TSTP Solution File: NUM504+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM504+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n014.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 : Thu Aug 31 12:10:18 EDT 2023
% Result : ContradictoryAxioms 5.71s 1.16s
% Output : Refutation 5.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 57 ( 16 unt; 0 def)
% Number of atoms : 251 ( 98 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 325 ( 131 ~; 125 |; 55 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 56 (; 52 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46774,plain,
$false,
inference(subsumption_resolution,[],[f46717,f252]) ).
fof(f252,plain,
~ isPrime0(sz00),
inference(subsumption_resolution,[],[f240,f170]) ).
fof(f170,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/tmp/tmp.UGvEtojo5u/Vampire---4.8_23146',mSortsC) ).
fof(f240,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f184]) ).
fof(f184,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0] :
( ( ( isPrime0(X0)
| ( sK0(X0) != X0
& sz10 != sK0(X0)
& doDivides0(sK0(X0),X0)
& aNaturalNumber0(sK0(X0)) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f126,f127]) ).
fof(f127,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( sK0(X0) != X0
& sz10 != sK0(X0)
& doDivides0(sK0(X0),X0)
& aNaturalNumber0(sK0(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f126,plain,
! [X0] :
( ( ( isPrime0(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ( ( isPrime0(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f124]) ).
fof(f124,plain,
! [X0] :
( ( ( isPrime0(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( ! [X1] :
( ( doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( X0 = X1
| sz10 = X1 ) )
& sz10 != X0
& sz00 != X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UGvEtojo5u/Vampire---4.8_23146',mDefPrime) ).
fof(f46717,plain,
isPrime0(sz00),
inference(superposition,[],[f147,f46712]) ).
fof(f46712,plain,
sz00 = xp,
inference(subsumption_resolution,[],[f46711,f152]) ).
fof(f152,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/tmp/tmp.UGvEtojo5u/Vampire---4.8_23146',m__1837) ).
fof(f46711,plain,
( sz00 = xp
| ~ aNaturalNumber0(xn) ),
inference(subsumption_resolution,[],[f46710,f153]) ).
fof(f153,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f46710,plain,
( sz00 = xp
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f46709,f195]) ).
fof(f195,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.UGvEtojo5u/Vampire---4.8_23146',mSortsB_02) ).
fof(f46709,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xp ),
inference(subsumption_resolution,[],[f46708,f154]) ).
fof(f154,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f46708,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xp
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f46705,f153]) ).
fof(f46705,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xp
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f46357,f195]) ).
fof(f46357,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xp ),
inference(subsumption_resolution,[],[f46355,f164]) ).
fof(f164,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f51]) ).
fof(f51,axiom,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
file('/export/starexec/sandbox/tmp/tmp.UGvEtojo5u/Vampire---4.8_23146',m__2414) ).
fof(f46355,plain,
( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xp ),
inference(duplicate_literal_removal,[],[f46352]) ).
fof(f46352,plain,
( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[],[f551,f5792]) ).
fof(f5792,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(subsumption_resolution,[],[f5791,f154]) ).
fof(f5791,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(subsumption_resolution,[],[f5711,f148]) ).
fof(f148,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox/tmp/tmp.UGvEtojo5u/Vampire---4.8_23146',m__1860) ).
fof(f5711,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f246,f146]) ).
fof(f146,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/tmp/tmp.UGvEtojo5u/Vampire---4.8_23146',m__2306) ).
fof(f246,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f214]) ).
fof(f214,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f133]) ).
fof(f133,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f96]) ).
fof(f96,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& sz00 != X0 )
=> ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UGvEtojo5u/Vampire---4.8_23146',mDefQuot) ).
fof(f551,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(subsumption_resolution,[],[f527,f165]) ).
fof(f165,plain,
sdtasdt0(xp,xm) != sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f51]) ).
fof(f527,plain,
( sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(resolution,[],[f217,f166]) ).
fof(f166,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
inference(cnf_transformation,[],[f51]) ).
fof(f217,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.UGvEtojo5u/Vampire---4.8_23146',mLEAsym) ).
fof(f147,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM504+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 13:33:48 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a FOF_CAX_RFO_SEQ problem
% 0.14/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.UGvEtojo5u/Vampire---4.8_23146
% 0.14/0.36 % (23318)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (23322)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.21/0.42 % (23324)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.21/0.42 % (23320)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.21/0.42 % (23321)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.21/0.42 % (23323)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.21/0.43 % (23325)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.21/0.43 % (23319)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 5.08/1.16 % (23319)First to succeed.
% 5.71/1.16 % (23319)Refutation found. Thanks to Tanya!
% 5.71/1.16 % SZS status ContradictoryAxioms for Vampire---4
% 5.71/1.16 % SZS output start Proof for Vampire---4
% See solution above
% 5.71/1.16 % (23319)------------------------------
% 5.71/1.16 % (23319)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 5.71/1.16 % (23319)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 5.71/1.16 % (23319)Termination reason: Refutation
% 5.71/1.16
% 5.71/1.16 % (23319)Memory used [KB]: 11641
% 5.71/1.16 % (23319)Time elapsed: 0.736 s
% 5.71/1.16 % (23319)------------------------------
% 5.71/1.16 % (23319)------------------------------
% 5.71/1.16 % (23318)Success in time 0.796 s
% 5.71/1.16 % Vampire---4.8 exiting
%------------------------------------------------------------------------------