%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM482+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 : n009.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 04:57:30 PM UTC 2026
% Result : Theorem 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 5 unt; 0 def)
% Number of atoms : 143 ( 67 equ)
% Maximal formula atoms : 83 ( 11 avg)
% Number of connectives : 189 ( 59 ~; 82 |; 41 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 10 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xk = sdtasdt0(X1,X2) )
| doDivides0(X1,xk) ) )
=> ( X1 = sz10
| X1 = xk ) )
& isPrime0(xk) )
=> ? [X1] :
( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xk = sdtasdt0(X1,X2) )
| doDivides0(X1,xk) )
& ( ( X1 != sz00
& X1 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& X1 = sdtasdt0(X2,X3) )
& doDivides0(X2,X1) )
=> ( X2 = sz10
| X2 = X1 ) ) )
| isPrime0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__1716,hypothesis,
aNaturalNumber0(xk),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1716) ).
fof(c_0_4,negated_conjecture,
~ ( ( ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xk = sdtasdt0(X1,X2) )
| doDivides0(X1,xk) ) )
=> ( X1 = sz10
| X1 = xk ) )
& isPrime0(xk) )
=> ? [X1] :
( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xk = sdtasdt0(X1,X2) )
| doDivides0(X1,xk) )
& ( ( X1 != sz00
& X1 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& X1 = sdtasdt0(X2,X3) )
& doDivides0(X2,X1) )
=> ( X2 = sz10
| X2 = X1 ) ) )
| isPrime0(X1) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_5,negated_conjecture,
! [X181,X182,X183,X184] :
( ( ~ aNaturalNumber0(X182)
| xk != sdtasdt0(X181,X182)
| ~ aNaturalNumber0(X181)
| X181 = sz10
| X181 = xk )
& ( ~ doDivides0(X181,xk)
| ~ aNaturalNumber0(X181)
| X181 = sz10
| X181 = xk )
& isPrime0(xk)
& ( aNaturalNumber0(esk6_1(X183))
| X183 = sz00
| X183 = sz10
| ~ aNaturalNumber0(X184)
| xk != sdtasdt0(X183,X184)
| ~ aNaturalNumber0(X183) )
& ( aNaturalNumber0(esk7_1(X183))
| X183 = sz00
| X183 = sz10
| ~ aNaturalNumber0(X184)
| xk != sdtasdt0(X183,X184)
| ~ aNaturalNumber0(X183) )
& ( X183 = sdtasdt0(esk6_1(X183),esk7_1(X183))
| X183 = sz00
| X183 = sz10
| ~ aNaturalNumber0(X184)
| xk != sdtasdt0(X183,X184)
| ~ aNaturalNumber0(X183) )
& ( doDivides0(esk6_1(X183),X183)
| X183 = sz00
| X183 = sz10
| ~ aNaturalNumber0(X184)
| xk != sdtasdt0(X183,X184)
| ~ aNaturalNumber0(X183) )
& ( esk6_1(X183) != sz10
| X183 = sz00
| X183 = sz10
| ~ aNaturalNumber0(X184)
| xk != sdtasdt0(X183,X184)
| ~ aNaturalNumber0(X183) )
& ( esk6_1(X183) != X183
| X183 = sz00
| X183 = sz10
| ~ aNaturalNumber0(X184)
| xk != sdtasdt0(X183,X184)
| ~ aNaturalNumber0(X183) )
& ( ~ isPrime0(X183)
| ~ aNaturalNumber0(X184)
| xk != sdtasdt0(X183,X184)
| ~ aNaturalNumber0(X183) )
& ( aNaturalNumber0(esk6_1(X183))
| X183 = sz00
| X183 = sz10
| ~ doDivides0(X183,xk)
| ~ aNaturalNumber0(X183) )
& ( aNaturalNumber0(esk7_1(X183))
| X183 = sz00
| X183 = sz10
| ~ doDivides0(X183,xk)
| ~ aNaturalNumber0(X183) )
& ( X183 = sdtasdt0(esk6_1(X183),esk7_1(X183))
| X183 = sz00
| X183 = sz10
| ~ doDivides0(X183,xk)
| ~ aNaturalNumber0(X183) )
& ( doDivides0(esk6_1(X183),X183)
| X183 = sz00
| X183 = sz10
| ~ doDivides0(X183,xk)
| ~ aNaturalNumber0(X183) )
& ( esk6_1(X183) != sz10
| X183 = sz00
| X183 = sz10
| ~ doDivides0(X183,xk)
| ~ aNaturalNumber0(X183) )
& ( esk6_1(X183) != X183
| X183 = sz00
| X183 = sz10
| ~ doDivides0(X183,xk)
| ~ aNaturalNumber0(X183) )
& ( ~ isPrime0(X183)
| ~ doDivides0(X183,xk)
| ~ 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)],[c_0_4])])])])]) ).
fof(c_0_6,plain,
! [X111] :
( ( sdtasdt0(X111,sz10) = X111
| ~ aNaturalNumber0(X111) )
& ( X111 = sdtasdt0(sz10,X111)
| ~ aNaturalNumber0(X111) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
cnf(c_0_7,negated_conjecture,
( ~ isPrime0(X1)
| ~ aNaturalNumber0(X2)
| xk != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_10,negated_conjecture,
isPrime0(xk),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__1716]) ).
cnf(c_0_12,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9])])]),c_0_10]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM482+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
% 0.16/0.33 % Computer : n009.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 00:37:41 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Theorem for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------