%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM482+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n020.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 1.31s 1.74s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 9 unt; 0 def)
% Number of atoms : 118 ( 40 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 149 ( 62 ~; 62 |; 17 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 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 : 37 ( 0 sgn 14 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(m__1716,hypothesis,
aNaturalNumber0(xk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__,conjecture,
( isPrime0(xk)
=> ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,xk)
& isPrime0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_6,plain,
! [X147,X148,X149] :
( ( aNaturalNumber0(X149)
| X149 != sdtsldt0(X148,X147)
| X147 = sz00
| ~ doDivides0(X147,X148)
| ~ aNaturalNumber0(X147)
| ~ aNaturalNumber0(X148) )
& ( X148 = sdtasdt0(X147,X149)
| X149 != sdtsldt0(X148,X147)
| X147 = sz00
| ~ doDivides0(X147,X148)
| ~ aNaturalNumber0(X147)
| ~ aNaturalNumber0(X148) )
& ( ~ aNaturalNumber0(X149)
| X148 != sdtasdt0(X147,X149)
| X149 = sdtsldt0(X148,X147)
| X147 = sz00
| ~ doDivides0(X147,X148)
| ~ aNaturalNumber0(X147)
| ~ aNaturalNumber0(X148) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
fof(c_0_7,plain,
! [X143,X144,X146] :
( ( aNaturalNumber0(esk2_2(X143,X144))
| ~ doDivides0(X143,X144)
| ~ aNaturalNumber0(X143)
| ~ aNaturalNumber0(X144) )
& ( X144 = sdtasdt0(X143,esk2_2(X143,X144))
| ~ doDivides0(X143,X144)
| ~ aNaturalNumber0(X143)
| ~ aNaturalNumber0(X144) )
& ( ~ aNaturalNumber0(X146)
| X144 != sdtasdt0(X143,X146)
| doDivides0(X143,X144)
| ~ aNaturalNumber0(X143)
| ~ aNaturalNumber0(X144) ) ),
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_8,plain,
! [X102] :
( ( sdtasdt0(X102,sz10) = X102
| ~ aNaturalNumber0(X102) )
& ( X102 = sdtasdt0(sz10,X102)
| ~ aNaturalNumber0(X102) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
cnf(c_0_9,plain,
( X1 = sdtsldt0(X2,X3)
| X3 = sz00
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__1716]) ).
cnf(c_0_13,plain,
( X1 = sdtsldt0(X2,X3)
| X3 = sz00
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,hypothesis,
sdtasdt0(sz10,xk) = xk,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_16,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_17,hypothesis,
( sdtsldt0(X1,sz10) = xk
| X1 != xk
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_12])]),c_0_16]) ).
cnf(c_0_18,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,hypothesis,
sdtsldt0(xk,sz10) = xk,
inference(spm,[status(thm)],[c_0_17,c_0_12]) ).
fof(c_0_20,negated_conjecture,
~ ( isPrime0(xk)
=> ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,xk)
& isPrime0(X1) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_21,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,hypothesis,
( aNaturalNumber0(X1)
| X1 != xk
| ~ doDivides0(sz10,xk) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_15]),c_0_12])]),c_0_16]) ).
cnf(c_0_23,hypothesis,
( doDivides0(sz10,X1)
| X1 != xk
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_14]),c_0_15]),c_0_12])]) ).
fof(c_0_24,negated_conjecture,
! [X169] :
( isPrime0(xk)
& ( ~ aNaturalNumber0(X169)
| ~ doDivides0(X169,xk)
| ~ isPrime0(X169) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
cnf(c_0_25,hypothesis,
sdtasdt0(xk,sz10) = xk,
inference(spm,[status(thm)],[c_0_21,c_0_12]) ).
cnf(c_0_26,hypothesis,
( aNaturalNumber0(X1)
| X1 != xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_12])]) ).
cnf(c_0_27,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xk)
| ~ isPrime0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,hypothesis,
( doDivides0(xk,X1)
| X1 != xk ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_25]),c_0_12]),c_0_15])]),c_0_26]) ).
cnf(c_0_29,negated_conjecture,
isPrime0(xk),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM482+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n020.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 00:38:05 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.31/1.74 % Version : CSE_E---1.7
% 1.31/1.74 % Problem : theBenchmark.p
% 1.31/1.74 % SZS status Theorem for theBenchmark.p
% 1.31/1.74 % SZS output start CNFRefutation
% See solution above
% 1.31/1.74 % Total time : 1.374s
%------------------------------------------------------------------------------