%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM501+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 : n014.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 04:57:34 PM UTC 2026
% Result : Theorem 2.28s 2.02s
% Output : CNFRefutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 7 unt; 0 def)
% Number of atoms : 94 ( 33 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 104 ( 39 ~; 33 |; 28 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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; 8 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
| doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(xr,X1) )
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xr = sdtasdt0(X1,X2) )
| doDivides0(X1,xr) ) )
=> ( X1 = sz10
| X1 = xr ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(m__2306,hypothesis,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(c_0_7,negated_conjecture,
~ ( ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
| doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_8,negated_conjecture,
! [X207] :
( ( ~ aNaturalNumber0(X207)
| sdtasdt0(xn,xm) != sdtasdt0(xr,X207) )
& ~ doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_9,plain,
! [X119,X120,X121] :
( ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120)
| ~ aNaturalNumber0(X121)
| sdtasdt0(sdtasdt0(X119,X120),X121) = sdtasdt0(X119,sdtasdt0(X120,X121)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(c_0_10,hypothesis,
! [X205,X206] :
( aNaturalNumber0(xr)
& aNaturalNumber0(esk12_0)
& xk = sdtasdt0(xr,esk12_0)
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ( ~ aNaturalNumber0(X206)
| xr != sdtasdt0(X205,X206)
| ~ aNaturalNumber0(X205)
| X205 = sz10
| X205 = xr )
& ( ~ doDivides0(X205,xr)
| ~ aNaturalNumber0(X205)
| X205 = sz10
| X205 = xr )
& isPrime0(xr) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2342])])])])]) ).
cnf(c_0_11,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xn,xm) != sdtasdt0(xr,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_13,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
xk = sdtasdt0(xr,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,hypothesis,
aNaturalNumber0(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
( sdtasdt0(xr,X1) != sdtasdt0(xp,xk)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,hypothesis,
( sdtasdt0(xr,sdtasdt0(esk12_0,X1)) = sdtasdt0(xk,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).
fof(c_0_19,plain,
! [X109,X110] :
( ~ aNaturalNumber0(X109)
| ~ aNaturalNumber0(X110)
| aNaturalNumber0(sdtasdt0(X109,X110)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_20,negated_conjecture,
( sdtasdt0(xk,X1) != sdtasdt0(xp,xk)
| ~ aNaturalNumber0(sdtasdt0(esk12_0,X1))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_22,plain,
! [X117,X118] :
( ~ aNaturalNumber0(X117)
| ~ aNaturalNumber0(X118)
| sdtasdt0(X117,X118) = sdtasdt0(X118,X117) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_23,negated_conjecture,
( sdtasdt0(xk,X1) != sdtasdt0(xp,xk)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_15])]) ).
cnf(c_0_24,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_26,negated_conjecture,
( sdtasdt0(X1,xk) != sdtasdt0(xp,xk)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_27,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_26]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM501+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
% 0.14/0.33 % Computer : n014.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 00:40:06 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 2.28/2.02 % Version : CSE_E---1.7
% 2.28/2.02 % Problem : theBenchmark.p
% 2.28/2.02 % SZS status Theorem for theBenchmark.p
% 2.28/2.02 % SZS output start CNFRefutation
% See solution above
% 2.41/2.03 % Total time : 1.374s
%------------------------------------------------------------------------------