%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM443+4 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 : Fri Jul 25 12:28:10 PM UTC 2025
% Result : Theorem 11.92s 1.83s
% Output : CNFRefutation 11.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 20 unt; 0 def)
% Number of atoms : 149 ( 20 equ)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 154 ( 41 ~; 42 |; 55 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 11 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,plain,
( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0] :
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(W0)
& ? [W1] :
( aInteger0(W1)
& sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ( aInteger0(W0)
& ( ? [W1] :
( aInteger0(W1)
& sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
=> aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xc,smndt0(xb)) )
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq) )
=> ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0] :
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(W0)
& ? [W1] :
( aInteger0(W1)
& sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ( aInteger0(W0)
& ( ? [W1] :
( aInteger0(W1)
& sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
=> aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m___negated,plain,
~ ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0] :
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(W0)
& ? [W1] :
( aInteger0(W1)
& sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ( aInteger0(W0)
& ( ? [W1] :
( aInteger0(W1)
& sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
=> aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xc,smndt0(xb)) )
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq) )
=> ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0] :
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(W0)
& ? [W1] :
( aInteger0(W1)
& sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ( aInteger0(W0)
& ( ? [W1] :
( aInteger0(W1)
& sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
=> aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(114,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X0) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l0,plain,
( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(xc) ),
inference(instantiation,[status(thm)],[114]) ).
cnf(137,plain,
aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l1,plain,
aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(instantiation,[status(thm)],[137]) ).
fof(mEquModTrn,plain,
! [W0,W1,W2,W3] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& W2 != sz00
& aInteger0(W3) )
=> ( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
=> sdteqdtlpzmzozddtrp0(W0,W3,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModTrn) ).
cnf(31,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X2)
| X2 = sz00
| sdteqdtlpzmzozddtrp0(X0,X3,X2) ),
inference(cnf,[status(esa)],[mEquModTrn]) ).
cnf(l59,plain,
( ~ aInteger0(xb)
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| xq = sz00
| sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
inference(instantiation,[status(thm)],[31]) ).
fof(mEquModSym,plain,
! [W0,W1,W2] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& W2 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
=> sdteqdtlpzmzozddtrp0(W1,W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModSym) ).
cnf(30,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| X2 = sz00
| sdteqdtlpzmzozddtrp0(X1,X0,X2) ),
inference(cnf,[status(esa)],[mEquModSym]) ).
cnf(l60,plain,
( ~ aInteger0(xc)
| ~ aInteger0(xb)
| ~ aInteger0(xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xb,xq)
| xq = sz00
| sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
inference(instantiation,[status(thm)],[30]) ).
cnf(127,plain,
sdteqdtlpzmzozddtrp0(xc,xb,xq),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l75,plain,
sdteqdtlpzmzozddtrp0(xc,xb,xq),
inference(instantiation,[status(thm)],[127]) ).
fof(m__2010,plain,
( aInteger0(xb)
& aInteger0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2010) ).
cnf(111,plain,
aInteger0(xb),
inference(cnf,[status(esa)],[m__2010]) ).
cnf(l96,plain,
aInteger0(xb),
inference(instantiation,[status(thm)],[111]) ).
fof(m__1962,plain,
( aInteger0(xa)
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1962) ).
cnf(109,plain,
aInteger0(xq),
inference(cnf,[status(esa)],[m__1962]) ).
cnf(l97,plain,
aInteger0(xq),
inference(instantiation,[status(thm)],[109]) ).
cnf(110,plain,
xq != sz00,
inference(cnf,[status(esa)],[m__1962]) ).
cnf(l73,plain,
xq != sz00,
inference(instantiation,[status(thm)],[110]) ).
cnf(l86,plain,
aInteger0(xq),
inference(instantiation,[status(thm)],[109]) ).
cnf(133,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sdteqdtlpzmzozddtrp0(X0,xa,xq) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l78,plain,
( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sdteqdtlpzmzozddtrp0(xc,xa,xq) ),
inference(instantiation,[status(thm)],[133]) ).
cnf(108,plain,
aInteger0(xa),
inference(cnf,[status(esa)],[m__1962]) ).
cnf(l88,plain,
aInteger0(xa),
inference(instantiation,[status(thm)],[108]) ).
cnf(l103,plain,
aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(instantiation,[status(thm)],[137]) ).
cnf(136,plain,
( ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l61,plain,
( ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(instantiation,[status(thm)],[136]) ).
cnf(l76,plain,
aInteger0(xb),
inference(instantiation,[status(thm)],[111]) ).
cnf(l62,plain,
aInteger0(xb),
inference(instantiation,[status(thm)],[111]) ).
cnf(l67,plain,
xq != sz00,
inference(instantiation,[status(thm)],[110]) ).
cnf(122,plain,
~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l130,plain,
~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(instantiation,[status(thm)],[122]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l59,l60,l75,l96,l97,l73,l86,l78,l88,l103,l61,l76,l62,l67,l130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM443+4 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 21 12:06:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.34 % launching worker at depth: 6
% 0.18/0.34 % launching worker at depth: 1
% 0.18/0.34 % launching worker at depth: 2
% 0.18/0.34 % launching worker at depth: 3
% 0.18/0.34 % launching worker at depth: 4
% 0.18/0.34 % launching worker at depth: 7
% 0.18/0.34 % launching worker at depth: 5
% 0.18/0.34 % launching worker at depth: 8
% 0.18/0.35 % launching worker at depth: 9
% 0.18/0.54 % launching worker at depth: 10
% 11.92/1.83 % SZS status Theorem for theBenchmark
% 11.92/1.83 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------