%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM568+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 21.33s 3.72s
% Output : Proof 21.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 49 ( 30 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 43 ( 19 ~; 18 |; 5 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 12 ( 0 sgn 5 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ? [W1] :
( W0 = szszuzczcdt0(W1)
& aElementOf0(W1,szNzAzT0) )
| W0 = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
fof(f26_nnf,plain,
! [W0] :
( ? [W1] :
( W0 = szszuzczcdt0(W1)
& aElementOf0(W1,szNzAzT0) )
| W0 = sz00
| ~ aElementOf0(W0,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [W0] :
( ( W0 = szszuzczcdt0(sk4(W0))
& aElementOf0(sk4(W0),szNzAzT0) )
| W0 = sz00
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f26_nnf]) ).
cnf(c59,plain,
( X0 = szszuzczcdt0(sk4(X0))
| X0 = sz00
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
fof(f73,hypothesis,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
fof(f73_nnf,plain,
aElementOf0(xK,szNzAzT0),
inference(nnf_transformation,[status(thm)],[f73]) ).
cnf(c167,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[status(esa)],[f73_nnf]) ).
cnf(p8551,plain,
( xK = szszuzczcdt0(sk4(xK))
| xK = sz00 ),
inference(resolution,[status(thm)],[c59,c167]) ).
cnf(c58,plain,
( aElementOf0(sk4(X0),szNzAzT0)
| X0 = sz00
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p1341,plain,
( aElementOf0(sk4(xK),szNzAzT0)
| xK = sz00 ),
inference(resolution,[status(thm)],[c58,c167]) ).
fof(f79,conjecture,
? [W0] :
( szszuzczcdt0(W0) = xK
& aElementOf0(W0,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f79_neg,negated_conjecture,
~ ? [W0] :
( szszuzczcdt0(W0) = xK
& aElementOf0(W0,szNzAzT0) ),
inference(negated_conjecture,[status(cth)],[f79]) ).
fof(f79_nnf,plain,
! [W0] :
( szszuzczcdt0(W0) != xK
| ~ aElementOf0(W0,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f79_neg]) ).
fof(f79_sk,plain,
! [W0] :
( szszuzczcdt0(W0) != xK
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemisation,[status(esa)],[f79_nnf]) ).
cnf(c319,plain,
( szszuzczcdt0(X0) != xK
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f79_sk]) ).
cnf(p1374,plain,
( szszuzczcdt0(sk4(xK)) != xK
| xK = sz00 ),
inference(resolution,[status(thm)],[p1341,c319]) ).
cnf(p8608,plain,
( xK != xK
| xK = sz00
| xK = sz00 ),
inference(superposition,[status(thm)],[p8551,p1374]) ).
cnf(p8621,plain,
( xK != xK
| xK = sz00 ),
inference(factoring,[status(thm)],[p8608]) ).
cnf(p8622,plain,
xK = sz00,
inference(equality_resolution,[status(thm)],[p8621]) ).
fof(f77,hypothesis,
xK != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).
fof(f77_nnf,plain,
xK != sz00,
inference(nnf_transformation,[status(thm)],[f77]) ).
fof(f77_sk,plain,
xK != sz00,
inference(skolemisation,[status(esa)],[f77_nnf]) ).
cnf(c317,plain,
xK != sz00,
inference(cnf_transformation,[status(esa)],[f77_sk]) ).
cnf(p8630,plain,
sz00 != sz00,
inference(demodulation,[status(thm)],[p8622,c317]) ).
cnf(p8678,plain,
$false,
inference(equality_resolution,[status(thm)],[p8630]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM568+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 04:40:43 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 21.33/3.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.33/3.72 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------