TSTP Solution File: NUM501+3 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM501+3 : 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 : n012.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 12:10:13 EDT 2023
% Result : Theorem 0.21s 0.53s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 17 unt; 0 def)
% Number of atoms : 230 ( 59 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 278 ( 107 ~; 91 |; 68 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 80 (; 65 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4223,plain,
$false,
inference(subsumption_resolution,[],[f4222,f184]) ).
fof(f184,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox2/tmp/tmp.MXu6MQPhDx/Vampire---4.8_12582',m__2306) ).
fof(f4222,plain,
~ aNaturalNumber0(xk),
inference(subsumption_resolution,[],[f4221,f198]) ).
fof(f198,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/tmp/tmp.MXu6MQPhDx/Vampire---4.8_12582',m__1837) ).
fof(f4221,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(subsumption_resolution,[],[f4189,f1275]) ).
fof(f1275,plain,
~ doDivides0(xk,sF18),
inference(subsumption_resolution,[],[f1268,f184]) ).
fof(f1268,plain,
( ~ doDivides0(xk,sF18)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f1240,f190]) ).
fof(f190,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
( isPrime0(xr)
& ! [X0] :
( xr = X0
| sz10 = X0
| ( ~ doDivides0(X0,xr)
& ! [X1] :
( sdtasdt0(X0,X1) != xr
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,sK6)
& aNaturalNumber0(sK6)
& aNaturalNumber0(xr) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f59,f139]) ).
fof(f139,plain,
( ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
=> ( xk = sdtasdt0(xr,sK6)
& aNaturalNumber0(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
( isPrime0(xr)
& ! [X0] :
( xr = X0
| sz10 = X0
| ( ~ doDivides0(X0,xr)
& ! [X1] :
( sdtasdt0(X0,X1) != xr
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(xr) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
( isPrime0(xr)
& ! [X0] :
( xr = X0
| sz10 = X0
| ( ~ doDivides0(X0,xr)
& ! [X1] :
( sdtasdt0(X0,X1) != xr
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(xr) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,plain,
( isPrime0(xr)
& ! [X0] :
( ( ( doDivides0(X0,xr)
| ? [X1] :
( sdtasdt0(X0,X1) = xr
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( xr = X0
| sz10 = X0 ) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(xr) ),
inference(rectify,[],[f48]) ).
fof(f48,axiom,
( isPrime0(xr)
& ! [X0] :
( ( ( doDivides0(X0,xr)
| ? [X1] :
( sdtasdt0(X0,X1) = xr
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( xr = X0
| sz10 = X0 ) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/tmp/tmp.MXu6MQPhDx/Vampire---4.8_12582',m__2342) ).
fof(f1240,plain,
! [X0] :
( ~ doDivides0(xr,X0)
| ~ doDivides0(X0,sF18)
| ~ aNaturalNumber0(X0) ),
inference(subsumption_resolution,[],[f1239,f187]) ).
fof(f187,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f140]) ).
fof(f1239,plain,
! [X0] :
( ~ doDivides0(X0,sF18)
| ~ doDivides0(xr,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr) ),
inference(subsumption_resolution,[],[f1232,f371]) ).
fof(f371,plain,
aNaturalNumber0(sF18),
inference(subsumption_resolution,[],[f370,f196]) ).
fof(f196,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f370,plain,
( aNaturalNumber0(sF18)
| ~ aNaturalNumber0(xn) ),
inference(subsumption_resolution,[],[f362,f197]) ).
fof(f197,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f362,plain,
( aNaturalNumber0(sF18)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f268,f323]) ).
fof(f323,plain,
sdtasdt0(xn,xm) = sF18,
introduced(function_definition,[]) ).
fof(f268,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f81]) ).
fof(f81,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/sandbox2/tmp/tmp.MXu6MQPhDx/Vampire---4.8_12582',mSortsB_02) ).
fof(f1232,plain,
! [X0] :
( ~ doDivides0(X0,sF18)
| ~ doDivides0(xr,X0)
| ~ aNaturalNumber0(sF18)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[],[f305,f324]) ).
fof(f324,plain,
~ doDivides0(xr,sF18),
inference(definition_folding,[],[f183,f323]) ).
fof(f183,plain,
~ doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
( ~ doDivides0(xr,sdtasdt0(xn,xm))
& ! [X0] :
( sdtasdt0(xn,xm) != sdtasdt0(xr,X0)
| ~ aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,negated_conjecture,
~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) ) ),
inference(negated_conjecture,[],[f49]) ).
fof(f49,conjecture,
( doDivides0(xr,sdtasdt0(xn,xm))
| ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MXu6MQPhDx/Vampire---4.8_12582',m__) ).
fof(f305,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f121]) ).
fof(f121,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MXu6MQPhDx/Vampire---4.8_12582',mDivTrans) ).
fof(f4189,plain,
( doDivides0(xk,sF18)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(superposition,[],[f333,f4169]) ).
fof(f4169,plain,
sF18 = sdtasdt0(xk,xp),
inference(forward_demodulation,[],[f4151,f328]) ).
fof(f328,plain,
sdtasdt0(xp,xk) = sF18,
inference(forward_demodulation,[],[f185,f323]) ).
fof(f185,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f4151,plain,
sdtasdt0(xp,xk) = sdtasdt0(xk,xp),
inference(resolution,[],[f452,f184]) ).
fof(f452,plain,
! [X10] :
( ~ aNaturalNumber0(X10)
| sdtasdt0(X10,xp) = sdtasdt0(xp,X10) ),
inference(resolution,[],[f270,f198]) ).
fof(f270,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.MXu6MQPhDx/Vampire---4.8_12582',mMulComm) ).
fof(f333,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(subsumption_resolution,[],[f321,f268]) ).
fof(f321,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f293]) ).
fof(f293,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f177]) ).
fof(f177,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtasdt0(X0,sK16(X0,X1)) = X1
& aNaturalNumber0(sK16(X0,X1)) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f175,f176]) ).
fof(f176,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X0,sK16(X0,X1)) = X1
& aNaturalNumber0(sK16(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f175,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f174]) ).
fof(f174,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MXu6MQPhDx/Vampire---4.8_12582',mDefDiv) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM501+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 17:43:26 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 This is a FOF_THM_RFO_SEQ problem
% 0.13/0.35 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.MXu6MQPhDx/Vampire---4.8_12582
% 0.13/0.35 % (12713)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.41 % (12716)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.21/0.41 % (12718)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.21/0.41 % (12717)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.21/0.41 % (12719)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.21/0.41 % (12720)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.21/0.41 % (12714)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.21/0.41 % (12715)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.21/0.53 % (12717)First to succeed.
% 0.21/0.53 % (12717)Refutation found. Thanks to Tanya!
% 0.21/0.53 % SZS status Theorem for Vampire---4
% 0.21/0.53 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.53 % (12717)------------------------------
% 0.21/0.53 % (12717)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.53 % (12717)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.53 % (12717)Termination reason: Refutation
% 0.21/0.53
% 0.21/0.53 % (12717)Memory used [KB]: 7931
% 0.21/0.53 % (12717)Time elapsed: 0.123 s
% 0.21/0.53 % (12717)------------------------------
% 0.21/0.53 % (12717)------------------------------
% 0.21/0.53 % (12713)Success in time 0.183 s
% 0.21/0.53 % Vampire---4.8 exiting
%------------------------------------------------------------------------------