%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM523+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 : 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 04:57:41 PM UTC 2026
% Result : Theorem 1.35s 1.74s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 134 ( 31 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 174 ( 72 ~; 67 |; 29 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 20 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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(m__,conjecture,
( ( ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xn) = sdtasdt0(xp,X1) )
| doDivides0(xp,sdtasdt0(xn,xn)) )
& ( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xp,X1) )
| doDivides0(xp,xn) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3014) ).
fof(m__2987,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2987) ).
fof(mPDP,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( isPrime0(X3)
& doDivides0(X3,sdtasdt0(X1,X2)) )
=> ( doDivides0(X3,X1)
| doDivides0(X3,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPDP) ).
fof(m__3025,hypothesis,
( xp != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xp = sdtasdt0(X1,X2) )
| doDivides0(X1,xp) ) )
=> ( X1 = sz10
| X1 = xp ) )
& isPrime0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3025) ).
fof(c_0_7,plain,
! [X156,X157,X159] :
( ( aNaturalNumber0(esk2_2(X156,X157))
| ~ doDivides0(X156,X157)
| ~ aNaturalNumber0(X156)
| ~ aNaturalNumber0(X157) )
& ( X157 = sdtasdt0(X156,esk2_2(X156,X157))
| ~ doDivides0(X156,X157)
| ~ aNaturalNumber0(X156)
| ~ aNaturalNumber0(X157) )
& ( ~ aNaturalNumber0(X159)
| X157 != sdtasdt0(X156,X159)
| doDivides0(X156,X157)
| ~ aNaturalNumber0(X156)
| ~ aNaturalNumber0(X157) ) ),
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,X103] :
( ~ aNaturalNumber0(X102)
| ~ aNaturalNumber0(X103)
| aNaturalNumber0(sdtasdt0(X102,X103)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_9,negated_conjecture,
~ ( ( ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xn) = sdtasdt0(xp,X1) )
| doDivides0(xp,sdtasdt0(xn,xn)) )
& ( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xp,X1) )
| doDivides0(xp,xn) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
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,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,negated_conjecture,
! [X192,X193] :
( ( ~ aNaturalNumber0(X193)
| xn != sdtasdt0(xp,X193)
| ~ aNaturalNumber0(X192)
| sdtasdt0(xn,xn) != sdtasdt0(xp,X192) )
& ( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(X192)
| sdtasdt0(xn,xn) != sdtasdt0(xp,X192) )
& ( ~ aNaturalNumber0(X193)
| xn != sdtasdt0(xp,X193)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) )
& ( ~ doDivides0(xp,xn)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
cnf(c_0_13,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_10]),c_0_11]) ).
cnf(c_0_14,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_15,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_16,negated_conjecture,
( ~ aNaturalNumber0(X1)
| xn != sdtasdt0(xp,X1)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_18,negated_conjecture,
( sdtasdt0(xp,X1) != xn
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_20,negated_conjecture,
( sdtasdt0(xp,X1) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_11]),c_0_19])]) ).
cnf(c_0_21,plain,
( X1 = sdtasdt0(X2,esk2_2(X2,X1))
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__2987]) ).
fof(c_0_23,plain,
! [X182,X183,X184] :
( ~ aNaturalNumber0(X182)
| ~ aNaturalNumber0(X183)
| ~ aNaturalNumber0(X184)
| ~ isPrime0(X184)
| ~ doDivides0(X184,sdtasdt0(X182,X183))
| doDivides0(X184,X182)
| doDivides0(X184,X183) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPDP])]) ).
fof(c_0_24,hypothesis,
! [X190,X191] :
( xp != sz10
& ( ~ aNaturalNumber0(X191)
| xp != sdtasdt0(X190,X191)
| ~ aNaturalNumber0(X190)
| X190 = sz10
| X190 = xp )
& ( ~ doDivides0(X190,xp)
| ~ aNaturalNumber0(X190)
| X190 = sz10
| X190 = xp )
& isPrime0(xp) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3025])])])]) ).
cnf(c_0_25,negated_conjecture,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(esk2_2(xp,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_15])])]),c_0_22])]) ).
cnf(c_0_26,plain,
( aNaturalNumber0(esk2_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,plain,
( doDivides0(X3,X1)
| doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ isPrime0(X3)
| ~ doDivides0(X3,sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
~ doDivides0(xp,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_22]),c_0_15])]) ).
cnf(c_0_30,hypothesis,
~ aNaturalNumber0(sdtasdt0(xm,xm)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_17]),c_0_28]),c_0_15]),c_0_22])]),c_0_29]) ).
cnf(c_0_31,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_11]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM523+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 : 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 00:42:34 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.35/1.74 % Version : CSE_E---1.7
% 1.35/1.74 % Problem : theBenchmark.p
% 1.35/1.74 % SZS status Theorem for theBenchmark.p
% 1.35/1.74 % SZS output start CNFRefutation
% See solution above
% 1.35/1.74 % Total time : 1.371s
%------------------------------------------------------------------------------