%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM505+1 : 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 : n013.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 04:57:36 PM UTC 2026
% Result : Theorem 1.35s 1.75s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 13 unt; 0 def)
% Number of atoms : 152 ( 48 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 181 ( 69 ~; 77 |; 24 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 20 !; 0 ?)
% 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/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(m__,conjecture,
( ~ sdtlseqdt0(xp,xk)
=> ( xk != xp
& sdtlseqdt0(xk,xp) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mLERefl,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).
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(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(c_0_10,plain,
! [X149,X150,X151] :
( ( aNaturalNumber0(X151)
| X151 != sdtsldt0(X150,X149)
| X149 = sz00
| ~ doDivides0(X149,X150)
| ~ aNaturalNumber0(X149)
| ~ aNaturalNumber0(X150) )
& ( X150 = sdtasdt0(X149,X151)
| X151 != sdtsldt0(X150,X149)
| X149 = sz00
| ~ doDivides0(X149,X150)
| ~ aNaturalNumber0(X149)
| ~ aNaturalNumber0(X150) )
& ( ~ aNaturalNumber0(X151)
| X150 != sdtasdt0(X149,X151)
| X151 = sdtsldt0(X150,X149)
| X149 = sz00
| ~ doDivides0(X149,X150)
| ~ aNaturalNumber0(X149)
| ~ aNaturalNumber0(X150) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
fof(c_0_11,negated_conjecture,
~ ( ~ sdtlseqdt0(xp,xk)
=> ( xk != xp
& sdtlseqdt0(xk,xp) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_12,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,negated_conjecture,
( ~ sdtlseqdt0(xp,xk)
& ( xk = xp
| ~ sdtlseqdt0(xk,xp) ) ),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X132,X133] :
( ( X133 != X132
| sdtlseqdt0(X132,X133)
| ~ aNaturalNumber0(X132)
| ~ aNaturalNumber0(X133) )
& ( sdtlseqdt0(X133,X132)
| sdtlseqdt0(X132,X133)
| ~ aNaturalNumber0(X132)
| ~ aNaturalNumber0(X133) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
cnf(c_0_15,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_16,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_17,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_18,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_19,plain,
! [X91,X92] :
( ~ aNaturalNumber0(X91)
| ~ aNaturalNumber0(X92)
| aNaturalNumber0(sdtasdt0(X91,X92)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_20,negated_conjecture,
( xk = xp
| ~ sdtlseqdt0(xk,xp) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
~ sdtlseqdt0(xp,xk),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,hypothesis,
( xp = sz00
| aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_24,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_26,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_27,negated_conjecture,
( xk = xp
| ~ aNaturalNumber0(xk) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_18])]),c_0_22]) ).
cnf(c_0_28,hypothesis,
( xp = sz00
| aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_29,negated_conjecture,
( xp = sz00
| xk = xp ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_30,plain,
! [X126] :
( ~ aNaturalNumber0(X126)
| sdtlseqdt0(X126,X126) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERefl])]) ).
fof(c_0_31,plain,
! [X166,X167] :
( ( X166 != sz00
| ~ isPrime0(X166)
| ~ aNaturalNumber0(X166) )
& ( X166 != sz10
| ~ isPrime0(X166)
| ~ aNaturalNumber0(X166) )
& ( ~ aNaturalNumber0(X167)
| ~ doDivides0(X167,X166)
| X167 = sz10
| X167 = X166
| ~ isPrime0(X166)
| ~ aNaturalNumber0(X166) )
& ( aNaturalNumber0(esk3_1(X166))
| X166 = sz00
| X166 = sz10
| isPrime0(X166)
| ~ aNaturalNumber0(X166) )
& ( doDivides0(esk3_1(X166),X166)
| X166 = sz00
| X166 = sz10
| isPrime0(X166)
| ~ aNaturalNumber0(X166) )
& ( esk3_1(X166) != sz10
| X166 = sz00
| X166 = sz10
| isPrime0(X166)
| ~ aNaturalNumber0(X166) )
& ( esk3_1(X166) != X166
| X166 = sz00
| X166 = sz10
| isPrime0(X166)
| ~ aNaturalNumber0(X166) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefPrime])])])])]) ).
cnf(c_0_32,negated_conjecture,
( xp = sz00
| ~ sdtlseqdt0(xp,xp) ),
inference(spm,[status(thm)],[c_0_22,c_0_29]) ).
cnf(c_0_33,plain,
( sdtlseqdt0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
( X1 != sz00
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_36,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_37,negated_conjecture,
xp = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_18])]) ).
cnf(c_0_38,plain,
~ isPrime0(sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_34]),c_0_35])]) ).
cnf(c_0_39,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM505+1 : 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
% 0.14/0.33 % Computer : n013.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 00:40:56 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.35/1.75 % Version : CSE_E---1.7
% 1.35/1.75 % Problem : theBenchmark.p
% 1.35/1.75 % SZS status Theorem for theBenchmark.p
% 1.35/1.75 % SZS output start CNFRefutation
% See solution above
% 1.35/1.75 % Total time : 1.374s
%------------------------------------------------------------------------------