%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM471+1 : 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 : n001.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 04:57:27 PM UTC 2026
% Result : Theorem 3.98s 3.24s
% Output : CNFRefutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 28
% Syntax : Number of formulae : 159 ( 54 unt; 0 def)
% Number of atoms : 547 ( 195 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 664 ( 276 ~; 293 |; 61 &)
% ( 4 <=>; 30 =>; 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 : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 200 ( 0 sgn 92 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(m__1324_04,hypothesis,
( doDivides0(xl,xm)
& doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324_04) ).
fof(m__1360,hypothesis,
xp = sdtsldt0(xm,xl),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1360) ).
fof(m__1324,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
fof(m__1347,hypothesis,
xl != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1347) ).
fof(mDivTrans,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X2,X3) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
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__,conjecture,
sdtlseqdt0(xp,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(m__1379,hypothesis,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1379) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
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/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
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(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/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
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/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(mMonMul,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( X1 != sz00
& X2 != X3
& sdtlseqdt0(X2,X3) )
=> ( sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(c_0_28,plain,
! [X130,X131,X133] :
( ( aNaturalNumber0(esk2_2(X130,X131))
| ~ doDivides0(X130,X131)
| ~ aNaturalNumber0(X130)
| ~ aNaturalNumber0(X131) )
& ( X131 = sdtasdt0(X130,esk2_2(X130,X131))
| ~ doDivides0(X130,X131)
| ~ aNaturalNumber0(X130)
| ~ aNaturalNumber0(X131) )
& ( ~ aNaturalNumber0(X133)
| X131 != sdtasdt0(X130,X133)
| doDivides0(X130,X131)
| ~ aNaturalNumber0(X130)
| ~ aNaturalNumber0(X131) ) ),
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_29,plain,
! [X76,X77] :
( ~ aNaturalNumber0(X76)
| ~ aNaturalNumber0(X77)
| aNaturalNumber0(sdtasdt0(X76,X77)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_30,plain,
! [X134,X135,X136] :
( ( aNaturalNumber0(X136)
| X136 != sdtsldt0(X135,X134)
| X134 = sz00
| ~ doDivides0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) )
& ( X135 = sdtasdt0(X134,X136)
| X136 != sdtsldt0(X135,X134)
| X134 = sz00
| ~ doDivides0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) )
& ( ~ aNaturalNumber0(X136)
| X135 != sdtasdt0(X134,X136)
| X136 = sdtsldt0(X135,X134)
| X134 = sz00
| ~ doDivides0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_31,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_33,plain,
! [X84,X85] :
( ~ aNaturalNumber0(X84)
| ~ aNaturalNumber0(X85)
| sdtasdt0(X84,X85) = sdtasdt0(X85,X84) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_34,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_30]) ).
cnf(c_0_35,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_31]),c_0_32]) ).
cnf(c_0_37,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_39,hypothesis,
doDivides0(xl,xm),
inference(split_conjunct,[status(thm)],[m__1324_04]) ).
cnf(c_0_40,hypothesis,
xp = sdtsldt0(xm,xl),
inference(split_conjunct,[status(thm)],[m__1360]) ).
cnf(c_0_41,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1324]) ).
cnf(c_0_42,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1324]) ).
cnf(c_0_43,hypothesis,
xl != sz00,
inference(split_conjunct,[status(thm)],[m__1347]) ).
cnf(c_0_44,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_35]) ).
fof(c_0_45,plain,
! [X137,X138,X139] :
( ~ aNaturalNumber0(X137)
| ~ aNaturalNumber0(X138)
| ~ aNaturalNumber0(X139)
| ~ doDivides0(X137,X138)
| ~ doDivides0(X138,X139)
| doDivides0(X137,X139) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])]) ).
cnf(c_0_46,plain,
( doDivides0(X1,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_47,hypothesis,
sdtasdt0(xl,xp) = xm,
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_38,c_0_39]),c_0_40]),c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_48,hypothesis,
aNaturalNumber0(xp),
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_39]),c_0_40]),c_0_41]),c_0_42])]),c_0_43]) ).
fof(c_0_49,plain,
! [X89] :
( ( sdtasdt0(X89,sz10) = X89
| ~ aNaturalNumber0(X89) )
& ( X89 = sdtasdt0(sz10,X89)
| ~ aNaturalNumber0(X89) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
cnf(c_0_50,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,hypothesis,
doDivides0(xp,xm),
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_41])]) ).
cnf(c_0_52,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_54,hypothesis,
( doDivides0(X1,xm)
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_42]),c_0_48])]) ).
cnf(c_0_55,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_52]),c_0_53])]) ).
fof(c_0_56,plain,
! [X102,X103] :
( ~ aNaturalNumber0(X102)
| ~ aNaturalNumber0(X103)
| sdtasdt0(X102,X103) != sz00
| X102 = sz00
| X103 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])]) ).
fof(c_0_57,plain,
! [X104,X105,X107] :
( ( aNaturalNumber0(esk1_2(X104,X105))
| ~ sdtlseqdt0(X104,X105)
| ~ aNaturalNumber0(X104)
| ~ aNaturalNumber0(X105) )
& ( sdtpldt0(X104,esk1_2(X104,X105)) = X105
| ~ sdtlseqdt0(X104,X105)
| ~ aNaturalNumber0(X104)
| ~ aNaturalNumber0(X105) )
& ( ~ aNaturalNumber0(X107)
| sdtpldt0(X104,X107) != X105
| sdtlseqdt0(X104,X105)
| ~ aNaturalNumber0(X104)
| ~ aNaturalNumber0(X105) ) ),
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_58,plain,
! [X74,X75] :
( ~ aNaturalNumber0(X74)
| ~ aNaturalNumber0(X75)
| aNaturalNumber0(sdtpldt0(X74,X75)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_59,hypothesis,
doDivides0(sz10,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_53]),c_0_48])]) ).
cnf(c_0_60,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
fof(c_0_61,negated_conjecture,
~ sdtlseqdt0(xp,xq),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_62,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_63,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_64,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_65,plain,
! [X83] :
( ( sdtpldt0(X83,sz00) = X83
| ~ aNaturalNumber0(X83) )
& ( X83 = sdtpldt0(sz00,X83)
| ~ aNaturalNumber0(X83) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
cnf(c_0_66,hypothesis,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(split_conjunct,[status(thm)],[m__1324_04]) ).
cnf(c_0_67,hypothesis,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(split_conjunct,[status(thm)],[m__1379]) ).
cnf(c_0_68,hypothesis,
sdtasdt0(sz10,sdtsldt0(xm,sz10)) = xm,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_59]),c_0_53]),c_0_42])]),c_0_60]) ).
cnf(c_0_69,hypothesis,
aNaturalNumber0(sdtsldt0(xm,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_59]),c_0_53]),c_0_42])]),c_0_60]) ).
cnf(c_0_70,negated_conjecture,
~ sdtlseqdt0(xp,xq),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_71,hypothesis,
( xp = sz00
| xm != sz00 ),
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_47]),c_0_48]),c_0_41])]),c_0_43]) ).
cnf(c_0_72,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_63]),c_0_64]) ).
cnf(c_0_73,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_74,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_75,hypothesis,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
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_66]),c_0_67]),c_0_41])]),c_0_43]) ).
cnf(c_0_76,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1324]) ).
cnf(c_0_77,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_30]) ).
cnf(c_0_78,hypothesis,
sdtsldt0(xm,sz10) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_68]),c_0_69])]) ).
cnf(c_0_79,negated_conjecture,
( xm != sz00
| ~ sdtlseqdt0(sz00,xq) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_80,plain,
( sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74])]) ).
cnf(c_0_81,hypothesis,
aNaturalNumber0(xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_64]),c_0_76]),c_0_42])]) ).
cnf(c_0_82,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_77]),c_0_32]),c_0_36]) ).
fof(c_0_83,plain,
! [X90] :
( ( sdtasdt0(X90,sz00) = sz00
| ~ aNaturalNumber0(X90) )
& ( sz00 = sdtasdt0(sz00,X90)
| ~ aNaturalNumber0(X90) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_84,hypothesis,
sdtasdt0(sz10,xm) = xm,
inference(rw,[status(thm)],[c_0_68,c_0_78]) ).
cnf(c_0_85,negated_conjecture,
xm != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81])]) ).
cnf(c_0_86,plain,
( sdtsldt0(sdtasdt0(sz10,X1),sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_53]),c_0_60]) ).
cnf(c_0_87,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
fof(c_0_88,plain,
! [X86,X87,X88] :
( ~ aNaturalNumber0(X86)
| ~ aNaturalNumber0(X87)
| ~ aNaturalNumber0(X88)
| sdtasdt0(sdtasdt0(X86,X87),X88) = sdtasdt0(X86,sdtasdt0(X87,X88)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_89,hypothesis,
doDivides0(xm,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_84]),c_0_42]),c_0_53])]) ).
cnf(c_0_90,hypothesis,
( sdtsldt0(sdtasdt0(xm,X1),xm) = X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_42]),c_0_85]) ).
cnf(c_0_91,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_92,plain,
( sdtasdt0(sz10,sdtsldt0(X1,sz10)) = X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_55]),c_0_53])]),c_0_60]) ).
cnf(c_0_93,plain,
sdtsldt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_74]),c_0_53])]) ).
cnf(c_0_94,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_95,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_96,hypothesis,
sdtasdt0(xm,sdtsldt0(xm,xm)) = xm,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_89]),c_0_42])]),c_0_85]) ).
cnf(c_0_97,hypothesis,
sdtsldt0(xm,xm) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_53]),c_0_42])]) ).
cnf(c_0_98,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_74])]) ).
fof(c_0_99,plain,
! [X91,X92,X93] :
( ( sdtasdt0(X91,sdtpldt0(X92,X93)) = sdtpldt0(sdtasdt0(X91,X92),sdtasdt0(X91,X93))
| ~ aNaturalNumber0(X91)
| ~ aNaturalNumber0(X92)
| ~ aNaturalNumber0(X93) )
& ( sdtasdt0(sdtpldt0(X92,X93),X91) = sdtpldt0(sdtasdt0(X92,X91),sdtasdt0(X93,X91))
| ~ aNaturalNumber0(X91)
| ~ aNaturalNumber0(X92)
| ~ aNaturalNumber0(X93) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
cnf(c_0_100,plain,
( sdtasdt0(sz00,sdtasdt0(X1,X2)) = sdtasdt0(sz00,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_74])]) ).
cnf(c_0_101,hypothesis,
sdtasdt0(xm,sz10) = xm,
inference(rw,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_102,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_98]),c_0_74]),c_0_53])]) ).
cnf(c_0_103,plain,
( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_104,hypothesis,
sdtasdt0(sz00,xm) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]),c_0_53]),c_0_42])]) ).
cnf(c_0_105,plain,
( sdtpldt0(sdtasdt0(X1,X2),X2) = sdtasdt0(sdtpldt0(X1,sz10),X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_52]),c_0_53])]) ).
cnf(c_0_106,hypothesis,
sdtasdt0(sz00,xp) = sz00,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_47]),c_0_48]),c_0_41])]),c_0_104]) ).
fof(c_0_107,plain,
! [X108,X109,X110] :
( ( aNaturalNumber0(X110)
| X110 != sdtmndt0(X109,X108)
| ~ sdtlseqdt0(X108,X109)
| ~ aNaturalNumber0(X108)
| ~ aNaturalNumber0(X109) )
& ( sdtpldt0(X108,X110) = X109
| X110 != sdtmndt0(X109,X108)
| ~ sdtlseqdt0(X108,X109)
| ~ aNaturalNumber0(X108)
| ~ aNaturalNumber0(X109) )
& ( ~ aNaturalNumber0(X110)
| sdtpldt0(X108,X110) != X109
| X110 = sdtmndt0(X109,X108)
| ~ sdtlseqdt0(X108,X109)
| ~ aNaturalNumber0(X108)
| ~ aNaturalNumber0(X109) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).
cnf(c_0_108,hypothesis,
sdtasdt0(sdtpldt0(sz00,sz10),xp) = sdtpldt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_48]),c_0_74])]) ).
fof(c_0_109,plain,
! [X97,X98,X99] :
( ( sdtasdt0(X97,X98) != sdtasdt0(X97,X99)
| X98 = X99
| ~ aNaturalNumber0(X98)
| ~ aNaturalNumber0(X99)
| X97 = sz00
| ~ aNaturalNumber0(X97) )
& ( sdtasdt0(X98,X97) != sdtasdt0(X99,X97)
| X98 = X99
| ~ aNaturalNumber0(X98)
| ~ aNaturalNumber0(X99)
| X97 = sz00
| ~ aNaturalNumber0(X97) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
cnf(c_0_110,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_107]) ).
fof(c_0_111,plain,
! [X78,X79] :
( ~ aNaturalNumber0(X78)
| ~ aNaturalNumber0(X79)
| sdtpldt0(X78,X79) = sdtpldt0(X79,X78) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_112,hypothesis,
sdtpldt0(sz00,xp) = sdtasdt0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_73]),c_0_53])]) ).
fof(c_0_113,plain,
! [X117,X118] :
( ( X118 != X117
| sdtlseqdt0(X117,X118)
| ~ aNaturalNumber0(X117)
| ~ aNaturalNumber0(X118) )
& ( sdtlseqdt0(X118,X117)
| sdtlseqdt0(X117,X118)
| ~ aNaturalNumber0(X117)
| ~ aNaturalNumber0(X118) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
cnf(c_0_114,plain,
( X2 = X3
| X1 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_115,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_110]),c_0_64]),c_0_72]) ).
cnf(c_0_116,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_117,hypothesis,
sdtasdt0(sz10,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_112]),c_0_48])]) ).
cnf(c_0_118,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_119,hypothesis,
( X1 = xn
| X2 = sz00
| sdtasdt0(X2,X1) != sdtasdt0(X2,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_114,c_0_76]) ).
cnf(c_0_120,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_94]),c_0_32]) ).
cnf(c_0_121,plain,
( sdtpldt0(X1,X2) = X3
| X2 != sdtmndt0(X3,X1)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_122,plain,
( sdtmndt0(sdtpldt0(X1,X2),X2) = X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_123,hypothesis,
sdtpldt0(sz00,xp) = xp,
inference(rw,[status(thm)],[c_0_112,c_0_117]) ).
cnf(c_0_124,hypothesis,
( sdtlseqdt0(X1,xp)
| sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_118,c_0_48]) ).
cnf(c_0_125,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_126,hypothesis,
( X1 = xn
| sdtasdt0(sz10,X1) != 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_119,c_0_52]),c_0_53]),c_0_76])]),c_0_60]) ).
cnf(c_0_127,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz00)) = sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_94]),c_0_74])]),c_0_32]) ).
cnf(c_0_128,plain,
( aNaturalNumber0(sdtasdt0(X1,sz00))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_98]),c_0_74]),c_0_53])]) ).
cnf(c_0_129,hypothesis,
( sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_66]),c_0_67]),c_0_41])]),c_0_43]) ).
cnf(c_0_130,plain,
( sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[c_0_121]) ).
cnf(c_0_131,hypothesis,
sdtmndt0(xp,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_48]),c_0_74])]) ).
cnf(c_0_132,hypothesis,
sdtlseqdt0(xp,xp),
inference(spm,[status(thm)],[c_0_124,c_0_48]) ).
fof(c_0_133,plain,
! [X94,X95,X96] :
( ( sdtpldt0(X94,X95) != sdtpldt0(X94,X96)
| X95 = X96
| ~ aNaturalNumber0(X94)
| ~ aNaturalNumber0(X95)
| ~ aNaturalNumber0(X96) )
& ( sdtpldt0(X95,X94) != sdtpldt0(X96,X94)
| X95 = X96
| ~ aNaturalNumber0(X94)
| ~ aNaturalNumber0(X95)
| ~ aNaturalNumber0(X96) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).
cnf(c_0_134,hypothesis,
( sdtpldt0(xm,sdtasdt0(xl,X1)) = sdtasdt0(xl,sdtpldt0(xp,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_47]),c_0_48]),c_0_41])]) ).
cnf(c_0_135,hypothesis,
( sdtasdt0(X1,sz00) = xn
| xn != sz00
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_53])]),c_0_128]) ).
cnf(c_0_136,hypothesis,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_64]),c_0_76]),c_0_42])]) ).
cnf(c_0_137,hypothesis,
sdtpldt0(xp,sz00) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_132]),c_0_48])]) ).
fof(c_0_138,plain,
! [X122,X123,X124] :
( ( sdtasdt0(X122,X123) != sdtasdt0(X122,X124)
| X122 = sz00
| X123 = X124
| ~ sdtlseqdt0(X123,X124)
| ~ aNaturalNumber0(X122)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) )
& ( sdtlseqdt0(sdtasdt0(X122,X123),sdtasdt0(X122,X124))
| X122 = sz00
| X123 = X124
| ~ sdtlseqdt0(X123,X124)
| ~ aNaturalNumber0(X122)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) )
& ( sdtasdt0(X123,X122) != sdtasdt0(X124,X122)
| X122 = sz00
| X123 = X124
| ~ sdtlseqdt0(X123,X124)
| ~ aNaturalNumber0(X122)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) )
& ( sdtlseqdt0(sdtasdt0(X123,X122),sdtasdt0(X124,X122))
| X122 = sz00
| X123 = X124
| ~ sdtlseqdt0(X123,X124)
| ~ aNaturalNumber0(X122)
| ~ aNaturalNumber0(X123)
| ~ aNaturalNumber0(X124) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).
cnf(c_0_139,plain,
( X2 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_140,hypothesis,
( X1 = xp
| X2 = sz00
| sdtasdt0(X2,X1) != sdtasdt0(X2,xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_114,c_0_48]) ).
cnf(c_0_141,hypothesis,
( sdtasdt0(xl,xq) = xm
| xn != sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_136]),c_0_137]),c_0_47]),c_0_74]),c_0_41])]) ).
cnf(c_0_142,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| X1 = sz00
| X2 = X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_143,hypothesis,
sdtlseqdt0(xq,xp),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_81]),c_0_70]) ).
cnf(c_0_144,hypothesis,
( xn = X1
| sdtpldt0(xm,X1) != sdtasdt0(xl,xq)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_136]),c_0_76]),c_0_42])]) ).
cnf(c_0_145,hypothesis,
sdtpldt0(xm,sz00) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_87]),c_0_137]),c_0_47]),c_0_74]),c_0_41])]) ).
cnf(c_0_146,hypothesis,
( xq = xp
| xn != sz00 ),
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_140,c_0_141]),c_0_47]),c_0_81]),c_0_41])]),c_0_43]) ).
fof(c_0_147,plain,
! [X112,X113] :
( ~ aNaturalNumber0(X112)
| ~ aNaturalNumber0(X113)
| ~ sdtlseqdt0(X112,X113)
| ~ sdtlseqdt0(X113,X112)
| X112 = X113 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_148,hypothesis,
( xq = xp
| X1 = sz00
| sdtlseqdt0(sdtasdt0(X1,xq),sdtasdt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_48]),c_0_81])]) ).
cnf(c_0_149,hypothesis,
( xn = X1
| sdtpldt0(X1,xm) != sdtasdt0(xl,xq)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_116]),c_0_42])]) ).
cnf(c_0_150,hypothesis,
sdtpldt0(sz00,xm) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_145]),c_0_74]),c_0_42])]) ).
cnf(c_0_151,negated_conjecture,
xn != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_146]),c_0_132])]) ).
cnf(c_0_152,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_147]) ).
cnf(c_0_153,hypothesis,
( xq = xp
| sdtlseqdt0(sdtasdt0(xl,xq),xm) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_41]),c_0_47]),c_0_43]) ).
cnf(c_0_154,hypothesis,
sdtlseqdt0(xm,sdtasdt0(xl,xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_136]),c_0_42]),c_0_76])]) ).
cnf(c_0_155,hypothesis,
aNaturalNumber0(sdtasdt0(xl,xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_136]),c_0_76]),c_0_42])]) ).
cnf(c_0_156,hypothesis,
sdtasdt0(xl,xq) != xm,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_74])]),c_0_151]) ).
cnf(c_0_157,hypothesis,
xq = xp,
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_152,c_0_153]),c_0_154]),c_0_155]),c_0_42])]),c_0_156]) ).
cnf(c_0_158,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_156,c_0_157]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM471+1 : 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
% 0.16/0.33 % Computer : n001.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 00:37:48 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 3.98/3.24 % Version : CSE_E---1.7
% 3.98/3.24 % Problem : theBenchmark.p
% 3.98/3.24 % SZS status Theorem for theBenchmark.p
% 3.98/3.24 % SZS output start CNFRefutation
% See solution above
% 3.98/3.25 % Total time : 2.372s
%------------------------------------------------------------------------------