%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM472+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 : n004.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 0.30s 1.62s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 80)
% Comments :
%------------------------------------------------------------------------------
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(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(mMonAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> ( sdtpldt0(X3,X1) != sdtpldt0(X3,X2)
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtpldt0(X1,X3) != sdtpldt0(X2,X3)
& sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).
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/sandbox2/benchmark/theBenchmark.p',mDivSum) ).
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(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
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(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(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(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
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(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(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(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(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(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(mIH_03,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> iLess0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
fof(m__,conjecture,
sdtlseqdt0(xm,sdtpldt0(xm,xn)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
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(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
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(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X1 = sz00
& X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
fof(mLENTr,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sz00
| X1 = sz10
| ( sz10 != X1
& sdtlseqdt0(sz10,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLENTr) ).
fof(mLERefl,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERefl) ).
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(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_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
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__1379,hypothesis,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1379) ).
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(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(m__1347,hypothesis,
xl != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1347) ).
fof(i_0_37,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])])]) ).
fof(i_0_38,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])])]) ).
fof(i_0_39,plain,
! [X119,X120,X121] :
( ( sdtpldt0(X121,X119) != sdtpldt0(X121,X120)
| ~ aNaturalNumber0(X121)
| X119 = X120
| ~ sdtlseqdt0(X119,X120)
| ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120) )
& ( sdtlseqdt0(sdtpldt0(X121,X119),sdtpldt0(X121,X120))
| ~ aNaturalNumber0(X121)
| X119 = X120
| ~ sdtlseqdt0(X119,X120)
| ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120) )
& ( sdtpldt0(X119,X121) != sdtpldt0(X120,X121)
| ~ aNaturalNumber0(X121)
| X119 = X120
| ~ sdtlseqdt0(X119,X120)
| ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120) )
& ( sdtlseqdt0(sdtpldt0(X119,X121),sdtpldt0(X120,X121))
| ~ aNaturalNumber0(X121)
| X119 = X120
| ~ sdtlseqdt0(X119,X120)
| ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonAdd])])])]) ).
fof(i_0_40,plain,
! [X140,X141,X142] :
( ~ aNaturalNumber0(X140)
| ~ aNaturalNumber0(X141)
| ~ aNaturalNumber0(X142)
| ~ doDivides0(X140,X141)
| ~ doDivides0(X140,X142)
| doDivides0(X140,sdtpldt0(X141,X142)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])]) ).
fof(i_0_41,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])]) ).
fof(i_0_42,plain,
! [X80,X81,X82] :
( ~ aNaturalNumber0(X80)
| ~ aNaturalNumber0(X81)
| ~ aNaturalNumber0(X82)
| sdtpldt0(sdtpldt0(X80,X81),X82) = sdtpldt0(X80,sdtpldt0(X81,X82)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(i_0_43,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])])])]) ).
fof(i_0_44,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])])])]) ).
fof(i_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])]) ).
fof(i_0_46,plain,
! [X114,X115,X116] :
( ~ aNaturalNumber0(X114)
| ~ aNaturalNumber0(X115)
| ~ aNaturalNumber0(X116)
| ~ sdtlseqdt0(X114,X115)
| ~ sdtlseqdt0(X115,X116)
| sdtlseqdt0(X114,X116) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
fof(i_0_47,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(i_0_48,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(i_0_49,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])])])]) ).
fof(i_0_50,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])])]) ).
fof(i_0_51,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])]) ).
fof(i_0_52,plain,
! [X126,X127] :
( ~ aNaturalNumber0(X126)
| ~ aNaturalNumber0(X127)
| X126 = sz00
| sdtlseqdt0(X127,sdtasdt0(X127,X126)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
fof(i_0_53,plain,
! [X128,X129] :
( ~ aNaturalNumber0(X128)
| ~ aNaturalNumber0(X129)
| X128 = X129
| ~ sdtlseqdt0(X128,X129)
| iLess0(X128,X129) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH_03])]) ).
fof(i_0_54,negated_conjecture,
~ sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(i_0_55,plain,
! [X76,X77] :
( ~ aNaturalNumber0(X76)
| ~ aNaturalNumber0(X77)
| aNaturalNumber0(sdtasdt0(X76,X77)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(i_0_56,plain,
! [X74,X75] :
( ~ aNaturalNumber0(X74)
| ~ aNaturalNumber0(X75)
| aNaturalNumber0(sdtpldt0(X74,X75)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(i_0_57,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])])]) ).
fof(i_0_58,plain,
! [X84,X85] :
( ~ aNaturalNumber0(X84)
| ~ aNaturalNumber0(X85)
| sdtasdt0(X84,X85) = sdtasdt0(X85,X84) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(i_0_59,plain,
! [X78,X79] :
( ~ aNaturalNumber0(X78)
| ~ aNaturalNumber0(X79)
| sdtpldt0(X78,X79) = sdtpldt0(X79,X78) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(i_0_60,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(i_0_61,plain,
! [X100,X101] :
( ( X100 = sz00
| sdtpldt0(X100,X101) != sz00
| ~ aNaturalNumber0(X100)
| ~ aNaturalNumber0(X101) )
& ( X101 = sz00
| sdtpldt0(X100,X101) != sz00
| ~ aNaturalNumber0(X100)
| ~ aNaturalNumber0(X101) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])]) ).
fof(i_0_62,plain,
! [X125] :
( ( sz10 != X125
| X125 = sz00
| X125 = sz10
| ~ aNaturalNumber0(X125) )
& ( sdtlseqdt0(sz10,X125)
| X125 = sz00
| X125 = sz10
| ~ aNaturalNumber0(X125) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLENTr])])]) ).
fof(i_0_63,plain,
! [X111] :
( ~ aNaturalNumber0(X111)
| sdtlseqdt0(X111,X111) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERefl])]) ).
fof(i_0_64,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])])]) ).
fof(i_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])])]) ).
fof(i_0_66,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(i_0_67,plain,
( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_68,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_69,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X3,X2))
| X2 = sz00
| X1 = X3
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_70,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)],[i_0_38]),
[final] ).
cnf(i_0_71,plain,
( sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X2))
| X1 = X3
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_72,plain,
( sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X1,X3))
| X2 = X3
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_73,plain,
( doDivides0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_74,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_75,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_76,plain,
( X2 = sz00
| X1 = X3
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_77,plain,
( X1 = sz00
| X2 = X3
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_78,plain,
( X1 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_79,plain,
( X2 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_80,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)],[i_0_43]),
[final] ).
cnf(i_0_81,plain,
( X1 = sdtmndt0(X3,X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_82,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_83,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_84,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_85,plain,
( X1 = sdtasdt0(X2,esk2_2(X2,X1))
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_86,plain,
( X1 = sdtasdt0(X2,X3)
| X2 = sz00
| X3 != sdtsldt0(X1,X2)
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_87,plain,
( sdtpldt0(X1,X2) = X3
| X2 != sdtmndt0(X3,X1)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_88,plain,
( X1 = X3
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_89,plain,
( X2 = X3
| X1 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_90,plain,
( X1 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_91,plain,
( X2 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_92,plain,
( aNaturalNumber0(esk2_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_93,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_94,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_95,plain,
( aNaturalNumber0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_96,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_97,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_98,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_99,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_100,plain,
( X1 = X2
| iLess0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_101,negated_conjecture,
~ sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_102,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_103,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_104,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_105,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_106,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_107,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_108,plain,
( X1 = sz00
| sdtpldt0(X1,X2) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_109,plain,
( X1 = sz00
| sdtpldt0(X2,X1) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_110,hypothesis,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(split_conjunct,[status(thm)],[m__1324_04]),
[final] ).
cnf(i_0_111,hypothesis,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(split_conjunct,[status(thm)],[m__1379]),
[final] ).
cnf(i_0_112,plain,
( sdtlseqdt0(X2,X1)
| X1 != X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_113,plain,
( sdtlseqdt0(sz10,X1)
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_114,plain,
( sdtlseqdt0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_115,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_116,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_117,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_118,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_119,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_120,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_121,hypothesis,
doDivides0(xl,xm),
inference(split_conjunct,[status(thm)],[m__1324_04]),
[final] ).
cnf(i_0_122,hypothesis,
xp = sdtsldt0(xm,xl),
inference(split_conjunct,[status(thm)],[m__1360]),
[final] ).
cnf(i_0_123,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1324]),
[final] ).
cnf(i_0_124,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1324]),
[final] ).
cnf(i_0_125,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1324]),
[final] ).
cnf(i_0_126,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]),
[final] ).
cnf(i_0_127,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]),
[final] ).
cnf(i_0_128,hypothesis,
xl != sz00,
inference(split_conjunct,[status(thm)],[m__1347]),
[final] ).
cnf(i_0_129,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]),
[final] ).
cnf(i_0_130,axiom,
X1 = X1 ).
cnf(i_0_131,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_132,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_133,axiom,
( X1 != X2
| sdtasdt0(X1,X3) = sdtasdt0(X2,X3) ) ).
cnf(i_0_134,axiom,
( X1 != X2
| sdtasdt0(X3,X1) = sdtasdt0(X3,X2) ) ).
cnf(i_0_135,axiom,
( X1 != X2
| sdtpldt0(X1,X3) = sdtpldt0(X2,X3) ) ).
cnf(i_0_136,axiom,
( X1 != X2
| sdtpldt0(X3,X1) = sdtpldt0(X3,X2) ) ).
cnf(i_0_137,axiom,
( X1 != X2
| sdtsldt0(X1,X3) = sdtsldt0(X2,X3) ) ).
cnf(i_0_138,axiom,
( X1 != X2
| sdtsldt0(X3,X1) = sdtsldt0(X3,X2) ) ).
cnf(i_0_139,axiom,
( X1 != X2
| sdtmndt0(X1,X3) = sdtmndt0(X2,X3) ) ).
cnf(i_0_140,axiom,
( X1 != X2
| sdtmndt0(X3,X1) = sdtmndt0(X3,X2) ) ).
cnf(i_0_141,axiom,
( X1 != X2
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(X2) ) ).
cnf(i_0_142,axiom,
( X1 != X2
| ~ sdtlseqdt0(X1,X3)
| sdtlseqdt0(X2,X3) ) ).
cnf(i_0_143,axiom,
( X1 != X2
| ~ sdtlseqdt0(X3,X1)
| sdtlseqdt0(X3,X2) ) ).
cnf(i_0_144,axiom,
( X1 != X2
| ~ doDivides0(X1,X3)
| doDivides0(X2,X3) ) ).
cnf(i_0_145,axiom,
( X1 != X2
| ~ doDivides0(X3,X1)
| doDivides0(X3,X2) ) ).
cnf(i_0_146,axiom,
( X1 != X2
| ~ iLess0(X1,X3)
| iLess0(X2,X3) ) ).
cnf(i_0_147,axiom,
( X1 != X2
| ~ iLess0(X3,X1)
| iLess0(X3,X2) ) ).
cnf(i_0_130_001,axiom,
X1 = X1 ).
cnf(i_0_131_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_132_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_133_004,axiom,
( X1 != X2
| sdtasdt0(X1,X3) = sdtasdt0(X2,X3) ) ).
cnf(i_0_134_005,axiom,
( X1 != X2
| sdtasdt0(X3,X1) = sdtasdt0(X3,X2) ) ).
cnf(i_0_135_006,axiom,
( X1 != X2
| sdtpldt0(X1,X3) = sdtpldt0(X2,X3) ) ).
cnf(i_0_136_007,axiom,
( X1 != X2
| sdtpldt0(X3,X1) = sdtpldt0(X3,X2) ) ).
cnf(i_0_137_008,axiom,
( X1 != X2
| sdtsldt0(X1,X3) = sdtsldt0(X2,X3) ) ).
cnf(i_0_138_009,axiom,
( X1 != X2
| sdtsldt0(X3,X1) = sdtsldt0(X3,X2) ) ).
cnf(i_0_139_010,axiom,
( X1 != X2
| sdtmndt0(X1,X3) = sdtmndt0(X2,X3) ) ).
cnf(i_0_140_011,axiom,
( X1 != X2
| sdtmndt0(X3,X1) = sdtmndt0(X3,X2) ) ).
cnf(i_0_141_012,axiom,
( X1 != X2
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(X2) ) ).
cnf(i_0_142_013,axiom,
( X1 != X2
| ~ sdtlseqdt0(X1,X3)
| sdtlseqdt0(X2,X3) ) ).
cnf(i_0_143_014,axiom,
( X1 != X2
| ~ sdtlseqdt0(X3,X1)
| sdtlseqdt0(X3,X2) ) ).
cnf(i_0_144_015,axiom,
( X1 != X2
| ~ doDivides0(X1,X3)
| doDivides0(X2,X3) ) ).
cnf(i_0_145_016,axiom,
( X1 != X2
| ~ doDivides0(X3,X1)
| doDivides0(X3,X2) ) ).
cnf(i_0_146_017,axiom,
( X1 != X2
| ~ iLess0(X1,X3)
| iLess0(X2,X3) ) ).
cnf(i_0_147_018,axiom,
( X1 != X2
| ~ iLess0(X3,X1)
| iLess0(X3,X2) ) ).
cnf(i_0_148,plain,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X2,X1))
| X2 = sz00
| X1 = sdtsldt0(sdtasdt0(X2,X1),X2) ),
inference(equality_inference,[],[80]) ).
cnf(i_0_149,plain,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X2,X1))
| X1 = sdtmndt0(sdtpldt0(X2,X1),X2) ),
inference(equality_inference,[],[81]) ).
cnf(i_0_150,plain,
( ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X1 = sz00
| X2 = sdtasdt0(X1,sdtsldt0(X2,X1)) ),
inference(equality_inference,[],[86]) ).
cnf(i_0_151,plain,
( ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,sdtmndt0(X2,X1)) = X2 ),
inference(equality_inference,[],[87]) ).
cnf(i_0_152,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X1 = X1
| X2 = sz00 ),
inference(equality_inference,[],[88]) ).
cnf(i_0_153,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X1 = X1
| X2 = sz00 ),
inference(equality_inference,[],[89]) ).
cnf(i_0_154,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X2)
| X2 = X2 ),
inference(equality_inference,[],[90]) ).
cnf(i_0_155,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X2)
| X2 = X2 ),
inference(equality_inference,[],[91]) ).
cnf(i_0_156,plain,
( ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtsldt0(X2,X1))
| X1 = sz00 ),
inference(equality_inference,[],[94]) ).
cnf(i_0_157,plain,
( ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtmndt0(X2,X1)) ),
inference(equality_inference,[],[95]) ).
cnf(i_0_158,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtpldt0(X1,X2))
| sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2) ),
inference(equality_inference,[],[97]) ).
cnf(i_0_159,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2) ),
inference(equality_inference,[],[98]) ).
cnf(i_0_160,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X1) ),
inference(equality_inference,[],[112]) ).
cnf(i_0_161,plain,
sdtlseqdt0(xn,xn),
inference(scs_inference,[],[i_0_123,i_0_114]) ).
cnf(i_0_162,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X1) ),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_163,plain,
sdtsldt0(xm,xl) = xp,
inference(scs_inference,[],[i_0_123,i_0_122,i_0_114,i_0_131]) ).
cnf(i_0_164,plain,
~ aNaturalNumber0(sdtpldt0(xm,xn)),
inference(scs_inference,[],[i_0_101,i_0_123,i_0_124,i_0_122,i_0_114,i_0_131,i_0_158]) ).
cnf(i_0_165,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X2,X1)) ),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_166,plain,
sdtpldt0(xn,sdtmndt0(xn,xn)) = xn,
inference(scs_inference,[],[i_0_101,i_0_123,i_0_124,i_0_122,i_0_114,i_0_131,i_0_158,i_0_151]) ).
cnf(i_0_167,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
| ~ sdtlseqdt0(X1,X2) ),
inference(rename_variables,[],[i_0_151]) ).
cnf(i_0_168,plain,
aNaturalNumber0(sdtmndt0(xn,xn)),
inference(scs_inference,[],[i_0_101,i_0_123,i_0_124,i_0_122,i_0_114,i_0_131,i_0_158,i_0_151,i_0_157]) ).
cnf(i_0_169,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtmndt0(X2,X1))
| ~ sdtlseqdt0(X1,X2) ),
inference(rename_variables,[],[i_0_157]) ).
cnf(i_0_170,plain,
xm = sdtasdt0(xl,xp),
inference(scs_inference,[],[i_0_101,i_0_121,i_0_123,i_0_124,i_0_125,i_0_128,i_0_122,i_0_114,i_0_131,i_0_158,i_0_151,i_0_157,i_0_86]) ).
cnf(i_0_171,plain,
( X1 = sz00
| X2 != sdtsldt0(X3,X1)
| X3 = sdtasdt0(X1,X2)
| ~ doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_172,plain,
aNaturalNumber0(xp),
inference(scs_inference,[],[i_0_101,i_0_121,i_0_123,i_0_124,i_0_125,i_0_128,i_0_122,i_0_114,i_0_131,i_0_158,i_0_151,i_0_157,i_0_86,i_0_94]) ).
cnf(i_0_173,plain,
( X1 != sdtsldt0(X2,X3)
| X3 = sz00
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(X1) ),
inference(rename_variables,[],[i_0_94]) ).
cnf(i_0_174,plain,
( X1 != xm
| ~ sdtlseqdt0(X1,sdtpldt0(xm,xn)) ),
inference(scs_inference,[],[i_0_101,i_0_121,i_0_123,i_0_124,i_0_125,i_0_128,i_0_122,i_0_114,i_0_131,i_0_158,i_0_151,i_0_157,i_0_86,i_0_94,i_0_142]) ).
cnf(i_0_175,plain,
( xn != sdtpldt0(xm,xn)
| xn != xm ),
inference(scs_inference,[],[i_0_101,i_0_121,i_0_123,i_0_124,i_0_125,i_0_128,i_0_122,i_0_114,i_0_131,i_0_158,i_0_151,i_0_157,i_0_86,i_0_94,i_0_142,i_0_143]) ).
cnf(i_0_176,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(rename_variables,[],[i_0_103]) ).
cnf(i_0_177,plain,
( xm != sdtpldt0(xm,xn)
| xn != xm ),
inference(scs_inference,[],[i_0_101,i_0_121,i_0_123,i_0_124,i_0_125,i_0_128,i_0_122,i_0_114,i_0_131,i_0_158,i_0_151,i_0_157,i_0_86,i_0_94,i_0_142,i_0_143,i_0_103,i_0_141]) ).
cnf(i_0_178,plain,
( sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1) ),
inference(rename_variables,[],[i_0_104]) ).
cnf(i_0_179,plain,
( doDivides0(xn,sdtasdt0(xn,xn))
| xn != xm
| sdtlseqdt0(sdtpldt0(xm,xn),xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(scs_inference,[],[i_0_101,i_0_121,i_0_123,i_0_124,i_0_125,i_0_128,i_0_122,i_0_111,i_0_114,i_0_131,i_0_158,i_0_151,i_0_157,i_0_86,i_0_94,i_0_142,i_0_143,i_0_103,i_0_141,i_0_104,i_0_159]) ).
cnf(i_0_180,plain,
~ sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(equality_inference,[],[174]) ).
cnf(i_0_181,plain,
sdtlseqdt0(sdtmndt0(xn,xn),sdtmndt0(xn,xn)),
inference(scs_inference,[],[i_0_168,i_0_114]) ).
cnf(i_0_182,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X1) ),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_183,plain,
xn = sdtpldt0(xn,sdtmndt0(xn,xn)),
inference(scs_inference,[],[i_0_168,i_0_166,i_0_114,i_0_131]) ).
cnf(i_0_184,plain,
$false,
inference(scs_inference,[],[i_0_164,i_0_168,i_0_166,i_0_123,i_0_124,i_0_114,i_0_131,i_0_103]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM472+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 : n004.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 00:37:02 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.30/1.62 % Version : CSE_E---1.7
% 0.30/1.62 % Problem : theBenchmark.p
% 0.30/1.62 % SZS status Theorem for theBenchmark.p
% 0.30/1.62 % SZS output start CNFRefutation
% See solution above
% 0.40/1.72 % Total time : 1.271s
%------------------------------------------------------------------------------