%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM496+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 : n015.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 04:57:33 PM UTC 2026
% Result : Theorem 2.07s 1.94s
% Output : CNFRefutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 13 unt; 0 def)
% Number of atoms : 216 ( 74 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 251 ( 78 ~; 104 |; 60 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 23 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ? [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__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(mPrimDiv,axiom,
! [X1] :
( ( aNaturalNumber0(X1)
& X1 != sz00
& X1 != sz10 )
=> ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimDiv) ).
fof(m__2027,hypothesis,
( ( ? [X1] :
( aNaturalNumber0(X1)
& xr = sdtasdt0(xp,X1) )
& doDivides0(xp,xr) )
| ( ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xp,X1) )
& doDivides0(xp,xm) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2027) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(mDefPrime,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( X1 != sz00
& X1 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& doDivides0(X2,X1) )
=> ( X2 = sz10
| X2 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(mDivTrans,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X2,X3) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mDivSum,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X1,X3) )
=> doDivides0(X1,sdtpldt0(X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivSum) ).
fof(m__1883,hypothesis,
( aNaturalNumber0(xr)
& sdtpldt0(xp,xr) = xn
& xr = sdtmndt0(xn,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
fof(c_0_10,negated_conjecture,
~ ( ? [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_11,hypothesis,
! [X196,X197] :
( xp != sz00
& xp != sz10
& ( ~ aNaturalNumber0(X197)
| xp != sdtasdt0(X196,X197)
| ~ aNaturalNumber0(X196)
| X196 = sz10
| X196 = xp )
& ( ~ doDivides0(X196,xp)
| ~ aNaturalNumber0(X196)
| X196 = sz10
| X196 = 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_12,plain,
! [X186] :
( ( aNaturalNumber0(esk4_1(X186))
| ~ aNaturalNumber0(X186)
| X186 = sz00
| X186 = sz10 )
& ( doDivides0(esk4_1(X186),X186)
| ~ aNaturalNumber0(X186)
| X186 = sz00
| X186 = sz10 )
& ( isPrime0(esk4_1(X186))
| ~ aNaturalNumber0(X186)
| X186 = sz00
| X186 = sz10 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPrimDiv])])])]) ).
fof(c_0_13,hypothesis,
( ( aNaturalNumber0(esk14_0)
| aNaturalNumber0(esk13_0) )
& ( xm = sdtasdt0(xp,esk14_0)
| aNaturalNumber0(esk13_0) )
& ( doDivides0(xp,xm)
| aNaturalNumber0(esk13_0) )
& ( aNaturalNumber0(esk14_0)
| xr = sdtasdt0(xp,esk13_0) )
& ( xm = sdtasdt0(xp,esk14_0)
| xr = sdtasdt0(xp,esk13_0) )
& ( doDivides0(xp,xm)
| xr = sdtasdt0(xp,esk13_0) )
& ( aNaturalNumber0(esk14_0)
| doDivides0(xp,xr) )
& ( xm = sdtasdt0(xp,esk14_0)
| doDivides0(xp,xr) )
& ( doDivides0(xp,xm)
| doDivides0(xp,xr) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2027])])]) ).
fof(c_0_14,negated_conjecture,
! [X204,X205] :
( ( ~ aNaturalNumber0(X204)
| xn != sdtasdt0(xp,X204) )
& ~ doDivides0(xp,xn)
& ( ~ aNaturalNumber0(X205)
| xm != sdtasdt0(xp,X205) )
& ~ doDivides0(xp,xm) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_15,hypothesis,
( X1 = sz10
| X1 = xp
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( doDivides0(esk4_1(X1),X1)
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_18,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,hypothesis,
xp != sz10,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_20,plain,
! [X183,X184] :
( ( X183 != sz00
| ~ isPrime0(X183)
| ~ aNaturalNumber0(X183) )
& ( X183 != sz10
| ~ isPrime0(X183)
| ~ aNaturalNumber0(X183) )
& ( ~ aNaturalNumber0(X184)
| ~ doDivides0(X184,X183)
| X184 = sz10
| X184 = X183
| ~ isPrime0(X183)
| ~ aNaturalNumber0(X183) )
& ( aNaturalNumber0(esk3_1(X183))
| X183 = sz00
| X183 = sz10
| isPrime0(X183)
| ~ aNaturalNumber0(X183) )
& ( doDivides0(esk3_1(X183),X183)
| X183 = sz00
| X183 = sz10
| isPrime0(X183)
| ~ aNaturalNumber0(X183) )
& ( esk3_1(X183) != sz10
| X183 = sz00
| X183 = sz10
| isPrime0(X183)
| ~ aNaturalNumber0(X183) )
& ( esk3_1(X183) != X183
| X183 = sz00
| X183 = sz10
| isPrime0(X183)
| ~ aNaturalNumber0(X183) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefPrime])])])])]) ).
fof(c_0_21,plain,
! [X169,X170,X171] :
( ~ aNaturalNumber0(X169)
| ~ aNaturalNumber0(X170)
| ~ aNaturalNumber0(X171)
| ~ doDivides0(X169,X170)
| ~ doDivides0(X170,X171)
| doDivides0(X169,X171) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])]) ).
cnf(c_0_22,hypothesis,
( doDivides0(xp,xm)
| doDivides0(xp,xr) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,negated_conjecture,
~ doDivides0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,hypothesis,
( esk4_1(xp) = xp
| esk4_1(xp) = sz10
| ~ aNaturalNumber0(esk4_1(xp)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),c_0_18]),c_0_19]) ).
cnf(c_0_25,plain,
( aNaturalNumber0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_26,plain,
( X1 != sz10
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
fof(c_0_28,plain,
! [X172,X173,X174] :
( ~ aNaturalNumber0(X172)
| ~ aNaturalNumber0(X173)
| ~ aNaturalNumber0(X174)
| ~ doDivides0(X172,X173)
| ~ doDivides0(X172,X174)
| doDivides0(X172,sdtpldt0(X173,X174)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])]) ).
cnf(c_0_29,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,hypothesis,
doDivides0(xp,xr),
inference(sr,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__1883]) ).
cnf(c_0_32,plain,
( isPrime0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_33,hypothesis,
( esk4_1(xp) = sz10
| esk4_1(xp) = xp ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_17])]),c_0_18]),c_0_19]) ).
cnf(c_0_34,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_26]),c_0_27])]) ).
cnf(c_0_35,plain,
( doDivides0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,hypothesis,
sdtpldt0(xp,xr) = xn,
inference(split_conjunct,[status(thm)],[m__1883]) ).
cnf(c_0_37,hypothesis,
( doDivides0(X1,xr)
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_17])]) ).
cnf(c_0_38,hypothesis,
esk4_1(xp) = xp,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_17])]),c_0_18]),c_0_19]),c_0_34]) ).
cnf(c_0_39,negated_conjecture,
~ doDivides0(xp,xn),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_40,hypothesis,
( doDivides0(X1,xn)
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_31]),c_0_17])]),c_0_37]) ).
cnf(c_0_41,hypothesis,
doDivides0(xp,xp),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_38]),c_0_17])]),c_0_18]),c_0_19]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM496+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 : n015.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 00:38:32 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 2.07/1.94 % Version : CSE_E---1.7
% 2.07/1.94 % Problem : theBenchmark.p
% 2.07/1.94 % SZS status Theorem for theBenchmark.p
% 2.07/1.94 % SZS output start CNFRefutation
% See solution above
% 2.07/1.94 % Total time : 1.372s
%------------------------------------------------------------------------------