TSTP Solution File: NUM561+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM561+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 : 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 : Tue Apr 30 14:33:25 EDT 2024
% Result : Theorem 0.22s 0.41s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 10 unt; 0 def)
% Number of atoms : 169 ( 36 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 208 ( 80 ~; 74 |; 40 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 98 ( 81 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f863,plain,
$false,
inference(resolution,[],[f862,f267]) ).
fof(f267,plain,
aElementOf0(xx,szDzozmdt0(xF)),
inference(cnf_transformation,[],[f70]) ).
fof(f70,axiom,
aElementOf0(xx,szDzozmdt0(xF)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2911_02) ).
fof(f862,plain,
~ aElementOf0(xx,szDzozmdt0(xF)),
inference(resolution,[],[f860,f266]) ).
fof(f266,plain,
aFunction0(xF),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
aFunction0(xF),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2911) ).
fof(f860,plain,
( ~ aFunction0(xF)
| ~ aElementOf0(xx,szDzozmdt0(xF)) ),
inference(resolution,[],[f856,f273]) ).
fof(f273,plain,
! [X0] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,axiom,
! [X0] :
( aFunction0(X0)
=> aSet0(szDzozmdt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDomSet) ).
fof(f856,plain,
( ~ aSet0(szDzozmdt0(xF))
| ~ aElementOf0(xx,szDzozmdt0(xF)) ),
inference(resolution,[],[f855,f286]) ).
fof(f286,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
fof(f855,plain,
( ~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF))
| ~ aElementOf0(xx,szDzozmdt0(xF)) ),
inference(resolution,[],[f854,f266]) ).
fof(f854,plain,
( ~ aFunction0(xF)
| ~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF))
| ~ aElementOf0(xx,szDzozmdt0(xF)) ),
inference(resolution,[],[f853,f284]) ).
fof(f284,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0] :
( ! [X1] :
( sP1(X1,X0)
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(definition_folding,[],[f84,f175,f174]) ).
fof(f174,plain,
! [X0,X1,X2] :
( sP0(X0,X1,X2)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& aSet0(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f175,plain,
! [X1,X0] :
( ! [X2] :
( sdtlcdtrc0(X0,X1) = X2
<=> sP0(X0,X1,X2) )
| ~ sP1(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( sdtlcdtrc0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& aSet0(X2) ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aSubsetOf0(X1,szDzozmdt0(X0))
=> ! [X2] :
( sdtlcdtrc0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& aSet0(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSImg) ).
fof(f853,plain,
( ~ sP1(szDzozmdt0(xF),xF)
| ~ aElementOf0(xx,szDzozmdt0(xF)) ),
inference(resolution,[],[f847,f408]) ).
fof(f408,plain,
! [X0,X1] :
( sP0(X1,X0,sdtlcdtrc0(X1,X0))
| ~ sP1(X0,X1) ),
inference(equality_resolution,[],[f275]) ).
fof(f275,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| sdtlcdtrc0(X1,X0) != X2
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f191]) ).
fof(f191,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtlcdtrc0(X1,X0) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| sdtlcdtrc0(X1,X0) != X2 ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f190]) ).
fof(f190,plain,
! [X1,X0] :
( ! [X2] :
( ( sdtlcdtrc0(X0,X1) = X2
| ~ sP0(X0,X1,X2) )
& ( sP0(X0,X1,X2)
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f175]) ).
fof(f847,plain,
! [X0] :
( ~ sP0(xF,X0,sdtlcdtrc0(xF,szDzozmdt0(xF)))
| ~ aElementOf0(xx,X0) ),
inference(resolution,[],[f409,f265]) ).
fof(f265,plain,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(flattening,[],[f72]) ).
fof(f72,negated_conjecture,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(negated_conjecture,[],[f71]) ).
fof(f71,conjecture,
aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f409,plain,
! [X2,X0,X1,X7] :
( aElementOf0(sdtlpdtrp0(X0,X7),X2)
| ~ aElementOf0(X7,X1)
| ~ sP0(X0,X1,X2) ),
inference(equality_resolution,[],[f280]) ).
fof(f280,plain,
! [X2,X0,X1,X6,X7] :
( aElementOf0(X6,X2)
| sdtlpdtrp0(X0,X7) != X6
| ~ aElementOf0(X7,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f198]) ).
fof(f198,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ! [X4] :
( sdtlpdtrp0(X0,X4) != sK10(X0,X1,X2)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(sK10(X0,X1,X2),X2) )
& ( ( sK10(X0,X1,X2) = sdtlpdtrp0(X0,sK11(X0,X1,X2))
& aElementOf0(sK11(X0,X1,X2),X1) )
| aElementOf0(sK10(X0,X1,X2),X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X6] :
( ( aElementOf0(X6,X2)
| ! [X7] :
( sdtlpdtrp0(X0,X7) != X6
| ~ aElementOf0(X7,X1) ) )
& ( ( sdtlpdtrp0(X0,sK12(X0,X1,X6)) = X6
& aElementOf0(sK12(X0,X1,X6),X1) )
| ~ aElementOf0(X6,X2) ) )
& aSet0(X2) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f194,f197,f196,f195]) ).
fof(f195,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) )
& ( ? [X5] :
( sdtlpdtrp0(X0,X5) = X3
& aElementOf0(X5,X1) )
| aElementOf0(X3,X2) ) )
=> ( ( ! [X4] :
( sdtlpdtrp0(X0,X4) != sK10(X0,X1,X2)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(sK10(X0,X1,X2),X2) )
& ( ? [X5] :
( sdtlpdtrp0(X0,X5) = sK10(X0,X1,X2)
& aElementOf0(X5,X1) )
| aElementOf0(sK10(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f196,plain,
! [X0,X1,X2] :
( ? [X5] :
( sdtlpdtrp0(X0,X5) = sK10(X0,X1,X2)
& aElementOf0(X5,X1) )
=> ( sK10(X0,X1,X2) = sdtlpdtrp0(X0,sK11(X0,X1,X2))
& aElementOf0(sK11(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f197,plain,
! [X0,X1,X6] :
( ? [X8] :
( sdtlpdtrp0(X0,X8) = X6
& aElementOf0(X8,X1) )
=> ( sdtlpdtrp0(X0,sK12(X0,X1,X6)) = X6
& aElementOf0(sK12(X0,X1,X6),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f194,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) )
& ( ? [X5] :
( sdtlpdtrp0(X0,X5) = X3
& aElementOf0(X5,X1) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X6] :
( ( aElementOf0(X6,X2)
| ! [X7] :
( sdtlpdtrp0(X0,X7) != X6
| ~ aElementOf0(X7,X1) ) )
& ( ? [X8] :
( sdtlpdtrp0(X0,X8) = X6
& aElementOf0(X8,X1) )
| ~ aElementOf0(X6,X2) ) )
& aSet0(X2) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f193]) ).
fof(f193,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) )
& ( ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) ) )
& ( ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP0(X0,X1,X2) ) ),
inference(flattening,[],[f192]) ).
fof(f192,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) )
& ( ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) ) )
& ( ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP0(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM561+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 23:25:57 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (16634)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (16637)WARNING: value z3 for option sas not known
% 0.14/0.38 % (16636)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (16635)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (16639)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)
% 0.14/0.38 % (16637)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)
% 0.14/0.38 % (16638)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (16640)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)
% 0.14/0.38 % (16641)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)
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [2]
% 0.14/0.40 TRYING [3]
% 0.14/0.40 TRYING [3]
% 0.22/0.41 % (16640)First to succeed.
% 0.22/0.41 % (16640)Refutation found. Thanks to Tanya!
% 0.22/0.41 % SZS status Theorem for theBenchmark
% 0.22/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.41 % (16640)------------------------------
% 0.22/0.41 % (16640)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.41 % (16640)Termination reason: Refutation
% 0.22/0.41
% 0.22/0.41 % (16640)Memory used [KB]: 1484
% 0.22/0.41 % (16640)Time elapsed: 0.033 s
% 0.22/0.41 % (16640)Instructions burned: 47 (million)
% 0.22/0.41 % (16640)------------------------------
% 0.22/0.41 % (16640)------------------------------
% 0.22/0.41 % (16634)Success in time 0.051 s
%------------------------------------------------------------------------------