%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM496+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 : n005.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 04:57:33 PM UTC 2026
% Result : Theorem 1.33s 1.74s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 42 ( 14 unt; 0 def)
% Number of atoms : 136 ( 24 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 163 ( 69 ~; 67 |; 18 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 23 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( doDivides0(xp,xn)
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( X3 = sdtmndt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
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(mDivSum,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X1,X3) )
=> doDivides0(X1,sdtpldt0(X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivSum) ).
fof(m__2027,hypothesis,
( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2027) ).
fof(m__1870,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
fof(m__1883,hypothesis,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
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(c_0_11,negated_conjecture,
~ ( doDivides0(xp,xn)
| doDivides0(xp,xm) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_12,plain,
! [X123,X124,X125] :
( ( aNaturalNumber0(X125)
| X125 != sdtmndt0(X124,X123)
| ~ sdtlseqdt0(X123,X124)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) )
& ( sdtpldt0(X123,X125) = X124
| X125 != sdtmndt0(X124,X123)
| ~ sdtlseqdt0(X123,X124)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) )
& ( ~ aNaturalNumber0(X125)
| sdtpldt0(X123,X125) != X124
| X125 = sdtmndt0(X124,X123)
| ~ sdtlseqdt0(X123,X124)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).
fof(c_0_13,negated_conjecture,
( ~ doDivides0(xp,xn)
& ~ doDivides0(xp,xm) ),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
cnf(c_0_14,plain,
( aNaturalNumber0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X145,X146,X148] :
( ( aNaturalNumber0(esk2_2(X145,X146))
| ~ doDivides0(X145,X146)
| ~ aNaturalNumber0(X145)
| ~ aNaturalNumber0(X146) )
& ( X146 = sdtasdt0(X145,esk2_2(X145,X146))
| ~ doDivides0(X145,X146)
| ~ aNaturalNumber0(X145)
| ~ aNaturalNumber0(X146) )
& ( ~ aNaturalNumber0(X148)
| X146 != sdtasdt0(X145,X148)
| doDivides0(X145,X146)
| ~ aNaturalNumber0(X145)
| ~ aNaturalNumber0(X146) ) ),
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_16,plain,
! [X91,X92] :
( ~ aNaturalNumber0(X91)
| ~ aNaturalNumber0(X92)
| aNaturalNumber0(sdtasdt0(X91,X92)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_17,plain,
! [X155,X156,X157] :
( ~ aNaturalNumber0(X155)
| ~ aNaturalNumber0(X156)
| ~ aNaturalNumber0(X157)
| ~ doDivides0(X155,X156)
| ~ doDivides0(X155,X157)
| doDivides0(X155,sdtpldt0(X156,X157)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])]) ).
cnf(c_0_18,hypothesis,
( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
inference(split_conjunct,[status(thm)],[m__2027]) ).
cnf(c_0_19,negated_conjecture,
~ doDivides0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( aNaturalNumber0(sdtmndt0(X1,X2))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_21,hypothesis,
sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[m__1870]) ).
cnf(c_0_22,hypothesis,
xr = sdtmndt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__1883]) ).
cnf(c_0_23,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_24,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_25,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_27,plain,
! [X104] :
( ( sdtasdt0(X104,sz10) = X104
| ~ aNaturalNumber0(X104) )
& ( X104 = sdtasdt0(sz10,X104)
| ~ aNaturalNumber0(X104) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
cnf(c_0_28,plain,
( doDivides0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_29,hypothesis,
doDivides0(xp,xr),
inference(sr,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_30,hypothesis,
aNaturalNumber0(xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23]),c_0_24])]) ).
cnf(c_0_31,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_25]),c_0_26]) ).
cnf(c_0_32,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_34,plain,
( sdtpldt0(X1,X2) = X3
| X2 != sdtmndt0(X3,X1)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_35,hypothesis,
( doDivides0(xp,sdtpldt0(X1,xr))
| ~ doDivides0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_23])]) ).
cnf(c_0_36,plain,
( doDivides0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_37,plain,
( sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_38,hypothesis,
doDivides0(xp,sdtpldt0(xp,xr)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_23])]) ).
cnf(c_0_39,hypothesis,
sdtpldt0(xp,xr) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_21]),c_0_22]),c_0_24]),c_0_23])]) ).
cnf(c_0_40,negated_conjecture,
~ doDivides0(xp,xn),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_41,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM496+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
% 0.14/0.32 % Computer : n005.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 00:38:00 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.33/1.74 % Version : CSE_E---1.7
% 1.33/1.74 % Problem : theBenchmark.p
% 1.33/1.74 % SZS status Theorem for theBenchmark.p
% 1.33/1.74 % SZS output start CNFRefutation
% See solution above
% 1.33/1.74 % Total time : 1.372s
%------------------------------------------------------------------------------