%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM513+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 : n022.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 04:57:38 PM UTC 2026
% Result : Theorem 10.76s 7.24s
% Output : CNFRefutation 10.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 23 unt; 0 def)
% Number of atoms : 204 ( 83 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 223 ( 75 ~; 74 |; 59 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 28 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
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__2487,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xr,X1) )
& doDivides0(xr,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2487) ).
fof(m__,conjecture,
( ( aNaturalNumber0(sdtsldt0(xk,xr))
& xk = sdtasdt0(xr,sdtsldt0(xk,xr)) )
=> ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__2576,hypothesis,
( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm)
& aNaturalNumber0(sdtsldt0(sdtasdt0(xp,xk),xr))
& sdtasdt0(xp,xk) = sdtasdt0(xr,sdtsldt0(sdtasdt0(xp,xk),xr))
& sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2576) ).
fof(m__2362,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xr,X1) = xk )
& ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2362) ).
fof(mDivAsso,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivAsso) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
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(c_0_12,plain,
! [X169,X170,X172] :
( ( aNaturalNumber0(esk2_2(X169,X170))
| ~ doDivides0(X169,X170)
| ~ aNaturalNumber0(X169)
| ~ aNaturalNumber0(X170) )
& ( X170 = sdtasdt0(X169,esk2_2(X169,X170))
| ~ doDivides0(X169,X170)
| ~ aNaturalNumber0(X169)
| ~ aNaturalNumber0(X170) )
& ( ~ aNaturalNumber0(X172)
| X170 != sdtasdt0(X169,X172)
| doDivides0(X169,X170)
| ~ aNaturalNumber0(X169)
| ~ aNaturalNumber0(X170) ) ),
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_13,plain,
! [X115,X116] :
( ~ aNaturalNumber0(X115)
| ~ aNaturalNumber0(X116)
| aNaturalNumber0(sdtasdt0(X115,X116)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_14,plain,
! [X173,X174,X175] :
( ( aNaturalNumber0(X175)
| X175 != sdtsldt0(X174,X173)
| X173 = sz00
| ~ doDivides0(X173,X174)
| ~ aNaturalNumber0(X173)
| ~ aNaturalNumber0(X174) )
& ( X174 = sdtasdt0(X173,X175)
| X175 != sdtsldt0(X174,X173)
| X173 = sz00
| ~ doDivides0(X173,X174)
| ~ aNaturalNumber0(X173)
| ~ aNaturalNumber0(X174) )
& ( ~ aNaturalNumber0(X175)
| X174 != sdtasdt0(X173,X175)
| X175 = sdtsldt0(X174,X173)
| X173 = sz00
| ~ doDivides0(X173,X174)
| ~ aNaturalNumber0(X173)
| ~ aNaturalNumber0(X174) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_15,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X123,X124] :
( ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124)
| sdtasdt0(X123,X124) = sdtasdt0(X124,X123) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(c_0_18,hypothesis,
! [X211,X212] :
( aNaturalNumber0(xr)
& aNaturalNumber0(esk12_0)
& xk = sdtasdt0(xr,esk12_0)
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ( ~ aNaturalNumber0(X212)
| xr != sdtasdt0(X211,X212)
| ~ aNaturalNumber0(X211)
| X211 = sz10
| X211 = xr )
& ( ~ doDivides0(X211,xr)
| ~ aNaturalNumber0(X211)
| X211 = sz10
| X211 = 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_19,plain,
( X1 = sdtsldt0(X2,X3)
| X3 = sz00
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_15]),c_0_16]) ).
fof(c_0_21,hypothesis,
( aNaturalNumber0(esk18_0)
& xn = sdtasdt0(xr,esk18_0)
& doDivides0(xr,xn) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2487])]) ).
fof(c_0_22,negated_conjecture,
~ ( ( aNaturalNumber0(sdtsldt0(xk,xr))
& xk = sdtasdt0(xr,sdtsldt0(xk,xr)) )
=> ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_23,hypothesis,
sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm),
inference(split_conjunct,[status(thm)],[m__2576]) ).
cnf(c_0_24,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
| X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_19]),c_0_16]),c_0_20]) ).
cnf(c_0_27,hypothesis,
xn = sdtasdt0(xr,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,hypothesis,
xr != sz00,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_30,hypothesis,
( aNaturalNumber0(esk13_0)
& sdtpldt0(xr,esk13_0) = xk
& aNaturalNumber0(esk14_0)
& sdtasdt0(xn,xm) = sdtasdt0(xr,esk14_0)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2362])]) ).
fof(c_0_31,negated_conjecture,
( aNaturalNumber0(sdtsldt0(xk,xr))
& xk = sdtasdt0(xr,sdtsldt0(xk,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& sdtasdt0(xp,sdtsldt0(xk,xr)) != sdtasdt0(sdtsldt0(xn,xr),xm) ),
inference(fof_nnf,[status(thm)],[c_0_22]) ).
cnf(c_0_32,hypothesis,
( sdtasdt0(xr,sdtasdt0(sdtsldt0(xn,xr),xm)) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_33,hypothesis,
sdtsldt0(xn,xr) = esk18_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_25]),c_0_28])]),c_0_29]) ).
cnf(c_0_34,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xr,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,hypothesis,
aNaturalNumber0(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
sdtasdt0(xp,sdtsldt0(xk,xr)) != sdtasdt0(sdtsldt0(xn,xr),xm),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,hypothesis,
xk = sdtasdt0(xr,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_38,hypothesis,
aNaturalNumber0(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_39,hypothesis,
( sdtasdt0(xr,sdtasdt0(esk18_0,xm)) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(esk18_0,xm)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_33]) ).
cnf(c_0_40,hypothesis,
sdtsldt0(sdtasdt0(xn,xm),xr) = esk14_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_34]),c_0_25]),c_0_35])]),c_0_29]) ).
fof(c_0_41,plain,
! [X187,X188,X189] :
( ~ aNaturalNumber0(X187)
| ~ aNaturalNumber0(X188)
| X187 = sz00
| ~ doDivides0(X187,X188)
| ~ aNaturalNumber0(X189)
| sdtasdt0(X189,sdtsldt0(X188,X187)) = sdtsldt0(sdtasdt0(X189,X188),X187) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivAsso])])]) ).
cnf(c_0_42,negated_conjecture,
sdtasdt0(xp,sdtsldt0(xk,xr)) != sdtasdt0(esk18_0,xm),
inference(rw,[status(thm)],[c_0_36,c_0_33]) ).
cnf(c_0_43,hypothesis,
sdtsldt0(xk,xr) = esk12_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_37]),c_0_25]),c_0_38])]),c_0_29]) ).
cnf(c_0_44,hypothesis,
( sdtasdt0(esk18_0,xm) = esk14_0
| ~ aNaturalNumber0(sdtasdt0(esk18_0,xm)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_39]),c_0_40]),c_0_25])]),c_0_29]) ).
cnf(c_0_45,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_46,plain,
( X1 = sz00
| sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_48,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_49,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_50,negated_conjecture,
sdtasdt0(esk18_0,xm) != sdtasdt0(xp,esk12_0),
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_51,hypothesis,
sdtasdt0(esk18_0,xm) = esk14_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_16]),c_0_45]),c_0_28])]) ).
cnf(c_0_52,hypothesis,
( sdtasdt0(xp,sdtsldt0(xk,X1)) = sdtsldt0(sdtasdt0(xn,xm),X1)
| X1 = sz00
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_49])]) ).
cnf(c_0_53,hypothesis,
doDivides0(xr,xk),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_54,negated_conjecture,
sdtasdt0(xp,esk12_0) != esk14_0,
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,hypothesis,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_43]),c_0_40]),c_0_53]),c_0_25])]),c_0_54]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM513+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
% 0.15/0.32 % Computer : n022.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 00:43:21 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 10.76/7.24 % Version : CSE_E---1.7
% 10.76/7.24 % Problem : theBenchmark.p
% 10.76/7.24 % SZS status Theorem for theBenchmark.p
% 10.76/7.24 % SZS output start CNFRefutation
% See solution above
% 10.76/7.28 % Total time : 5.375s
%------------------------------------------------------------------------------