%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM423+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 : n001.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 02:19:59 PM UTC 2026
% Result : Theorem 28.40s 4.13s
% Output : Proof 28.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 11 unt; 0 def)
% Number of atoms : 60 ( 27 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 56 ( 23 ~; 13 |; 18 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [W0] :
( aInteger0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(f14_nnf,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aInteger0(W0) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aInteger0(W0) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c18,plain,
( sdtasdt0(X0,sz00) = sz00
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f19,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__671) ).
fof(f19_nnf,plain,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c31,plain,
aInteger0(xq),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p320,plain,
sdtasdt0(xq,sz00) = sz00,
inference(resolution,[status(thm)],[c18,c31]) ).
fof(f9,axiom,
! [W0] :
( aInteger0(W0)
=> ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(f9_nnf,plain,
! [W0] :
( ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 )
| ~ aInteger0(W0) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [W0] :
( ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 )
| ~ aInteger0(W0) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c10,plain,
( sdtpldt0(X0,smndt0(X0)) = sz00
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(c30,plain,
aInteger0(xa),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p173,plain,
sdtpldt0(xa,smndt0(xa)) = sz00,
inference(resolution,[status(thm)],[c10,c30]) ).
fof(f20,conjecture,
( sdteqdtlpzmzozddtrp0(xa,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa))
& aInteger0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f20_neg,negated_conjecture,
~ ( sdteqdtlpzmzozddtrp0(xa,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa))
& aInteger0(W0) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f20_nnf,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
& ! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa))
| ~ aInteger0(W0) ) ),
inference(nnf_transformation,[status(thm)],[f20_neg]) ).
fof(f20_sk,plain,
! [W0] :
( ~ sdteqdtlpzmzozddtrp0(xa,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
& ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa))
| ~ aInteger0(W0) ) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c33,plain,
( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xa))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f1,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(f1_nnf,plain,
aInteger0(sz00),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
aInteger0(sz00),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(p37,plain,
sdtasdt0(xq,sz00) != sdtpldt0(xa,smndt0(xa)),
inference(resolution,[status(thm)],[c33,c1]) ).
cnf(p176,plain,
sdtasdt0(xq,sz00) != sz00,
inference(demodulation,[status(thm)],[p173,p37]) ).
cnf(p321,plain,
sz00 != sz00,
inference(demodulation,[status(thm)],[p320,p176]) ).
cnf(p331,plain,
$false,
inference(equality_resolution,[status(thm)],[p321]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM423+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 03:59:21 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 28.40/4.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.40/4.13 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------