%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM500+3 : 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 : 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 04:57:34 PM UTC 2026
% Result : Theorem 1.91s 1.90s
% Output : CNFRefutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 4 unt; 0 def)
% Number of atoms : 147 ( 73 equ)
% Maximal formula atoms : 73 ( 8 avg)
% Number of connectives : 194 ( 64 ~; 89 |; 38 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 6 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [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/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mPrimDiv,axiom,
! [X1] :
( ( aNaturalNumber0(X1)
& X1 != sz00
& X1 != sz10 )
=> ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimDiv) ).
fof(m__2315,hypothesis,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).
fof(m__2306,hypothesis,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(c_0_4,negated_conjecture,
~ ? [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,
! [X204,X205] :
( ( aNaturalNumber0(esk12_1(X204))
| X204 = sz00
| X204 = sz10
| ~ aNaturalNumber0(X205)
| xk != sdtasdt0(X204,X205)
| ~ aNaturalNumber0(X204) )
& ( aNaturalNumber0(esk13_1(X204))
| X204 = sz00
| X204 = sz10
| ~ aNaturalNumber0(X205)
| xk != sdtasdt0(X204,X205)
| ~ aNaturalNumber0(X204) )
& ( X204 = sdtasdt0(esk12_1(X204),esk13_1(X204))
| X204 = sz00
| X204 = sz10
| ~ aNaturalNumber0(X205)
| xk != sdtasdt0(X204,X205)
| ~ aNaturalNumber0(X204) )
& ( doDivides0(esk12_1(X204),X204)
| X204 = sz00
| X204 = sz10
| ~ aNaturalNumber0(X205)
| xk != sdtasdt0(X204,X205)
| ~ aNaturalNumber0(X204) )
& ( esk12_1(X204) != sz10
| X204 = sz00
| X204 = sz10
| ~ aNaturalNumber0(X205)
| xk != sdtasdt0(X204,X205)
| ~ aNaturalNumber0(X204) )
& ( esk12_1(X204) != X204
| X204 = sz00
| X204 = sz10
| ~ aNaturalNumber0(X205)
| xk != sdtasdt0(X204,X205)
| ~ aNaturalNumber0(X204) )
& ( ~ isPrime0(X204)
| ~ aNaturalNumber0(X205)
| xk != sdtasdt0(X204,X205)
| ~ aNaturalNumber0(X204) )
& ( aNaturalNumber0(esk12_1(X204))
| X204 = sz00
| X204 = sz10
| ~ doDivides0(X204,xk)
| ~ aNaturalNumber0(X204) )
& ( aNaturalNumber0(esk13_1(X204))
| X204 = sz00
| X204 = sz10
| ~ doDivides0(X204,xk)
| ~ aNaturalNumber0(X204) )
& ( X204 = sdtasdt0(esk12_1(X204),esk13_1(X204))
| X204 = sz00
| X204 = sz10
| ~ doDivides0(X204,xk)
| ~ aNaturalNumber0(X204) )
& ( doDivides0(esk12_1(X204),X204)
| X204 = sz00
| X204 = sz10
| ~ doDivides0(X204,xk)
| ~ aNaturalNumber0(X204) )
& ( esk12_1(X204) != sz10
| X204 = sz00
| X204 = sz10
| ~ doDivides0(X204,xk)
| ~ aNaturalNumber0(X204) )
& ( esk12_1(X204) != X204
| X204 = sz00
| X204 = sz10
| ~ doDivides0(X204,xk)
| ~ aNaturalNumber0(X204) )
& ( ~ isPrime0(X204)
| ~ doDivides0(X204,xk)
| ~ aNaturalNumber0(X204) ) ),
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,
! [X187] :
( ( aNaturalNumber0(esk4_1(X187))
| ~ aNaturalNumber0(X187)
| X187 = sz00
| X187 = sz10 )
& ( doDivides0(esk4_1(X187),X187)
| ~ aNaturalNumber0(X187)
| X187 = sz00
| X187 = sz10 )
& ( isPrime0(esk4_1(X187))
| ~ aNaturalNumber0(X187)
| X187 = sz00
| X187 = sz10 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPrimDiv])])])]) ).
cnf(c_0_7,negated_conjecture,
( ~ isPrime0(X1)
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( isPrime0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( aNaturalNumber0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,hypothesis,
( xk != sz00
& xk != sz10 ),
inference(fof_nnf,[status(thm)],[m__2315]) ).
cnf(c_0_11,negated_conjecture,
( X1 = sz10
| X1 = sz00
| ~ doDivides0(esk4_1(X1),xk)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
cnf(c_0_12,plain,
( doDivides0(esk4_1(X1),X1)
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_14,hypothesis,
xk != sz10,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]),c_0_14]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM500+3 : 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 : n015.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 00:40:17 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.91/1.90 % Version : CSE_E---1.7
% 1.91/1.90 % Problem : theBenchmark.p
% 1.91/1.90 % SZS status Theorem for theBenchmark.p
% 1.91/1.90 % SZS output start CNFRefutation
% See solution above
% 1.91/1.90 % Total time : 1.377s
%------------------------------------------------------------------------------