%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM434+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n029.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 12:28:09 PM UTC 2025
% Result : Theorem 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 31 unt; 0 def)
% Number of atoms : 139 ( 32 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 137 ( 59 ~; 53 |; 16 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 12 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,plain,
? [W0] :
( aInteger0(W0)
& sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m___negated,plain,
~ ? [W0] :
( aInteger0(W0)
& sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb)) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(39,plain,
( ~ aInteger0(X0)
| sdtasdt0(sdtasdt0(xp,xq),X0) != sdtpldt0(xa,smndt0(xb)) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l0,plain,
( ~ aInteger0(sK1(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq)))
| sdtasdt0(sdtasdt0(xp,xq),sK1(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq))) != sdtpldt0(xa,smndt0(xb)) ),
inference(instantiation,[status(thm)],[39]) ).
fof(mDivisor,plain,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& W1 != sz00
& ? [W2] :
( aInteger0(W2)
& sdtasdt0(W1,W2) = W0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
cnf(25,plain,
( ~ aInteger0(X0)
| ~ aDivisorOf0(X1,X0)
| sdtasdt0(X1,sK1(X0,X1)) = X0 ),
inference(cnf,[status(esa)],[mDivisor]) ).
cnf(l2,plain,
( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
| sdtasdt0(sdtasdt0(xp,xq),sK1(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq))) = sdtpldt0(xa,smndt0(xb)) ),
inference(instantiation,[status(thm)],[25]) ).
fof(mIntPlus,plain,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
cnf(3,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| aInteger0(sdtpldt0(X0,X1)) ),
inference(cnf,[status(esa)],[mIntPlus]) ).
cnf(l3,plain,
( ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(instantiation,[status(thm)],[3]) ).
fof(mIntNeg,plain,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
cnf(2,plain,
( ~ aInteger0(X0)
| aInteger0(smndt0(X0)) ),
inference(cnf,[status(esa)],[mIntNeg]) ).
cnf(l5,plain,
( ~ aInteger0(xb)
| aInteger0(smndt0(xb)) ),
inference(instantiation,[status(thm)],[2]) ).
fof(m__979,plain,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xp)
& xp != sz00
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__979) ).
cnf(33,plain,
aInteger0(xb),
inference(cnf,[status(esa)],[m__979]) ).
cnf(l8,plain,
aInteger0(xb),
inference(instantiation,[status(thm)],[33]) ).
fof(mEquMod,plain,
! [W0,W1,W2] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& W2 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).
cnf(27,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| X2 = sz00
| aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ),
inference(cnf,[status(esa)],[mEquMod]) ).
cnf(l15,plain,
( ~ aInteger0(xa)
| ~ aInteger0(xb)
| ~ aInteger0(sdtasdt0(xp,xq))
| ~ sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
| sdtasdt0(xp,xq) = sz00
| aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))) ),
inference(instantiation,[status(thm)],[27]) ).
cnf(32,plain,
aInteger0(xa),
inference(cnf,[status(esa)],[m__979]) ).
cnf(l4,plain,
aInteger0(xa),
inference(instantiation,[status(thm)],[32]) ).
fof(mIntMult,plain,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
cnf(4,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(cnf,[status(esa)],[mIntMult]) ).
cnf(l43,plain,
( ~ aInteger0(xp)
| ~ aInteger0(xq)
| aInteger0(sdtasdt0(xp,xq)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l16,plain,
aInteger0(xa),
inference(instantiation,[status(thm)],[32]) ).
fof(m__1003,plain,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1003) ).
cnf(38,plain,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
inference(cnf,[status(esa)],[m__1003]) ).
cnf(l64,plain,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
inference(instantiation,[status(thm)],[38]) ).
cnf(l17,plain,
aInteger0(xb),
inference(instantiation,[status(thm)],[33]) ).
fof(mZeroDiv,plain,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W0 = sz00
| W1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).
cnf(21,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtasdt0(X0,X1) != sz00
| X0 = sz00
| X1 = sz00 ),
inference(cnf,[status(esa)],[mZeroDiv]) ).
cnf(l70,plain,
( ~ aInteger0(xp)
| ~ aInteger0(xq)
| sdtasdt0(xp,xq) != sz00
| xp = sz00
| xq = sz00 ),
inference(instantiation,[status(thm)],[21]) ).
cnf(36,plain,
aInteger0(xq),
inference(cnf,[status(esa)],[m__979]) ).
cnf(l89,plain,
aInteger0(xq),
inference(instantiation,[status(thm)],[36]) ).
cnf(34,plain,
aInteger0(xp),
inference(cnf,[status(esa)],[m__979]) ).
cnf(l44,plain,
aInteger0(xp),
inference(instantiation,[status(thm)],[34]) ).
cnf(l90,plain,
aInteger0(xp),
inference(instantiation,[status(thm)],[34]) ).
cnf(l48,plain,
aInteger0(xq),
inference(instantiation,[status(thm)],[36]) ).
cnf(24,plain,
( ~ aInteger0(X0)
| ~ aDivisorOf0(X1,X0)
| aInteger0(sK1(X0,X1)) ),
inference(cnf,[status(esa)],[mDivisor]) ).
cnf(l1,plain,
( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
| aInteger0(sK1(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq))) ),
inference(instantiation,[status(thm)],[24]) ).
cnf(37,plain,
xq != sz00,
inference(cnf,[status(esa)],[m__979]) ).
cnf(l91,plain,
xq != sz00,
inference(instantiation,[status(thm)],[37]) ).
cnf(l50,plain,
( ~ aInteger0(xa)
| ~ aInteger0(xb)
| ~ aInteger0(sdtasdt0(xp,xq))
| ~ sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
| sdtasdt0(xp,xq) = sz00
| aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))) ),
inference(instantiation,[status(thm)],[27]) ).
cnf(l53,plain,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
inference(instantiation,[status(thm)],[38]) ).
cnf(l52,plain,
aInteger0(xa),
inference(instantiation,[status(thm)],[32]) ).
cnf(l61,plain,
( ~ aInteger0(xp)
| ~ aInteger0(xq)
| aInteger0(sdtasdt0(xp,xq)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l78,plain,
aInteger0(xp),
inference(instantiation,[status(thm)],[34]) ).
cnf(35,plain,
xp != sz00,
inference(cnf,[status(esa)],[m__979]) ).
cnf(l73,plain,
xp != sz00,
inference(instantiation,[status(thm)],[35]) ).
cnf(l63,plain,
aInteger0(xq),
inference(instantiation,[status(thm)],[36]) ).
cnf(l60,plain,
aInteger0(xb),
inference(instantiation,[status(thm)],[33]) ).
cnf(l49,plain,
( ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l57,plain,
( ~ aInteger0(xb)
| aInteger0(smndt0(xb)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l59,plain,
aInteger0(xa),
inference(instantiation,[status(thm)],[32]) ).
cnf(l81,plain,
aInteger0(xb),
inference(instantiation,[status(thm)],[33]) ).
cnf(l51,plain,
( ~ aInteger0(xp)
| ~ aInteger0(xq)
| sdtasdt0(xp,xq) != sz00
| xp = sz00
| xq = sz00 ),
inference(instantiation,[status(thm)],[21]) ).
cnf(l95,plain,
aInteger0(xq),
inference(instantiation,[status(thm)],[36]) ).
cnf(l80,plain,
aInteger0(xp),
inference(instantiation,[status(thm)],[34]) ).
cnf(l83,plain,
xp != sz00,
inference(instantiation,[status(thm)],[35]) ).
cnf(l82,plain,
xq != sz00,
inference(instantiation,[status(thm)],[37]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l2,l3,l5,l8,l15,l4,l43,l16,l64,l17,l70,l89,l44,l90,l48,l1,l91,l50,l53,l52,l61,l78,l73,l63,l60,l49,l57,l59,l81,l51,l95,l80,l83,l82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM434+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Jul 21 12:02:49 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.33 % launching worker at depth: 1
% 0.13/0.33 % launching worker at depth: 4
% 0.13/0.33 % launching worker at depth: 7
% 0.13/0.33 % launching worker at depth: 5
% 0.13/0.33 % launching worker at depth: 3
% 0.13/0.33 % launching worker at depth: 6
% 0.13/0.33 % launching worker at depth: 2
% 0.13/0.33 % launching worker at depth: 8
% 0.13/0.33 % launching worker at depth: 9
% 0.13/0.34 % launching worker at depth: 10
% 0.13/0.36 % launching worker at depth: 11
% 0.20/0.47 % SZS status Theorem for theBenchmark
% 0.20/0.47 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------