TSTP Solution File: NUM609+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM609+1 : 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 : n010.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 14:35:04 EDT 2024
% Result : Theorem 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of formulae : 62 ( 16 unt; 0 def)
% Number of atoms : 282 ( 39 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 370 ( 150 ~; 132 |; 70 &)
% ( 11 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 95 ( 87 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1347,plain,
$false,
inference(resolution,[],[f1346,f359]) ).
fof(f359,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,axiom,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5173) ).
fof(f1346,plain,
~ aElementOf0(xp,xQ),
inference(resolution,[],[f1344,f386]) ).
fof(f386,plain,
aSet0(xO),
inference(cnf_transformation,[],[f96]) ).
fof(f96,axiom,
( isCountable0(xO)
& aSet0(xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4908) ).
fof(f1344,plain,
( ~ aSet0(xO)
| ~ aElementOf0(xp,xQ) ),
inference(resolution,[],[f1343,f628]) ).
fof(f628,plain,
( aSet0(xQ)
| ~ aSet0(xO) ),
inference(resolution,[],[f466,f394]) ).
fof(f394,plain,
aSubsetOf0(xQ,xO),
inference(cnf_transformation,[],[f100]) ).
fof(f100,axiom,
( slcrc0 != xQ
& aSubsetOf0(xQ,xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
fof(f466,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f293,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ( ~ aElementOf0(sK24(X0,X1),X0)
& aElementOf0(sK24(X0,X1),X1) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f291,f292]) ).
fof(f292,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK24(X0,X1),X0)
& aElementOf0(sK24(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f291,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f290]) ).
fof(f290,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f289]) ).
fof(f289,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f168]) ).
fof(f168,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f1343,plain,
( ~ aSet0(xQ)
| ~ aElementOf0(xp,xQ) ),
inference(resolution,[],[f1332,f384]) ).
fof(f384,plain,
aSet0(xP),
inference(cnf_transformation,[],[f104]) ).
fof(f104,axiom,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& aSet0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(f1332,plain,
( ~ aSet0(xP)
| ~ aElementOf0(xp,xQ)
| ~ aSet0(xQ) ),
inference(resolution,[],[f1307,f353]) ).
fof(f353,plain,
~ aSubsetOf0(xP,xQ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
~ aSubsetOf0(xP,xQ),
inference(flattening,[],[f108]) ).
fof(f108,negated_conjecture,
~ aSubsetOf0(xP,xQ),
inference(negated_conjecture,[],[f107]) ).
fof(f107,conjecture,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f1307,plain,
( aSubsetOf0(xP,xQ)
| ~ aElementOf0(xp,xQ)
| ~ aSet0(xP)
| ~ aSet0(xQ) ),
inference(resolution,[],[f1306,f468]) ).
fof(f468,plain,
! [X0,X1] :
( aElementOf0(sK24(X0,X1),X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f1306,plain,
( ~ aElementOf0(sK24(xQ,xP),xP)
| ~ aElementOf0(xp,xQ) ),
inference(resolution,[],[f1301,f386]) ).
fof(f1301,plain,
( ~ aSet0(xO)
| ~ aElementOf0(sK24(xQ,xP),xP)
| ~ aElementOf0(xp,xQ) ),
inference(resolution,[],[f1297,f628]) ).
fof(f1297,plain,
( ~ aSet0(xQ)
| ~ aElementOf0(xp,xQ)
| ~ aElementOf0(sK24(xQ,xP),xP) ),
inference(factoring,[],[f1264]) ).
fof(f1264,plain,
! [X0] :
( ~ aSet0(xQ)
| ~ aSet0(X0)
| ~ aElementOf0(xp,X0)
| ~ aElementOf0(sK24(xQ,xP),xP) ),
inference(resolution,[],[f1260,f462]) ).
fof(f462,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f1260,plain,
( ~ aElement0(xp)
| ~ aElementOf0(sK24(xQ,xP),xP)
| ~ aSet0(xQ) ),
inference(resolution,[],[f1259,f789]) ).
fof(f789,plain,
! [X0] :
( aElementOf0(X0,xQ)
| ~ aSet0(xQ)
| ~ aElementOf0(X0,xP)
| ~ aElement0(xp) ),
inference(resolution,[],[f788,f537]) ).
fof(f537,plain,
! [X2,X0,X1,X4] :
( ~ sP9(X0,X1,X2)
| ~ aElementOf0(X4,X2)
| aElementOf0(X4,X1) ),
inference(cnf_transformation,[],[f336]) ).
fof(f336,plain,
! [X0,X1,X2] :
( ( sP9(X0,X1,X2)
| ( ( sK33(X0,X1,X2) = X0
| ~ aElementOf0(sK33(X0,X1,X2),X1)
| ~ aElement0(sK33(X0,X1,X2))
| ~ aElementOf0(sK33(X0,X1,X2),X2) )
& ( ( sK33(X0,X1,X2) != X0
& aElementOf0(sK33(X0,X1,X2),X1)
& aElement0(sK33(X0,X1,X2)) )
| aElementOf0(sK33(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( aElementOf0(X4,X2)
| X0 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4) )
& ( ( X0 != X4
& aElementOf0(X4,X1)
& aElement0(X4) )
| ~ aElementOf0(X4,X2) ) )
| ~ sP9(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f334,f335]) ).
fof(f335,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( X0 = X3
| ~ aElementOf0(X3,X1)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( X0 != X3
& aElementOf0(X3,X1)
& aElement0(X3) )
| aElementOf0(X3,X2) ) )
=> ( ( sK33(X0,X1,X2) = X0
| ~ aElementOf0(sK33(X0,X1,X2),X1)
| ~ aElement0(sK33(X0,X1,X2))
| ~ aElementOf0(sK33(X0,X1,X2),X2) )
& ( ( sK33(X0,X1,X2) != X0
& aElementOf0(sK33(X0,X1,X2),X1)
& aElement0(sK33(X0,X1,X2)) )
| aElementOf0(sK33(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f334,plain,
! [X0,X1,X2] :
( ( sP9(X0,X1,X2)
| ? [X3] :
( ( X0 = X3
| ~ aElementOf0(X3,X1)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( X0 != X3
& aElementOf0(X3,X1)
& aElement0(X3) )
| aElementOf0(X3,X2) ) ) )
& ( ! [X4] :
( ( aElementOf0(X4,X2)
| X0 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4) )
& ( ( X0 != X4
& aElementOf0(X4,X1)
& aElement0(X4) )
| ~ aElementOf0(X4,X2) ) )
| ~ sP9(X0,X1,X2) ) ),
inference(rectify,[],[f333]) ).
fof(f333,plain,
! [X1,X0,X2] :
( ( sP9(X1,X0,X2)
| ? [X3] :
( ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| aElementOf0(X3,X2) ) ) )
& ( ! [X3] :
( ( aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| ~ aElementOf0(X3,X2) ) )
| ~ sP9(X1,X0,X2) ) ),
inference(flattening,[],[f332]) ).
fof(f332,plain,
! [X1,X0,X2] :
( ( sP9(X1,X0,X2)
| ? [X3] :
( ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| aElementOf0(X3,X2) ) ) )
& ( ! [X3] :
( ( aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| ~ aElementOf0(X3,X2) ) )
| ~ sP9(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f254]) ).
fof(f254,plain,
! [X1,X0,X2] :
( sP9(X1,X0,X2)
<=> ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f788,plain,
( sP9(xp,xQ,xP)
| ~ aElement0(xp)
| ~ aSet0(xQ) ),
inference(superposition,[],[f596,f603]) ).
fof(f603,plain,
xP = sdtmndt0(xQ,xp),
inference(forward_demodulation,[],[f385,f361]) ).
fof(f361,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,axiom,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
fof(f385,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[],[f104]) ).
fof(f596,plain,
! [X0,X1] :
( sP9(X1,X0,sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f545]) ).
fof(f545,plain,
! [X2,X0,X1] :
( sP9(X1,X0,X2)
| sdtmndt0(X0,X1) != X2
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f338,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X0,X1) = X2
| ~ sP9(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP9(X1,X0,X2)
& aSet0(X2) )
| sdtmndt0(X0,X1) != X2 ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f337]) ).
fof(f337,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X0,X1) = X2
| ~ sP9(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP9(X1,X0,X2)
& aSet0(X2) )
| sdtmndt0(X0,X1) != X2 ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f255]) ).
fof(f255,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( sP9(X1,X0,X2)
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f213,f254]) ).
fof(f213,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f212]) ).
fof(f212,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aSet0(X0) )
=> ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f1259,plain,
~ aElementOf0(sK24(xQ,xP),xQ),
inference(resolution,[],[f1257,f386]) ).
fof(f1257,plain,
( ~ aSet0(xO)
| ~ aElementOf0(sK24(xQ,xP),xQ) ),
inference(resolution,[],[f1256,f628]) ).
fof(f1256,plain,
( ~ aSet0(xQ)
| ~ aElementOf0(sK24(xQ,xP),xQ) ),
inference(resolution,[],[f1235,f384]) ).
fof(f1235,plain,
( ~ aSet0(xP)
| ~ aElementOf0(sK24(xQ,xP),xQ)
| ~ aSet0(xQ) ),
inference(resolution,[],[f469,f353]) ).
fof(f469,plain,
! [X0,X1] :
( aSubsetOf0(X1,X0)
| ~ aElementOf0(sK24(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f293]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM609+1 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 29 23:54:50 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (19352)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (19356)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37 % (19355)WARNING: value z3 for option sas not known
% 0.20/0.37 % (19353)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37 % (19355)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)
% 0.20/0.37 % (19354)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.37 % (19357)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)
% 0.20/0.37 % (19358)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)
% 0.20/0.37 % (19359)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)
% 0.20/0.38 TRYING [1]
% 0.20/0.38 TRYING [2]
% 0.20/0.39 TRYING [3]
% 0.20/0.39 TRYING [1]
% 0.20/0.39 TRYING [2]
% 0.20/0.41 TRYING [3]
% 0.20/0.41 % (19358)First to succeed.
% 0.20/0.41 % (19358)Refutation found. Thanks to Tanya!
% 0.20/0.41 % SZS status Theorem for theBenchmark
% 0.20/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.42 % (19358)------------------------------
% 0.20/0.42 % (19358)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.42 % (19358)Termination reason: Refutation
% 0.20/0.42
% 0.20/0.42 % (19358)Memory used [KB]: 1756
% 0.20/0.42 % (19358)Time elapsed: 0.045 s
% 0.20/0.42 % (19358)Instructions burned: 68 (million)
% 0.20/0.42 % (19358)------------------------------
% 0.20/0.42 % (19358)------------------------------
% 0.20/0.42 % (19352)Success in time 0.065 s
%------------------------------------------------------------------------------