%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM469+2 : 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 : n023.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 04:57:27 PM UTC 2026
% Result : Theorem 1.27s 1.73s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 89 ( 39 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 76 ( 21 ~; 23 |; 28 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 9 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X1) )
| doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1298,hypothesis,
( xl != sz00
=> ( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xn,xl))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1298) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(m__1240_04,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xl,X1) )
& doDivides0(xl,xm)
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xl,X1) )
& doDivides0(xl,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1240_04) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(m__1240,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1240) ).
fof(c_0_7,negated_conjecture,
~ ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X1) )
| doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_8,negated_conjecture,
! [X142] :
( ( ~ aNaturalNumber0(X142)
| sdtpldt0(xm,xn) != sdtasdt0(xl,X142) )
& ~ doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_9,hypothesis,
( ( aNaturalNumber0(sdtsldt0(xm,xl))
| xl = sz00 )
& ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
| xl = sz00 )
& ( aNaturalNumber0(sdtsldt0(xn,xl))
| xl = sz00 )
& ( xn = sdtasdt0(xl,sdtsldt0(xn,xl))
| xl = sz00 )
& ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| xl = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1298])]) ).
cnf(c_0_10,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(xm,xn) != sdtasdt0(xl,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,hypothesis,
( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| xl = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X74,X75] :
( ~ aNaturalNumber0(X74)
| ~ aNaturalNumber0(X75)
| aNaturalNumber0(sdtpldt0(X74,X75)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(c_0_13,hypothesis,
( aNaturalNumber0(esk3_0)
& xm = sdtasdt0(xl,esk3_0)
& doDivides0(xl,xm)
& aNaturalNumber0(esk4_0)
& xn = sdtasdt0(xl,esk4_0)
& doDivides0(xl,xn) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__1240_04])]) ).
cnf(c_0_14,negated_conjecture,
( xl = sz00
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,hypothesis,
( aNaturalNumber0(sdtsldt0(xm,xl))
| xl = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,hypothesis,
( aNaturalNumber0(sdtsldt0(xn,xl))
| xl = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_18,plain,
! [X90] :
( ( sdtasdt0(X90,sz00) = sz00
| ~ aNaturalNumber0(X90) )
& ( sz00 = sdtasdt0(sz00,X90)
| ~ aNaturalNumber0(X90) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_19,hypothesis,
xn = sdtasdt0(xl,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
xl = sz00,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17]) ).
cnf(c_0_21,negated_conjecture,
~ doDivides0(xl,sdtpldt0(xm,xn)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,hypothesis,
sdtasdt0(sz00,esk4_0) = xn,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,hypothesis,
aNaturalNumber0(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_25,negated_conjecture,
~ doDivides0(sz00,sdtpldt0(xm,xn)),
inference(rw,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_26,hypothesis,
xn = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
fof(c_0_27,plain,
! [X83] :
( ( sdtpldt0(X83,sz00) = X83
| ~ aNaturalNumber0(X83) )
& ( X83 = sdtpldt0(sz00,X83)
| ~ aNaturalNumber0(X83) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
cnf(c_0_28,hypothesis,
doDivides0(xl,xm),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_29,negated_conjecture,
~ doDivides0(sz00,sdtpldt0(xm,sz00)),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,hypothesis,
doDivides0(sz00,xm),
inference(rw,[status(thm)],[c_0_28,c_0_20]) ).
cnf(c_0_32,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1240]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM469+2 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % 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
% 0.15/0.34 % Computer : n023.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 00:38:08 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.27/1.73 % Version : CSE_E---1.7
% 1.27/1.73 % Problem : theBenchmark.p
% 1.27/1.73 % SZS status Theorem for theBenchmark.p
% 1.27/1.73 % SZS output start CNFRefutation
% See solution above
% 1.27/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------