%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM501+1 : 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 : n005.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 15.46s 9.85s
% Output : CNFRefutation 15.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 24
% Syntax : Number of formulae : 140 ( 53 unt; 0 def)
% Number of atoms : 412 ( 100 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 468 ( 196 ~; 203 |; 44 &)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 157 ( 0 sgn 72 !; 2 ?)
% 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(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mDivTrans,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X2,X3) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
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(mAddCanc,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtpldt0(X1,X2) = sdtpldt0(X1,X3)
| sdtpldt0(X2,X1) = sdtpldt0(X3,X1) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
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/sandbox/benchmark/theBenchmark.p',mDivMin) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(mDivSum,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X1,X3) )
=> doDivides0(X1,sdtpldt0(X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivSum) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
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(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(m__,conjecture,
doDivides0(xr,sdtasdt0(xn,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__2075,hypothesis,
~ sdtlseqdt0(xp,xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2075) ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(c_0_24,plain,
! [X145,X146,X148] :
( ( aNaturalNumber0(esk2_2(X145,X146))
| ~ doDivides0(X145,X146)
| ~ aNaturalNumber0(X145)
| ~ aNaturalNumber0(X146) )
& ( X146 = sdtasdt0(X145,esk2_2(X145,X146))
| ~ doDivides0(X145,X146)
| ~ aNaturalNumber0(X145)
| ~ aNaturalNumber0(X146) )
& ( ~ aNaturalNumber0(X148)
| X146 != sdtasdt0(X145,X148)
| doDivides0(X145,X146)
| ~ aNaturalNumber0(X145)
| ~ aNaturalNumber0(X146) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).
cnf(c_0_25,plain,
( X1 = sdtasdt0(X2,esk2_2(X2,X1))
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_26,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_27,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_28,plain,
! [X91,X92] :
( ~ aNaturalNumber0(X91)
| ~ aNaturalNumber0(X92)
| aNaturalNumber0(sdtasdt0(X91,X92)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_29,plain,
( aNaturalNumber0(esk2_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,hypothesis,
( sdtasdt0(xp,esk2_2(xp,sdtasdt0(xn,xm))) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_31,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_33,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_34,hypothesis,
( aNaturalNumber0(esk2_2(xp,sdtasdt0(xn,xm)))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_26]),c_0_27])]) ).
fof(c_0_35,plain,
! [X152,X153,X154] :
( ~ aNaturalNumber0(X152)
| ~ aNaturalNumber0(X153)
| ~ aNaturalNumber0(X154)
| ~ doDivides0(X152,X153)
| ~ doDivides0(X153,X154)
| doDivides0(X152,X154) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])]) ).
cnf(c_0_36,hypothesis,
sdtasdt0(xp,esk2_2(xp,sdtasdt0(xn,xm))) = sdtasdt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]) ).
cnf(c_0_37,hypothesis,
aNaturalNumber0(esk2_2(xp,sdtasdt0(xn,xm))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_31]),c_0_32]),c_0_33])]) ).
cnf(c_0_38,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_39,plain,
! [X104] :
( ( sdtasdt0(X104,sz10) = X104
| ~ aNaturalNumber0(X104) )
& ( X104 = sdtasdt0(sz10,X104)
| ~ aNaturalNumber0(X104) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
cnf(c_0_40,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,hypothesis,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_36]),c_0_37]),c_0_27])]) ).
cnf(c_0_42,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_38]),c_0_31]) ).
cnf(c_0_43,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_45,hypothesis,
( doDivides0(X1,sdtasdt0(xn,xm))
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_26]),c_0_27])]),c_0_41])]) ).
cnf(c_0_46,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_47,hypothesis,
doDivides0(sz10,sdtasdt0(xn,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_44]),c_0_27])]) ).
cnf(c_0_48,hypothesis,
sdtasdt0(sz10,esk2_2(sz10,sdtasdt0(xn,xm))) = sdtasdt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_47]),c_0_44]),c_0_41])]) ).
cnf(c_0_49,hypothesis,
aNaturalNumber0(esk2_2(sz10,sdtasdt0(xn,xm))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_47]),c_0_41]),c_0_44])]) ).
fof(c_0_50,plain,
! [X141,X142] :
( ~ aNaturalNumber0(X141)
| ~ aNaturalNumber0(X142)
| X141 = sz00
| sdtlseqdt0(X142,sdtasdt0(X142,X141)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
fof(c_0_51,plain,
! [X99,X100] :
( ~ aNaturalNumber0(X99)
| ~ aNaturalNumber0(X100)
| sdtasdt0(X99,X100) = sdtasdt0(X100,X99) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(c_0_52,plain,
! [X101,X102,X103] :
( ~ aNaturalNumber0(X101)
| ~ aNaturalNumber0(X102)
| ~ aNaturalNumber0(X103)
| sdtasdt0(sdtasdt0(X101,X102),X103) = sdtasdt0(X101,sdtasdt0(X102,X103)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_53,hypothesis,
esk2_2(sz10,sdtasdt0(xn,xm)) = sdtasdt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_48]),c_0_49])]) ).
cnf(c_0_54,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_55,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_56,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_57,hypothesis,
sdtasdt0(sz10,sdtasdt0(xn,xm)) = sdtasdt0(xn,xm),
inference(rw,[status(thm)],[c_0_48,c_0_53]) ).
cnf(c_0_58,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_59,plain,
! [X109,X110,X111] :
( ( sdtpldt0(X109,X110) != sdtpldt0(X109,X111)
| X110 = X111
| ~ aNaturalNumber0(X109)
| ~ aNaturalNumber0(X110)
| ~ aNaturalNumber0(X111) )
& ( sdtpldt0(X110,X109) != sdtpldt0(X111,X109)
| X110 = X111
| ~ aNaturalNumber0(X109)
| ~ aNaturalNumber0(X110)
| ~ aNaturalNumber0(X111) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).
fof(c_0_60,plain,
! [X98] :
( ( sdtpldt0(X98,sz00) = X98
| ~ aNaturalNumber0(X98) )
& ( X98 = sdtpldt0(sz00,X98)
| ~ aNaturalNumber0(X98) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
fof(c_0_61,plain,
! [X119,X120,X122] :
( ( aNaturalNumber0(esk1_2(X119,X120))
| ~ sdtlseqdt0(X119,X120)
| ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120) )
& ( sdtpldt0(X119,esk1_2(X119,X120)) = X120
| ~ sdtlseqdt0(X119,X120)
| ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120) )
& ( ~ aNaturalNumber0(X122)
| sdtpldt0(X119,X122) != X120
| sdtlseqdt0(X119,X120)
| ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])]) ).
cnf(c_0_62,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_63,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_64,hypothesis,
( sdtasdt0(sz10,sdtasdt0(sdtasdt0(xn,xm),X1)) = sdtasdt0(sdtasdt0(xn,xm),X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_41]),c_0_44])]) ).
cnf(c_0_65,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_56]),c_0_44])]),c_0_31]) ).
cnf(c_0_66,plain,
( X2 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_67,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_68,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_69,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_70,hypothesis,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xn,xm)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_57]),c_0_41]),c_0_44])]),c_0_63]) ).
cnf(c_0_71,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_72,hypothesis,
sdtasdt0(sdtasdt0(xn,xm),sz10) = sdtasdt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_57]),c_0_44]),c_0_41])]) ).
fof(c_0_73,plain,
! [X158,X159,X160] :
( ~ aNaturalNumber0(X158)
| ~ aNaturalNumber0(X159)
| ~ aNaturalNumber0(X160)
| ~ doDivides0(X158,X159)
| ~ doDivides0(X158,sdtpldt0(X159,X160))
| doDivides0(X158,X160) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivMin])]) ).
cnf(c_0_74,plain,
( X1 = sz00
| sdtpldt0(X2,X1) != X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68])]) ).
cnf(c_0_75,hypothesis,
sdtpldt0(sdtasdt0(xn,xm),esk1_2(sdtasdt0(xn,xm),sdtasdt0(xn,xm))) = sdtasdt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_41])]) ).
cnf(c_0_76,hypothesis,
aNaturalNumber0(esk1_2(sdtasdt0(xn,xm),sdtasdt0(xn,xm))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_70]),c_0_41])]) ).
cnf(c_0_77,plain,
( doDivides0(X1,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_55]) ).
cnf(c_0_78,hypothesis,
sdtasdt0(xn,sdtasdt0(xm,sz10)) = sdtasdt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_72]),c_0_44]),c_0_32]),c_0_33])]) ).
fof(c_0_79,plain,
! [X105] :
( ( sdtasdt0(X105,sz00) = sz00
| ~ aNaturalNumber0(X105) )
& ( sz00 = sdtasdt0(sz00,X105)
| ~ aNaturalNumber0(X105) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_80,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_73]) ).
cnf(c_0_81,plain,
( doDivides0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_58]),c_0_44])]) ).
cnf(c_0_82,hypothesis,
esk1_2(sdtasdt0(xn,xm),sdtasdt0(xn,xm)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_41])]) ).
cnf(c_0_83,hypothesis,
( doDivides0(sdtasdt0(xm,sz10),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_33])]) ).
cnf(c_0_84,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_85,plain,
( doDivides0(X1,X2)
| ~ doDivides0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_86,hypothesis,
sdtpldt0(sdtasdt0(xn,xm),sz00) = sdtasdt0(xn,xm),
inference(rw,[status(thm)],[c_0_75,c_0_82]) ).
cnf(c_0_87,hypothesis,
doDivides0(sdtasdt0(xn,xm),sdtasdt0(xn,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_57]),c_0_41]),c_0_44])]) ).
cnf(c_0_88,plain,
( doDivides0(X1,sdtasdt0(X2,X3))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_42]),c_0_31]) ).
cnf(c_0_89,hypothesis,
doDivides0(xm,sdtasdt0(xn,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_58]),c_0_32])]) ).
cnf(c_0_90,plain,
( doDivides0(X1,sz00)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_84]),c_0_68])]) ).
cnf(c_0_91,hypothesis,
doDivides0(sdtasdt0(xn,xm),sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]),c_0_68]),c_0_41])]) ).
cnf(c_0_92,hypothesis,
( doDivides0(xm,sdtasdt0(sdtasdt0(xn,xm),X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_41]),c_0_32])]) ).
cnf(c_0_93,plain,
( sdtasdt0(X1,esk2_2(X1,sz00)) = sz00
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_90]),c_0_68])]) ).
cnf(c_0_94,hypothesis,
aNaturalNumber0(esk2_2(sdtasdt0(xn,xm),sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_91]),c_0_68]),c_0_41])]) ).
fof(c_0_95,plain,
! [X155,X156,X157] :
( ~ aNaturalNumber0(X155)
| ~ aNaturalNumber0(X156)
| ~ aNaturalNumber0(X157)
| ~ doDivides0(X155,X156)
| ~ doDivides0(X155,X157)
| doDivides0(X155,sdtpldt0(X156,X157)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])]) ).
cnf(c_0_96,hypothesis,
doDivides0(xm,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]),c_0_41])]) ).
fof(c_0_97,plain,
! [X93,X94] :
( ~ aNaturalNumber0(X93)
| ~ aNaturalNumber0(X94)
| sdtpldt0(X93,X94) = sdtpldt0(X94,X93) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_98,plain,
( doDivides0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_99,hypothesis,
( doDivides0(xm,X1)
| ~ doDivides0(xm,sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_96]),c_0_68]),c_0_32])]) ).
cnf(c_0_100,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_101,hypothesis,
( doDivides0(xm,sdtpldt0(X1,sz00))
| ~ doDivides0(xm,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_96]),c_0_68]),c_0_32])]) ).
cnf(c_0_102,hypothesis,
( doDivides0(xm,X1)
| ~ doDivides0(xm,sdtpldt0(X1,sz00))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_68])]) ).
cnf(c_0_103,hypothesis,
doDivides0(xm,sdtpldt0(xm,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_81]),c_0_32])]) ).
cnf(c_0_104,hypothesis,
doDivides0(xm,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_32])]) ).
cnf(c_0_105,plain,
( sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_43]),c_0_44])]) ).
cnf(c_0_106,hypothesis,
sdtasdt0(xm,esk2_2(xm,xm)) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_104]),c_0_32])]) ).
cnf(c_0_107,hypothesis,
aNaturalNumber0(esk2_2(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_104]),c_0_32])]) ).
fof(c_0_108,plain,
! [X149,X150,X151] :
( ( aNaturalNumber0(X151)
| X151 != sdtsldt0(X150,X149)
| X149 = sz00
| ~ doDivides0(X149,X150)
| ~ aNaturalNumber0(X149)
| ~ aNaturalNumber0(X150) )
& ( X150 = sdtasdt0(X149,X151)
| X151 != sdtsldt0(X150,X149)
| X149 = sz00
| ~ doDivides0(X149,X150)
| ~ aNaturalNumber0(X149)
| ~ aNaturalNumber0(X150) )
& ( ~ aNaturalNumber0(X151)
| X150 != sdtasdt0(X149,X151)
| X151 = sdtsldt0(X150,X149)
| X149 = sz00
| ~ doDivides0(X149,X150)
| ~ aNaturalNumber0(X149)
| ~ aNaturalNumber0(X150) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_109,hypothesis,
sdtasdt0(sz10,xm) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_32])]),c_0_107])]) ).
cnf(c_0_110,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_108]) ).
cnf(c_0_111,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_112,hypothesis,
sdtlseqdt0(xm,xm),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_109]),c_0_32]),c_0_44])]),c_0_63]) ).
cnf(c_0_113,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_110]),c_0_31]),c_0_42]) ).
cnf(c_0_114,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_115,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_111]) ).
cnf(c_0_116,hypothesis,
sdtpldt0(xm,esk1_2(xm,xm)) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_112]),c_0_32])]) ).
cnf(c_0_117,hypothesis,
aNaturalNumber0(esk1_2(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_112]),c_0_32])]) ).
cnf(c_0_118,hypothesis,
doDivides0(esk2_2(xp,sdtasdt0(xn,xm)),sdtasdt0(xn,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_36]),c_0_37]),c_0_27])]) ).
cnf(c_0_119,hypothesis,
( esk2_2(xp,sdtasdt0(xn,xm)) = xk
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_36]),c_0_114]),c_0_27]),c_0_37])]) ).
cnf(c_0_120,hypothesis,
( xp = sz00
| aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_26]),c_0_114]),c_0_27])]) ).
fof(c_0_121,plain,
! [X89,X90] :
( ~ aNaturalNumber0(X89)
| ~ aNaturalNumber0(X90)
| aNaturalNumber0(sdtpldt0(X89,X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_122,hypothesis,
esk1_2(xm,xm) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_116]),c_0_117]),c_0_32])]) ).
cnf(c_0_123,hypothesis,
( xp = sz00
| doDivides0(xk,sdtasdt0(xn,xm)) ),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_124,hypothesis,
( xp = sz00
| aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_31]),c_0_32]),c_0_33])]) ).
fof(c_0_125,negated_conjecture,
~ doDivides0(xr,sdtasdt0(xn,xm)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_126,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_127,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_128,hypothesis,
sdtpldt0(xm,sz00) = xm,
inference(rw,[status(thm)],[c_0_116,c_0_122]) ).
fof(c_0_129,hypothesis,
~ sdtlseqdt0(xp,xm),
inference(fof_simplification,[status(thm)],[m__2075]) ).
cnf(c_0_130,hypothesis,
( xp = sz00
| doDivides0(X1,sdtasdt0(xn,xm))
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_123]),c_0_41])]),c_0_124]) ).
cnf(c_0_131,hypothesis,
doDivides0(xr,xk),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_132,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_133,negated_conjecture,
~ doDivides0(xr,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_134,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_126]),c_0_127]) ).
cnf(c_0_135,hypothesis,
sdtpldt0(sz00,xm) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_128]),c_0_68]),c_0_32])]) ).
cnf(c_0_136,hypothesis,
~ sdtlseqdt0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_137,hypothesis,
xp = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_132])]),c_0_133]) ).
cnf(c_0_138,hypothesis,
sdtlseqdt0(sz00,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_68]),c_0_32])]) ).
cnf(c_0_139,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_137]),c_0_138])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM501+1 : 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
% 0.16/0.33 % Computer : n005.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 00:39:30 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 15.46/9.85 % Version : CSE_E---1.7
% 15.46/9.85 % Problem : theBenchmark.p
% 15.46/9.85 % SZS status Theorem for theBenchmark.p
% 15.46/9.85 % SZS output start CNFRefutation
% See solution above
% 15.57/9.91 % Total time : 7.386s
%------------------------------------------------------------------------------