%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM498+3 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n014.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 : Tue May 5 04:57:34 PM UTC 2026
% Result : Theorem 1.77s 1.86s
% Output : CNFRefutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 17 unt; 0 def)
% Number of atoms : 179 ( 83 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 197 ( 69 ~; 66 |; 52 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 22 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( xk = sz00
| xk = sz10 )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xp,X1) )
| doDivides0(xp,xn)
| ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xp,X1) )
| doDivides0(xp,xm) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(m__2306,hypothesis,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(m__1860,hypothesis,
( xp != sz00
& xp != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xp = sdtasdt0(X1,X2) )
| doDivides0(X1,xp) ) )
=> ( X1 = sz10
| X1 = xp ) )
& isPrime0(xp)
& ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X1) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(m__2287,hypothesis,
( xn != xp
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = xp )
& sdtlseqdt0(xn,xp)
& xm != xp
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,X1) = xp )
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(c_0_12,negated_conjecture,
~ ( ( xk = sz00
| xk = sz10 )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xp,X1) )
| doDivides0(xp,xn)
| ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xp,X1) )
| doDivides0(xp,xm) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_13,negated_conjecture,
! [X202,X203] :
( ( xk = sz00
| xk = sz10 )
& ( ~ aNaturalNumber0(X202)
| xn != sdtasdt0(xp,X202) )
& ~ doDivides0(xp,xn)
& ( ~ aNaturalNumber0(X203)
| xm != sdtasdt0(xp,X203) )
& ~ doDivides0(xp,xm) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_14,plain,
! [X121] :
( ( sdtasdt0(X121,sz00) = sz00
| ~ aNaturalNumber0(X121) )
& ( sz00 = sdtasdt0(sz00,X121)
| ~ aNaturalNumber0(X121) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
fof(c_0_15,plain,
! [X133,X134] :
( ~ aNaturalNumber0(X133)
| ~ aNaturalNumber0(X134)
| sdtasdt0(X133,X134) != sz00
| X133 = sz00
| X134 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])]) ).
cnf(c_0_16,negated_conjecture,
( ~ aNaturalNumber0(X1)
| xm != sdtasdt0(xp,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_19,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_20,negated_conjecture,
( ~ aNaturalNumber0(X1)
| xn != sdtasdt0(xp,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_23,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_24,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_25,negated_conjecture,
xm != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19])]) ).
cnf(c_0_26,negated_conjecture,
xn != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_17]),c_0_18]),c_0_19])]) ).
fof(c_0_27,hypothesis,
! [X195,X196] :
( xp != sz00
& xp != sz10
& ( ~ aNaturalNumber0(X196)
| xp != sdtasdt0(X195,X196)
| ~ aNaturalNumber0(X195)
| X195 = sz10
| X195 = xp )
& ( ~ doDivides0(X195,xp)
| ~ aNaturalNumber0(X195)
| X195 = sz10
| X195 = xp )
& isPrime0(xp)
& aNaturalNumber0(esk9_0)
& sdtasdt0(xn,xm) = sdtasdt0(xp,esk9_0)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1860])])])])]) ).
fof(c_0_28,hypothesis,
( xn != xp
& aNaturalNumber0(esk10_0)
& sdtpldt0(xn,esk10_0) = xp
& sdtlseqdt0(xn,xp)
& xm != xp
& aNaturalNumber0(esk11_0)
& sdtpldt0(xm,esk11_0) = xp
& sdtlseqdt0(xm,xp) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2287])]) ).
cnf(c_0_29,hypothesis,
sdtasdt0(xp,xk) != sz00,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]),c_0_25]),c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( xk = sz00
| xk = sz10 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_31,hypothesis,
( X2 = sz10
| X2 = xp
| ~ aNaturalNumber0(X1)
| xp != sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,negated_conjecture,
( xk = sz10
| sdtasdt0(xp,sz00) != sz00 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,hypothesis,
( xn = sz10
| sdtasdt0(xp,xk) != xp ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_22]),c_0_24]),c_0_23])]),c_0_32]) ).
cnf(c_0_35,negated_conjecture,
xk = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_17]),c_0_19])]) ).
fof(c_0_36,plain,
! [X120] :
( ( sdtasdt0(X120,sz10) = X120
| ~ aNaturalNumber0(X120) )
& ( X120 = sdtasdt0(sz10,X120)
| ~ aNaturalNumber0(X120) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
cnf(c_0_37,hypothesis,
( xn = sz10
| sdtasdt0(xp,sz10) != xp ),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_39,plain,
! [X161,X162,X164] :
( ( aNaturalNumber0(esk2_2(X161,X162))
| ~ doDivides0(X161,X162)
| ~ aNaturalNumber0(X161)
| ~ aNaturalNumber0(X162) )
& ( X162 = sdtasdt0(X161,esk2_2(X161,X162))
| ~ doDivides0(X161,X162)
| ~ aNaturalNumber0(X161)
| ~ aNaturalNumber0(X162) )
& ( ~ aNaturalNumber0(X164)
| X162 != sdtasdt0(X161,X164)
| doDivides0(X161,X162)
| ~ aNaturalNumber0(X161)
| ~ aNaturalNumber0(X162) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).
fof(c_0_40,plain,
! [X107,X108] :
( ~ aNaturalNumber0(X107)
| ~ aNaturalNumber0(X108)
| aNaturalNumber0(sdtasdt0(X107,X108)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_41,hypothesis,
xn = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_19])]) ).
cnf(c_0_42,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_43,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,hypothesis,
sdtasdt0(sz10,xm) = sdtasdt0(xp,sz10),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_35]),c_0_41]) ).
cnf(c_0_46,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_42]),c_0_43]) ).
cnf(c_0_47,hypothesis,
sdtasdt0(xp,sz10) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_23])]) ).
cnf(c_0_48,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_49,negated_conjecture,
~ doDivides0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_50,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_19]),c_0_48])]),c_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM498+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.33 % Computer : n014.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 00:40:36 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 1.77/1.86 % Version : CSE_E---1.7
% 1.77/1.86 % Problem : theBenchmark.p
% 1.77/1.86 % SZS status Theorem for theBenchmark.p
% 1.77/1.86 % SZS output start CNFRefutation
% See solution above
% 1.77/1.87 % Total time : 1.371s
%------------------------------------------------------------------------------