%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM494+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 : 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 12:28:18 PM UTC 2025
% Result : Theorem 38.63s 5.23s
% Output : CNFRefutation 38.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of formulae : 83 ( 51 unt; 0 def)
% Number of atoms : 187 ( 46 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 189 ( 85 ~; 78 |; 16 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,plain,
( sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
& sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m___negated,plain,
~ ( sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
& sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(79,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l0,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(instantiation,[status(thm)],[79]) ).
fof(mAddCanc,plain,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2)
| sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
=> W1 = W2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
cnf(18,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| X1 = X2 ),
inference(cnf,[status(esa)],[mAddCanc]) ).
cnf(l4,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xr,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(xr,xm) = sdtpldt0(xn,xm) ),
inference(instantiation,[status(thm)],[18]) ).
fof(m__1837,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
cnf(70,plain,
aNaturalNumber0(xp),
inference(cnf,[status(esa)],[m__1837]) ).
cnf(l182,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
fof(mMonAdd,plain,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 != W1
& sdtlseqdt0(W0,W1) )
=> ! [W2] :
( aNaturalNumber0(W2)
=> ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1)
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
cnf(38,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) ),
inference(cnf,[status(esa)],[mMonAdd]) ).
cnf(l1,plain,
( ~ aNaturalNumber0(sdtpldt0(xr,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))
| sdtpldt0(xr,xm) = sdtpldt0(xn,xm)
| sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(instantiation,[status(thm)],[38]) ).
cnf(l18,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xr,xn)
| xr = xn
| sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm)) ),
inference(instantiation,[status(thm)],[38]) ).
cnf(69,plain,
aNaturalNumber0(xm),
inference(cnf,[status(esa)],[m__1837]) ).
cnf(l38,plain,
aNaturalNumber0(xm),
inference(instantiation,[status(thm)],[69]) ).
fof(mSortsB,plain,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
cnf(3,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf,[status(esa)],[mSortsB]) ).
cnf(l143,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xr,xm)) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l187,plain,
aNaturalNumber0(xm),
inference(instantiation,[status(thm)],[69]) ).
fof(mDefDiff,plain,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( aNaturalNumber0(W2)
& sdtpldt0(W0,W2) = W1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
cnf(27,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X2 != sdtmndt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(X2) ),
inference(cnf,[status(esa)],[mDefDiff]) ).
cnf(l43,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| xr != sdtmndt0(xn,xp)
| ~ sdtlseqdt0(xp,xn)
| aNaturalNumber0(xr) ),
inference(instantiation,[status(thm)],[27]) ).
cnf(68,plain,
aNaturalNumber0(xn),
inference(cnf,[status(esa)],[m__1837]) ).
cnf(l34,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
fof(m__1883,plain,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
cnf(75,plain,
xr = sdtmndt0(xn,xp),
inference(cnf,[status(esa)],[m__1883]) ).
cnf(l91,plain,
xr = sdtmndt0(xn,xp),
inference(instantiation,[status(thm)],[75]) ).
cnf(l92,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
cnf(l2,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| sdtpldt0(xr,xm) != sdtpldt0(xn,xm)
| xr = xn ),
inference(instantiation,[status(thm)],[18]) ).
fof(m__1870,plain,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
cnf(74,plain,
sdtlseqdt0(xp,xn),
inference(cnf,[status(esa)],[m__1870]) ).
cnf(l112,plain,
sdtlseqdt0(xp,xn),
inference(instantiation,[status(thm)],[74]) ).
cnf(l74,plain,
aNaturalNumber0(xm),
inference(instantiation,[status(thm)],[69]) ).
cnf(l14,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| xr != sdtmndt0(xn,xp)
| ~ sdtlseqdt0(xp,xn)
| aNaturalNumber0(xr) ),
inference(instantiation,[status(thm)],[27]) ).
cnf(l47,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
cnf(l15,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xr,xm)) ),
inference(instantiation,[status(thm)],[3]) ).
fof(m__1894,plain,
( xr != xn
& sdtlseqdt0(xr,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1894) ).
cnf(76,plain,
xr != xn,
inference(cnf,[status(esa)],[m__1894]) ).
cnf(l80,plain,
xr != xn,
inference(instantiation,[status(thm)],[76]) ).
cnf(l122,plain,
xr != xn,
inference(instantiation,[status(thm)],[76]) ).
cnf(l51,plain,
xr = sdtmndt0(xn,xp),
inference(instantiation,[status(thm)],[75]) ).
cnf(l39,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| xr != sdtmndt0(xn,xp)
| ~ sdtlseqdt0(xp,xn)
| aNaturalNumber0(xr) ),
inference(instantiation,[status(thm)],[27]) ).
cnf(l64,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
cnf(l16,plain,
sdtlseqdt0(xp,xn),
inference(instantiation,[status(thm)],[74]) ).
cnf(l184,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| xr != sdtmndt0(xn,xp)
| ~ sdtlseqdt0(xp,xn)
| aNaturalNumber0(xr) ),
inference(instantiation,[status(thm)],[27]) ).
cnf(77,plain,
sdtlseqdt0(xr,xn),
inference(cnf,[status(esa)],[m__1894]) ).
cnf(l67,plain,
sdtlseqdt0(xr,xn),
inference(instantiation,[status(thm)],[77]) ).
cnf(l116,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
cnf(l20,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
cnf(l3,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l70,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
cnf(l42,plain,
sdtlseqdt0(xp,xn),
inference(instantiation,[status(thm)],[74]) ).
cnf(l5,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
cnf(l129,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
cnf(37,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf,[status(esa)],[mMonAdd]) ).
cnf(l125,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sdtpldt0(xr,xm) != sdtpldt0(xn,xm)
| ~ sdtlseqdt0(xr,xn)
| xr = xn ),
inference(instantiation,[status(thm)],[37]) ).
cnf(l214,plain,
sdtlseqdt0(xp,xn),
inference(instantiation,[status(thm)],[74]) ).
cnf(l35,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
cnf(l504,plain,
sdtlseqdt0(xr,xn),
inference(instantiation,[status(thm)],[77]) ).
cnf(l274,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
cnf(l23,plain,
aNaturalNumber0(xm),
inference(instantiation,[status(thm)],[69]) ).
cnf(l72,plain,
xr = sdtmndt0(xn,xp),
inference(instantiation,[status(thm)],[75]) ).
cnf(l275,plain,
aNaturalNumber0(xm),
inference(instantiation,[status(thm)],[69]) ).
cnf(l212,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
cnf(l133,plain,
aNaturalNumber0(xm),
inference(instantiation,[status(thm)],[69]) ).
cnf(l284,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| xr != sdtmndt0(xn,xp)
| ~ sdtlseqdt0(xp,xn)
| aNaturalNumber0(xr) ),
inference(instantiation,[status(thm)],[27]) ).
fof(mAddComm,plain,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
cnf(5,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf,[status(esa)],[mAddComm]) ).
cnf(l21,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sdtpldt0(xm,xn) = sdtpldt0(xn,xm) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l320,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
cnf(l313,plain,
sdtlseqdt0(xp,xn),
inference(instantiation,[status(thm)],[74]) ).
cnf(l329,plain,
xr = sdtmndt0(xn,xp),
inference(instantiation,[status(thm)],[75]) ).
cnf(l210,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
cnf(l25,plain,
aNaturalNumber0(xm),
inference(instantiation,[status(thm)],[69]) ).
cnf(l59,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
cnf(l315,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
cnf(l109,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l211,plain,
xr = sdtmndt0(xn,xp),
inference(instantiation,[status(thm)],[75]) ).
cnf(l165,plain,
aNaturalNumber0(xm),
inference(instantiation,[status(thm)],[69]) ).
cnf(l166,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
cnf(l528,plain,
xr != xn,
inference(instantiation,[status(thm)],[76]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l4,l182,l1,l18,l38,l143,l187,l43,l34,l91,l92,l2,l112,l74,l14,l47,l15,l80,l122,l51,l39,l64,l16,l184,l67,l116,l20,l3,l70,l42,l5,l129,l125,l214,l35,l504,l274,l23,l72,l275,l212,l133,l284,l21,l320,l313,l329,l210,l25,l59,l315,l109,l211,l165,l166,l528]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM494+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/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 12:27:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.34 % launching worker at depth: 10
% 0.18/0.46 % launching worker at depth: 11
% 38.63/5.23 % SZS status Theorem for theBenchmark
% 38.63/5.23 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------