain,
( spl5_11
<=> sz00 = xq ),
introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).
fof(f75,plain,
sz00 != xq,
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
( aInteger0(xc)
& sz00 != xq
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__818) ).
fof(f169,plain,
( spl5_10
| ~ spl5_9 ),
inference(avatar_split_clause,[],[f165,f162,f167]) ).
fof(f162,plain,
( spl5_9
<=> ! [X0] :
( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).
fof(f165,plain,
( ! [X0] :
( sdtasdt0(xq,X0) != sdtasdt0(xq,sK3)
| ~ aInteger0(X0) )
| ~ spl5_9 ),
inference(forward_demodulation,[],[f163,f78]) ).
fof(f78,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sK3),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
( sdteqdtlpzmzozddtrp0(xb,xc,xq)
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& sdtpldt0(xb,smndt0(xc)) = sdtasdt0(xq,sK2)
& aInteger0(sK2)
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sK3)
& aInteger0(sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f26,f62,f61]) ).
fof(f61,plain,
( ? [X0] :
( sdtasdt0(xq,X0) = sdtpldt0(xb,smndt0(xc))
& aInteger0(X0) )
=> ( sdtpldt0(xb,smndt0(xc)) = sdtasdt0(xq,sK2)
& aInteger0(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
( ? [X1] :
( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,X1)
& aInteger0(X1) )
=> ( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sK3)
& aInteger0(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
( sdteqdtlpzmzozddtrp0(xb,xc,xq)
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& ? [X0] :
( sdtasdt0(xq,X0) = sdtpldt0(xb,smndt0(xc))
& aInteger0(X0) )
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& ? [X1] :
( sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,X1)
& aInteger0(X1) ) ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
( sdteqdtlpzmzozddtrp0(xb,xc,xq)
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& ? [X0] :
( sdtasdt0(xq,X0) = sdtpldt0(xb,smndt0(xc))
& aInteger0(X0) )
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& ? [X0] :
( sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__853) ).
fof(f163,plain,
( ! [X0] :
( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X0) )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f164,plain,
spl5_9,
inference(avatar_split_clause,[],[f71,f162]) ).
fof(f71,plain,
! [X0] :
( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0] :
( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,negated_conjecture,
~ ? [X0] :
( sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(X0) ),
inference(negated_conjecture,[],[f24]) ).
fof(f24,conjecture,
? [X0] :
( sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f160,plain,
spl5_8,
inference(avatar_split_clause,[],[f86,f157]) ).
fof(f157,plain,
( spl5_8
<=> aInteger0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).
fof(f86,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(f155,plain,
spl5_7,
inference(avatar_split_clause,[],[f85,f152]) ).
fof(f152,plain,
( spl5_7
<=> aInteger0(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).
fof(f85,plain,
aInteger0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
fof(f150,plain,
spl5_6,
inference(avatar_split_clause,[],[f81,f147]) ).
fof(f147,plain,
( spl5_6
<=> aInteger0(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).
fof(f81,plain,
aInteger0(sK2),
inference(cnf_transformation,[],[f63]) ).
fof(f145,plain,
spl5_5,
inference(avatar_split_clause,[],[f77,f142]) ).
fof(f77,plain,
aInteger0(sK3),
inference(cnf_transformation,[],[f63]) ).
fof(f140,plain,
spl5_4,
inference(avatar_split_clause,[],[f76,f137]) ).
fof(f137,plain,
( spl5_4
<=> aInteger0(xc) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f76,plain,
aInteger0(xc),
inference(cnf_transformation,[],[f22]) ).
fof(f135,plain,
spl5_3,
inference(avatar_split_clause,[],[f74,f132]) ).
fof(f132,plain,
( spl5_3
<=> aInteger0(xq) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f74,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f22]) ).
fof(f130,plain,
spl5_2,
inference(avatar_split_clause,[],[f73,f127]) ).
fof(f127,plain,
( spl5_2
<=> aInteger0(xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f73,plain,
aInteger0(xb),
inference(cnf_transformation,[],[f22]) ).
fof(f125,plain,
spl5_1,
inference(avatar_split_clause,[],[f72,f122]) ).
fof(f122,plain,
( spl5_1
<=> aInteger0(xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f72,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM429+3 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri May 3 14:10:42 EDT 2024
% 0.18/0.33 % CPUTime :
% 0.18/0.33 % (23426)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.35 % (23433)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)
% 0.18/0.35 % (23429)WARNING: value z3 for option sas not known
% 0.18/0.35 % (23427)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.18/0.35 % (23431)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)
% 0.18/0.35 % (23428)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.18/0.35 % (23430)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.18/0.35 % (23432)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)
% 0.18/0.35 % (23429)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)
% 0.18/0.35 TRYING [1]
% 0.18/0.35 % (23431)First to succeed.
% 0.18/0.35 % (23432)Also succeeded, but the first one will report.
% 0.18/0.35 TRYING [1]
% 0.18/0.35 TRYING [2]
% 0.18/0.35 TRYING [2]
% 0.18/0.35 % (23431)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23426"
% 0.18/0.35 % (23431)Refutation found. Thanks to Tanya!
% 0.18/0.35 % SZS status Theorem for theBenchmark
% 0.18/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.35 % (23431)------------------------------
% 0.18/0.35 % (23431)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.18/0.35 % (23431)Termination reason: Refutation
% 0.18/0.35
% 0.18/0.35 % (23431)Memory used [KB]: 854
% 0.18/0.35 % (23431)Time elapsed: 0.004 s
% 0.18/0.35 % (23431)Instructions burned: 6 (million)
% 0.18/0.35 % (23426)Success in time 0.017 s
%------------------------------------------------------------------------------