%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM528+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 : n003.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 04:57:42 PM UTC 2026
% Result : Theorem 3.70s 3.14s
% Output : CNFRefutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 24
% Syntax : Number of formulae : 134 ( 42 unt; 0 def)
% Number of atoms : 449 ( 148 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 526 ( 211 ~; 235 |; 51 &)
% ( 3 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 142 ( 0 sgn 71 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( xm != xn
& sdtlseqdt0(xm,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
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(m__3152,hypothesis,
( sdtlseqdt0(xn,xm)
=> sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3152) ).
fof(m__2987,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2987) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3014) ).
fof(m__3082,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3082) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(m__3046,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3046) ).
fof(m__3059,hypothesis,
xq = sdtsldt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3059) ).
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(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(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(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
| sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
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(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(mDefPrime,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( X1 != sz00
& X1 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& doDivides0(X2,X1) )
=> ( X2 = sz10
| X2 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(m__3025,hypothesis,
isPrime0(xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3025) ).
fof(c_0_24,negated_conjecture,
~ ( xm != xn
& sdtlseqdt0(xm,xn) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_25,negated_conjecture,
( xm = xn
| ~ sdtlseqdt0(xm,xn) ),
inference(fof_nnf,[status(thm)],[c_0_24]) ).
fof(c_0_26,plain,
! [X135,X136] :
( ( X136 != X135
| sdtlseqdt0(X135,X136)
| ~ aNaturalNumber0(X135)
| ~ aNaturalNumber0(X136) )
& ( sdtlseqdt0(X136,X135)
| sdtlseqdt0(X135,X136)
| ~ aNaturalNumber0(X135)
| ~ aNaturalNumber0(X136) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
fof(c_0_27,plain,
! [X94,X95] :
( ~ aNaturalNumber0(X94)
| ~ aNaturalNumber0(X95)
| aNaturalNumber0(sdtasdt0(X94,X95)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_28,plain,
! [X152,X153,X154] :
( ( aNaturalNumber0(X154)
| X154 != sdtsldt0(X153,X152)
| X152 = sz00
| ~ doDivides0(X152,X153)
| ~ aNaturalNumber0(X152)
| ~ aNaturalNumber0(X153) )
& ( X153 = sdtasdt0(X152,X154)
| X154 != sdtsldt0(X153,X152)
| X152 = sz00
| ~ doDivides0(X152,X153)
| ~ aNaturalNumber0(X152)
| ~ aNaturalNumber0(X153) )
& ( ~ aNaturalNumber0(X154)
| X153 != sdtasdt0(X152,X154)
| X154 = sdtsldt0(X153,X152)
| X152 = sz00
| ~ doDivides0(X152,X153)
| ~ aNaturalNumber0(X152)
| ~ aNaturalNumber0(X153) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
fof(c_0_29,hypothesis,
( ~ sdtlseqdt0(xn,xm)
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
inference(fof_nnf,[status(thm)],[m__3152]) ).
cnf(c_0_30,negated_conjecture,
( xm = xn
| ~ sdtlseqdt0(xm,xn) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_33,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_34,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_36,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_37,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(split_conjunct,[status(thm)],[m__3082]) ).
cnf(c_0_38,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_39,plain,
! [X130,X131] :
( ~ aNaturalNumber0(X130)
| ~ aNaturalNumber0(X131)
| ~ sdtlseqdt0(X130,X131)
| ~ sdtlseqdt0(X131,X130)
| X130 = X131 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_40,hypothesis,
( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ~ sdtlseqdt0(xn,xm) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_41,negated_conjecture,
( xm = xn
| sdtlseqdt0(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_42,hypothesis,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_43,hypothesis,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xq,xq)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_37]),c_0_36])]) ).
cnf(c_0_44,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_45,hypothesis,
doDivides0(xp,xn),
inference(split_conjunct,[status(thm)],[m__3046]) ).
cnf(c_0_46,hypothesis,
xq = sdtsldt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_47,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[m__2987]) ).
fof(c_0_48,plain,
! [X144,X145] :
( ~ aNaturalNumber0(X144)
| ~ aNaturalNumber0(X145)
| X144 = sz00
| sdtlseqdt0(X145,sdtasdt0(X145,X144)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
fof(c_0_49,plain,
! [X102,X103] :
( ~ aNaturalNumber0(X102)
| ~ aNaturalNumber0(X103)
| sdtasdt0(X102,X103) = sdtasdt0(X103,X102) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_50,plain,
( X1 = sdtasdt0(X2,X3)
| X2 = sz00
| X3 != sdtsldt0(X1,X2)
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_51,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_52,hypothesis,
( xm = xn
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_53,hypothesis,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_34]),c_0_33])]) ).
cnf(c_0_54,hypothesis,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xq) ),
inference(spm,[status(thm)],[c_0_43,c_0_34]) ).
cnf(c_0_55,hypothesis,
aNaturalNumber0(xq),
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_44,c_0_45]),c_0_46]),c_0_36]),c_0_32])]),c_0_47]) ).
cnf(c_0_56,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_57,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
fof(c_0_58,plain,
! [X104,X105,X106] :
( ~ aNaturalNumber0(X104)
| ~ aNaturalNumber0(X105)
| ~ aNaturalNumber0(X106)
| sdtasdt0(sdtasdt0(X104,X105),X106) = sdtasdt0(X104,sdtasdt0(X105,X106)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_59,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_50]) ).
fof(c_0_60,plain,
! [X148,X149,X151] :
( ( aNaturalNumber0(esk2_2(X148,X149))
| ~ doDivides0(X148,X149)
| ~ aNaturalNumber0(X148)
| ~ aNaturalNumber0(X149) )
& ( X149 = sdtasdt0(X148,esk2_2(X148,X149))
| ~ doDivides0(X148,X149)
| ~ aNaturalNumber0(X148)
| ~ aNaturalNumber0(X149) )
& ( ~ aNaturalNumber0(X151)
| X149 != sdtasdt0(X148,X151)
| doDivides0(X148,X149)
| ~ aNaturalNumber0(X148)
| ~ aNaturalNumber0(X149) ) ),
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_61,hypothesis,
( sdtasdt0(xm,xm) = sdtasdt0(xn,xn)
| xm = xn
| ~ sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]) ).
cnf(c_0_62,hypothesis,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
cnf(c_0_63,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_65,hypothesis,
sdtasdt0(xp,xq) = xn,
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_59,c_0_45]),c_0_46]),c_0_36]),c_0_32])]),c_0_47]) ).
cnf(c_0_66,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_67,hypothesis,
( sdtasdt0(xm,xm) = sdtasdt0(xn,xn)
| xm = xn
| ~ sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]) ).
cnf(c_0_68,hypothesis,
sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_35]),c_0_62]),c_0_36])]),c_0_47]) ).
cnf(c_0_69,hypothesis,
( sdtasdt0(xp,sdtasdt0(xq,X1)) = sdtasdt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_55]),c_0_36])]) ).
fof(c_0_70,plain,
! [X155,X156,X157] :
( ~ aNaturalNumber0(X155)
| ~ aNaturalNumber0(X156)
| ~ aNaturalNumber0(X157)
| ~ doDivides0(X155,X156)
| ~ doDivides0(X156,X157)
| doDivides0(X155,X157) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])]) ).
fof(c_0_71,plain,
! [X107] :
( ( sdtasdt0(X107,sz10) = X107
| ~ aNaturalNumber0(X107) )
& ( X107 = sdtasdt0(sz10,X107)
| ~ aNaturalNumber0(X107) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
fof(c_0_72,plain,
! [X115,X116,X117] :
( ( sdtasdt0(X115,X116) != sdtasdt0(X115,X117)
| X116 = X117
| ~ aNaturalNumber0(X116)
| ~ aNaturalNumber0(X117)
| X115 = sz00
| ~ aNaturalNumber0(X115) )
& ( sdtasdt0(X116,X115) != sdtasdt0(X117,X115)
| X116 = X117
| ~ aNaturalNumber0(X116)
| ~ aNaturalNumber0(X117)
| X115 = sz00
| ~ aNaturalNumber0(X115) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
cnf(c_0_73,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_28]) ).
cnf(c_0_74,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_66]),c_0_34]) ).
cnf(c_0_75,hypothesis,
( sdtasdt0(xm,xm) = sdtasdt0(xn,xn)
| xm = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
cnf(c_0_76,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xn,xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_69]),c_0_55])]) ).
cnf(c_0_77,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_78,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_79,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_80,plain,
( X1 = X3
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_81,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_73]),c_0_34]),c_0_74]) ).
cnf(c_0_82,hypothesis,
( sdtasdt0(xn,xq) = sdtasdt0(xn,xn)
| xm = xn ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_83,hypothesis,
xn != sz00,
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_84,hypothesis,
( doDivides0(X1,xn)
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_45]),c_0_32]),c_0_36])]) ).
cnf(c_0_85,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_78]),c_0_79])]) ).
fof(c_0_86,plain,
! [X161,X162,X163] :
( ~ aNaturalNumber0(X161)
| ~ aNaturalNumber0(X162)
| ~ aNaturalNumber0(X163)
| ~ doDivides0(X161,X162)
| ~ doDivides0(X161,sdtpldt0(X162,X163))
| doDivides0(X161,X163) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivMin])]) ).
cnf(c_0_87,plain,
( doDivides0(X1,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_74,c_0_57]) ).
fof(c_0_88,plain,
! [X158,X159,X160] :
( ~ aNaturalNumber0(X158)
| ~ aNaturalNumber0(X159)
| ~ aNaturalNumber0(X160)
| ~ doDivides0(X158,X159)
| ~ doDivides0(X158,X160)
| doDivides0(X158,sdtpldt0(X159,X160)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])]) ).
cnf(c_0_89,hypothesis,
( xq = sz00
| xp = X1
| sdtasdt0(X1,xq) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_65]),c_0_55]),c_0_36])]) ).
cnf(c_0_90,hypothesis,
( sdtsldt0(sdtasdt0(xn,xn),xn) = xq
| xm = xn ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_32]),c_0_55])]),c_0_83]) ).
fof(c_0_91,plain,
! [X169,X170] :
( ( X169 != sz00
| ~ isPrime0(X169)
| ~ aNaturalNumber0(X169) )
& ( X169 != sz10
| ~ isPrime0(X169)
| ~ aNaturalNumber0(X169) )
& ( ~ aNaturalNumber0(X170)
| ~ doDivides0(X170,X169)
| X170 = sz10
| X170 = X169
| ~ isPrime0(X169)
| ~ aNaturalNumber0(X169) )
& ( aNaturalNumber0(esk3_1(X169))
| X169 = sz00
| X169 = sz10
| isPrime0(X169)
| ~ aNaturalNumber0(X169) )
& ( doDivides0(esk3_1(X169),X169)
| X169 = sz00
| X169 = sz10
| isPrime0(X169)
| ~ aNaturalNumber0(X169) )
& ( esk3_1(X169) != sz10
| X169 = sz00
| X169 = sz10
| isPrime0(X169)
| ~ aNaturalNumber0(X169) )
& ( esk3_1(X169) != X169
| X169 = sz00
| X169 = sz10
| isPrime0(X169)
| ~ aNaturalNumber0(X169) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefPrime])])])])]) ).
cnf(c_0_92,hypothesis,
doDivides0(sz10,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_79]),c_0_36])]) ).
cnf(c_0_93,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_94,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_86]) ).
cnf(c_0_95,hypothesis,
doDivides0(xq,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_65]),c_0_55]),c_0_36])]) ).
fof(c_0_96,plain,
! [X96,X97] :
( ~ aNaturalNumber0(X96)
| ~ aNaturalNumber0(X97)
| sdtpldt0(X96,X97) = sdtpldt0(X97,X96) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_97,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_88]) ).
cnf(c_0_98,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_99,hypothesis,
( xp = sz10
| xq = sz00
| xq != xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_78]),c_0_79]),c_0_55])]) ).
cnf(c_0_100,hypothesis,
( xm = xn
| xq = xn ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_90]),c_0_32])]),c_0_83]) ).
cnf(c_0_101,plain,
( X1 != sz10
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_102,hypothesis,
sdtasdt0(sz10,sdtsldt0(xn,sz10)) = xn,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_92]),c_0_79]),c_0_32])]),c_0_93]) ).
cnf(c_0_103,hypothesis,
aNaturalNumber0(sdtsldt0(xn,sz10)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_92]),c_0_79]),c_0_32])]),c_0_93]) ).
cnf(c_0_104,hypothesis,
( doDivides0(xq,X1)
| ~ doDivides0(xq,sdtpldt0(xn,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_32]),c_0_55])]) ).
cnf(c_0_105,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_106,hypothesis,
( doDivides0(xq,sdtpldt0(X1,xn))
| ~ doDivides0(xq,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_95]),c_0_32]),c_0_55])]) ).
cnf(c_0_107,plain,
( doDivides0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_98]),c_0_79])]) ).
cnf(c_0_108,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__3025]) ).
cnf(c_0_109,hypothesis,
( xm = xn
| xp = sz10 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_83]) ).
cnf(c_0_110,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_101]),c_0_79])]) ).
cnf(c_0_111,hypothesis,
sdtsldt0(xn,sz10) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_102]),c_0_103])]) ).
cnf(c_0_112,hypothesis,
( doDivides0(xq,X1)
| ~ doDivides0(xq,sdtpldt0(X1,xn))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_32])]) ).
cnf(c_0_113,hypothesis,
doDivides0(xq,sdtpldt0(xq,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_55])]) ).
cnf(c_0_114,hypothesis,
xm = xn,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_110]) ).
cnf(c_0_115,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(rw,[status(thm)],[c_0_102,c_0_111]) ).
cnf(c_0_116,plain,
( X1 = sdtasdt0(X2,esk2_2(X2,X1))
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_117,plain,
( aNaturalNumber0(esk2_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_118,hypothesis,
doDivides0(xq,xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_55])]) ).
cnf(c_0_119,hypothesis,
sdtasdt0(xn,xq) = sdtasdt0(xn,xn),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_114]),c_0_114]) ).
cnf(c_0_120,hypothesis,
( sz10 = X1
| sdtasdt0(X1,xn) != xn
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_115]),c_0_32]),c_0_79])]),c_0_83]) ).
cnf(c_0_121,hypothesis,
doDivides0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_115]),c_0_32]),c_0_79])]) ).
cnf(c_0_122,hypothesis,
( xq = sz00
| xp = X1
| sdtasdt0(xq,X1) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_57]),c_0_55])]) ).
cnf(c_0_123,plain,
( sdtasdt0(X1,esk2_2(X1,X1)) = X1
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_116,c_0_107]) ).
cnf(c_0_124,hypothesis,
aNaturalNumber0(esk2_2(xq,xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_55])]) ).
cnf(c_0_125,hypothesis,
sdtsldt0(sdtasdt0(xn,xn),xn) = xq,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_119]),c_0_32]),c_0_55])]),c_0_83]) ).
cnf(c_0_126,hypothesis,
( sz10 = X1
| sdtasdt0(xn,X1) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_57]),c_0_32])]) ).
cnf(c_0_127,hypothesis,
sdtasdt0(xn,esk2_2(xn,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_121]),c_0_32])]) ).
cnf(c_0_128,hypothesis,
aNaturalNumber0(esk2_2(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_121]),c_0_32])]) ).
cnf(c_0_129,hypothesis,
( esk2_2(xq,xq) = xp
| xq = sz00
| xq != xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_124]),c_0_55])]) ).
cnf(c_0_130,hypothesis,
xq = xn,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_125]),c_0_32])]),c_0_83]) ).
cnf(c_0_131,hypothesis,
esk2_2(xn,xn) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128])]) ).
cnf(c_0_132,hypothesis,
xp = sz10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_130]),c_0_130]),c_0_131]),c_0_130]),c_0_130])]),c_0_83]) ).
cnf(c_0_133,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_132]),c_0_110]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM528+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n003.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 00:42:11 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 3.70/3.14 % Version : CSE_E---1.7
% 3.70/3.14 % Problem : theBenchmark.p
% 3.70/3.14 % SZS status Theorem for theBenchmark.p
% 3.70/3.14 % SZS output start CNFRefutation
% See solution above
% 3.70/3.15 % Total time : 2.372s
%------------------------------------------------------------------------------