%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM571+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:20:24 PM UTC 2026
% Result : Theorem 5.60s 2.90s
% Output : Proof 5.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 6 unt; 0 def)
% Number of atoms : 73 ( 19 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 67 ( 20 ~; 17 |; 27 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn 3 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f80,hypothesis,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(f80_nnf,plain,
( ! [W0] :
( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(nnf_transformation,[status(thm)],[f80]) ).
fof(f80_sk,plain,
! [W0] :
( ( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
| ~ isCountable0(sdtlpdtrp0(xN,W0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(skolemisation,[status(esa)],[f80_nnf]) ).
cnf(c183,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(cnf_transformation,[status(esa)],[f80_sk]) ).
fof(f83,hypothesis,
( xi != sz00
=> ( isCountable0(sdtlpdtrp0(xN,xi))
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& ? [W0] :
( szszuzczcdt0(W0) = xi
& aElementOf0(W0,szNzAzT0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3702_02) ).
fof(f83_nnf,plain,
( ( isCountable0(sdtlpdtrp0(xN,xi))
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& ? [W0] :
( szszuzczcdt0(W0) = xi
& aElementOf0(W0,szNzAzT0) ) )
| xi = sz00 ),
inference(nnf_transformation,[status(thm)],[f83]) ).
fof(f83_sk,plain,
( ( isCountable0(sdtlpdtrp0(xN,xi))
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& szszuzczcdt0(sk21) = xi
& aElementOf0(sk21,szNzAzT0) )
| xi = sz00 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk21])],[f83_nnf]) ).
cnf(c192,plain,
( isCountable0(sdtlpdtrp0(xN,xi))
| xi = sz00 ),
inference(cnf_transformation,[status(esa)],[f83_sk]) ).
cnf(c191,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| xi = sz00 ),
inference(cnf_transformation,[status(esa)],[f83_sk]) ).
fof(f84,conjecture,
( isCountable0(sdtlpdtrp0(xN,xi))
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f84_neg,negated_conjecture,
~ ( isCountable0(sdtlpdtrp0(xN,xi))
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(negated_conjecture,[status(cth)],[f84]) ).
fof(f84_nnf,plain,
( ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f84_neg]) ).
fof(f84_sk,plain,
( ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(skolemisation,[status(esa)],[f84_nnf]) ).
cnf(c193,plain,
( ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f84_sk]) ).
cnf(p6747,plain,
( ~ isCountable0(sdtlpdtrp0(xN,xi))
| xi = sz00 ),
inference(resolution,[status(thm)],[c191,c193]) ).
cnf(p6760,plain,
( xi = sz00
| xi = sz00 ),
inference(resolution,[status(thm)],[c192,p6747]) ).
cnf(p6761,plain,
xi = sz00,
inference(factoring,[status(thm)],[p6760]) ).
cnf(p6764,plain,
( ~ isCountable0(sdtlpdtrp0(xN,sz00))
| ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szNzAzT0) ),
inference(demodulation,[status(thm)],[p6761,c193]) ).
cnf(p6848,plain,
( ~ isCountable0(xS)
| ~ aSubsetOf0(xS,szNzAzT0) ),
inference(superposition,[status(thm)],[c183,p6764]) ).
fof(f74,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
fof(f74_nnf,plain,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f74]) ).
fof(f74_sk,plain,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
inference(skolemisation,[status(esa)],[f74_nnf]) ).
cnf(c168,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[status(esa)],[f74_sk]) ).
cnf(p6850,plain,
~ isCountable0(xS),
inference(resolution,[status(thm)],[p6848,c168]) ).
cnf(c169,plain,
isCountable0(xS),
inference(cnf_transformation,[status(esa)],[f74_sk]) ).
cnf(p6851,plain,
$false,
inference(resolution,[status(thm)],[p6850,c169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM571+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Thu Sep 24 04:40:50 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.60/2.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.60/2.90 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------