%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM492+3 : 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 : n002.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 04:57:32 PM UTC 2026
% Result : Theorem 79.69s 46.53s
% Output : CNFRefutation 80.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 53 ( 21 unt; 0 def)
% Number of atoms : 183 ( 52 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 207 ( 77 ~; 74 |; 45 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 33 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(m__1860,hypothesis,
( xp != sz00
& xp != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xp = sdtasdt0(X1,X2) )
| doDivides0(X1,xp) ) )
=> ( X1 = sz10
| X1 = xp ) )
& isPrime0(xp)
& ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X1) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(m__1951,hypothesis,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1951) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__2001,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X1) )
& ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xp,xm) = sdtasdt0(xp,X1) )
& doDivides0(xp,sdtasdt0(xp,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2001) ).
fof(m__1883,hypothesis,
( aNaturalNumber0(xr)
& sdtpldt0(xp,xr) = xn
& xr = sdtmndt0(xn,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(m__1978,hypothesis,
( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm)
& sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1978) ).
fof(m__,conjecture,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xr,xm) = sdtasdt0(xp,X1) )
| doDivides0(xp,sdtasdt0(xr,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mDivMin,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X1,sdtpldt0(X2,X3)) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivMin) ).
fof(c_0_13,plain,
! [X134,X135,X137] :
( ( aNaturalNumber0(esk1_2(X134,X135))
| ~ sdtlseqdt0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) )
& ( sdtpldt0(X134,esk1_2(X134,X135)) = X135
| ~ sdtlseqdt0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) )
& ( ~ aNaturalNumber0(X137)
| sdtpldt0(X134,X137) != X135
| sdtlseqdt0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])]) ).
fof(c_0_14,plain,
! [X104,X105] :
( ~ aNaturalNumber0(X104)
| ~ aNaturalNumber0(X105)
| aNaturalNumber0(sdtpldt0(X104,X105)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(c_0_15,hypothesis,
! [X194,X195] :
( xp != sz00
& xp != sz10
& ( ~ aNaturalNumber0(X195)
| xp != sdtasdt0(X194,X195)
| ~ aNaturalNumber0(X194)
| X194 = sz10
| X194 = xp )
& ( ~ doDivides0(X194,xp)
| ~ aNaturalNumber0(X194)
| X194 = sz10
| X194 = xp )
& isPrime0(xp)
& aNaturalNumber0(esk9_0)
& sdtasdt0(xn,xm) = sdtasdt0(xp,esk9_0)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1860])])])])]) ).
fof(c_0_16,plain,
! [X138,X139,X140] :
( ( aNaturalNumber0(X140)
| X140 != sdtmndt0(X139,X138)
| ~ sdtlseqdt0(X138,X139)
| ~ aNaturalNumber0(X138)
| ~ aNaturalNumber0(X139) )
& ( sdtpldt0(X138,X140) = X139
| X140 != sdtmndt0(X139,X138)
| ~ sdtlseqdt0(X138,X139)
| ~ aNaturalNumber0(X138)
| ~ aNaturalNumber0(X139) )
& ( ~ aNaturalNumber0(X140)
| sdtpldt0(X138,X140) != X139
| X140 = sdtmndt0(X139,X138)
| ~ sdtlseqdt0(X138,X139)
| ~ aNaturalNumber0(X138)
| ~ aNaturalNumber0(X139) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).
cnf(c_0_17,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,hypothesis,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(split_conjunct,[status(thm)],[m__1951]) ).
cnf(c_0_20,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_21,plain,
! [X114,X115] :
( ~ aNaturalNumber0(X114)
| ~ aNaturalNumber0(X115)
| sdtasdt0(X114,X115) = sdtasdt0(X115,X114) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(c_0_22,plain,
! [X106,X107] :
( ~ aNaturalNumber0(X106)
| ~ aNaturalNumber0(X107)
| aNaturalNumber0(sdtasdt0(X106,X107)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_23,hypothesis,
( aNaturalNumber0(esk12_0)
& sdtasdt0(xn,xm) = sdtasdt0(xp,esk12_0)
& aNaturalNumber0(esk13_0)
& sdtasdt0(xp,xm) = sdtasdt0(xp,esk13_0)
& doDivides0(xp,sdtasdt0(xp,xm)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2001])]) ).
cnf(c_0_24,plain,
( X1 = sdtmndt0(X3,X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_17]),c_0_18]) ).
cnf(c_0_26,hypothesis,
sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xp,esk9_0),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__1883]) ).
cnf(c_0_29,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_30,hypothesis,
sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(split_conjunct,[status(thm)],[m__1978]) ).
cnf(c_0_31,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,hypothesis,
sdtasdt0(xp,xm) = sdtasdt0(xp,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,hypothesis,
aNaturalNumber0(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_35,plain,
( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_24]),c_0_18]),c_0_25]) ).
cnf(c_0_36,hypothesis,
sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xm,xr)) = sdtasdt0(xp,esk9_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29])]) ).
cnf(c_0_37,hypothesis,
sdtmndt0(sdtasdt0(xp,esk9_0),sdtasdt0(xp,xm)) = sdtasdt0(xr,xm),
inference(rw,[status(thm)],[c_0_30,c_0_20]) ).
cnf(c_0_38,hypothesis,
aNaturalNumber0(sdtasdt0(xp,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34])]) ).
fof(c_0_39,negated_conjecture,
~ ( ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xr,xm) = sdtasdt0(xp,X1) )
| doDivides0(xp,sdtasdt0(xr,xm)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_40,hypothesis,
( sdtasdt0(xr,xm) = sdtasdt0(xm,xr)
| ~ aNaturalNumber0(sdtasdt0(xm,xr)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38])]) ).
fof(c_0_41,negated_conjecture,
! [X201] :
( ( ~ aNaturalNumber0(X201)
| sdtasdt0(xr,xm) != sdtasdt0(xp,X201) )
& ~ doDivides0(xp,sdtasdt0(xr,xm)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])]) ).
fof(c_0_42,plain,
! [X173,X174,X175] :
( ~ aNaturalNumber0(X173)
| ~ aNaturalNumber0(X174)
| ~ aNaturalNumber0(X175)
| ~ doDivides0(X173,X174)
| ~ doDivides0(X173,sdtpldt0(X174,X175))
| doDivides0(X173,X175) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivMin])]) ).
cnf(c_0_43,hypothesis,
sdtasdt0(xr,xm) = sdtasdt0(xm,xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_31]),c_0_28]),c_0_29])]) ).
cnf(c_0_44,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_45,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_46,hypothesis,
aNaturalNumber0(sdtasdt0(xm,xr)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_43]),c_0_29]),c_0_28])]) ).
cnf(c_0_47,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_48,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xm,xr)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_27]),c_0_28]),c_0_29])]) ).
cnf(c_0_49,hypothesis,
( doDivides0(X1,sdtasdt0(xm,xr))
| ~ doDivides0(X1,sdtasdt0(xp,esk9_0))
| ~ doDivides0(X1,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_36]),c_0_38])]),c_0_46])]) ).
cnf(c_0_50,hypothesis,
doDivides0(xp,sdtasdt0(xp,esk9_0)),
inference(rw,[status(thm)],[c_0_47,c_0_20]) ).
cnf(c_0_51,hypothesis,
doDivides0(xp,sdtasdt0(xp,xm)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_51]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM492+3 : 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
% 0.16/0.34 % Computer : n002.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 00:38:46 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 79.69/46.53 % Version : CSE_E---1.7
% 79.69/46.53 % Problem : theBenchmark.p
% 79.69/46.53 % SZS status Theorem for theBenchmark.p
% 79.69/46.53 % SZS output start CNFRefutation
% See solution above
% 80.00/46.81 % Total time : 35.726s
%------------------------------------------------------------------------------