%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM476+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 : n001.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 04:57:28 PM UTC 2026
% Result : Theorem 1.30s 1.72s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 16 unt; 0 def)
% Number of atoms : 122 ( 72 equ)
% Maximal formula atoms : 31 ( 3 avg)
% Number of connectives : 107 ( 16 ~; 26 |; 59 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 5 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( xl != sz00
=> ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xl,X1)
& X1 = sdtsldt0(xm,xl)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X2)
& X2 = sdtsldt0(sdtpldt0(xm,xn),xl)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 )
& sdtlseqdt0(X1,X2)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2
& X3 = sdtmndt0(X2,X1)
& sdtpldt0(sdtasdt0(xl,X1),sdtasdt0(xl,X3)) = sdtpldt0(sdtasdt0(xl,X1),xn)
& xn = sdtasdt0(xl,X3) ) ) ) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xl,X1) )
| doDivides0(xl,xn) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1324_04,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xl,X1) )
& doDivides0(xl,xm)
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X1) )
& doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324_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__1324,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
fof(c_0_5,negated_conjecture,
~ ( ( xl != sz00
=> ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xl,X1)
& X1 = sdtsldt0(xm,xl)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X2)
& X2 = sdtsldt0(sdtpldt0(xm,xn),xl)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 )
& sdtlseqdt0(X1,X2)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2
& X3 = sdtmndt0(X2,X1)
& sdtpldt0(sdtasdt0(xl,X1),sdtasdt0(xl,X3)) = sdtpldt0(sdtasdt0(xl,X1),xn)
& xn = sdtasdt0(xl,X3) ) ) ) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xl,X1) )
| doDivides0(xl,xn) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_6,negated_conjecture,
! [X156] :
( ( aNaturalNumber0(esk5_0)
| xl = sz00 )
& ( xm = sdtasdt0(xl,esk5_0)
| xl = sz00 )
& ( esk5_0 = sdtsldt0(xm,xl)
| xl = sz00 )
& ( aNaturalNumber0(esk6_0)
| xl = sz00 )
& ( sdtpldt0(xm,xn) = sdtasdt0(xl,esk6_0)
| xl = sz00 )
& ( esk6_0 = sdtsldt0(sdtpldt0(xm,xn),xl)
| xl = sz00 )
& ( aNaturalNumber0(esk7_0)
| xl = sz00 )
& ( sdtpldt0(esk5_0,esk7_0) = esk6_0
| xl = sz00 )
& ( sdtlseqdt0(esk5_0,esk6_0)
| xl = sz00 )
& ( aNaturalNumber0(esk8_0)
| xl = sz00 )
& ( sdtpldt0(esk5_0,esk8_0) = esk6_0
| xl = sz00 )
& ( esk8_0 = sdtmndt0(esk6_0,esk5_0)
| xl = sz00 )
& ( sdtpldt0(sdtasdt0(xl,esk5_0),sdtasdt0(xl,esk8_0)) = sdtpldt0(sdtasdt0(xl,esk5_0),xn)
| xl = sz00 )
& ( xn = sdtasdt0(xl,esk8_0)
| xl = sz00 )
& ( ~ aNaturalNumber0(X156)
| xn != sdtasdt0(xl,X156) )
& ~ doDivides0(xl,xn) ),
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_5])])])])]) ).
fof(c_0_7,hypothesis,
( aNaturalNumber0(esk3_0)
& xm = sdtasdt0(xl,esk3_0)
& doDivides0(xl,xm)
& aNaturalNumber0(esk4_0)
& sdtpldt0(xm,xn) = sdtasdt0(xl,esk4_0)
& doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__1324_04])]) ).
cnf(c_0_8,negated_conjecture,
( ~ aNaturalNumber0(X1)
| xn != sdtasdt0(xl,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( xn = sdtasdt0(xl,esk8_0)
| xl = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( aNaturalNumber0(esk8_0)
| xl = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,hypothesis,
xm = sdtasdt0(xl,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
xl = sz00,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
fof(c_0_13,plain,
! [X97] :
( ( sdtasdt0(X97,sz00) = sz00
| ~ aNaturalNumber0(X97) )
& ( sz00 = sdtasdt0(sz00,X97)
| ~ aNaturalNumber0(X97) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_14,hypothesis,
sdtpldt0(xm,xn) = sdtasdt0(xl,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,hypothesis,
sdtasdt0(sz00,esk3_0) = xm,
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,hypothesis,
aNaturalNumber0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,hypothesis,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_19,plain,
! [X90] :
( ( sdtpldt0(X90,sz00) = X90
| ~ aNaturalNumber0(X90) )
& ( X90 = sdtpldt0(sz00,X90)
| ~ aNaturalNumber0(X90) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
cnf(c_0_20,hypothesis,
sdtpldt0(xm,xn) = sdtasdt0(sz00,esk4_0),
inference(rw,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_21,hypothesis,
xm = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_22,hypothesis,
doDivides0(xl,sdtasdt0(xl,esk4_0)),
inference(rw,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_23,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,hypothesis,
sdtpldt0(sz00,xn) = sdtasdt0(sz00,esk4_0),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1324]) ).
cnf(c_0_26,negated_conjecture,
~ doDivides0(xl,xn),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_27,hypothesis,
doDivides0(sz00,sdtasdt0(sz00,esk4_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_12]),c_0_12]) ).
cnf(c_0_28,hypothesis,
sdtasdt0(sz00,esk4_0) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_29,negated_conjecture,
~ doDivides0(sz00,xn),
inference(rw,[status(thm)],[c_0_26,c_0_12]) ).
cnf(c_0_30,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM476+2 : 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
% 0.14/0.33 % Computer : n001.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 00:38:18 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.30/1.72 % Version : CSE_E---1.7
% 1.30/1.72 % Problem : theBenchmark.p
% 1.30/1.72 % SZS status Theorem for theBenchmark.p
% 1.30/1.72 % SZS output start CNFRefutation
% See solution above
% 1.30/1.72 % Total time : 1.370s
%------------------------------------------------------------------------------