%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM475+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:52:21 AM UTC 2026
% Result : Theorem 199.39s 199.71s
% Output : Proof 199.59s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(mNatSort,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> $true ),
file('theBenchmark.p',mNatSort) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('theBenchmark.p',mSortsC) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('theBenchmark.p',mSortsC_01) ).
fof(mSortsB,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mSortsB) ).
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mSortsB_02) ).
fof(mAddComm,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('theBenchmark.p',mAddComm) ).
fof(mAddAsso,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ),
file('theBenchmark.p',mAddAsso) ).
fof(m_AddZero,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('theBenchmark.p',m_AddZero) ).
fof(mMulComm,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('theBenchmark.p',mMulComm) ).
fof(mMulAsso,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
file('theBenchmark.p',mMulAsso) ).
fof(m_MulUnit,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('theBenchmark.p',m_MulUnit) ).
fof(m_MulZero,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('theBenchmark.p',m_MulZero) ).
fof(mAMDistr,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('theBenchmark.p',mAMDistr) ).
fof(mAddCanc,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0)
| sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
=> W1 = W2 ) ),
file('theBenchmark.p',mAddCanc) ).
fof(mMulCanc,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 != sz00
=> ! [W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1) )
=> ( ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0)
| sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
=> W1 = W2 ) ) ) ),
file('theBenchmark.p',mMulCanc) ).
fof(mZeroAdd,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtpldt0(W0,W1) = sz00
=> ( W1 = sz00
& W0 = sz00 ) ) ),
file('theBenchmark.p',mZeroAdd) ).
fof(mZeroMul,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W1 = sz00
| W0 = sz00 ) ) ),
file('theBenchmark.p',mZeroMul) ).
fof(mDefLE,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ),
file('theBenchmark.p',mDefLE) ).
fof(mDefDiff,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ) ),
file('theBenchmark.p',mDefDiff) ).
fof(mLERefl,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> sdtlseqdt0(W0,W0) ),
file('theBenchmark.p',mLERefl) ).
fof(mLEAsym,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('theBenchmark.p',mLEAsym) ).
fof(mLETran,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W2)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(W0,W2) ) ),
file('theBenchmark.p',mLETran) ).
fof(mLETotal,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1) ) ),
file('theBenchmark.p',mLETotal) ).
fof(mMonAdd,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W0,W1)
& W0 != W1 )
=> ! [W2] :
( aNaturalNumber0(W2)
=> ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2))
& sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& sdtpldt0(W2,W0) != sdtpldt0(W2,W1) ) ) ) ),
file('theBenchmark.p',mMonAdd) ).
fof(mMonMul,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W2)
& W1 != W2
& W0 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& sdtasdt0(W0,W1) != sdtasdt0(W0,W2) ) ) ),
file('theBenchmark.p',mMonMul) ).
fof(mLENTr,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtlseqdt0(sz10,W0)
& sz10 != W0 )
| W0 = sz10
| W0 = sz00 ) ),
file('theBenchmark.p',mLENTr) ).
fof(mMonMul2,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( W0 != sz00
=> sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ),
file('theBenchmark.p',mMonMul2) ).
fof(mIH,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( iLess0(W0,W1)
=> $true ) ),
file('theBenchmark.p',mIH) ).
fof(mIH_03,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W0,W1)
& W0 != W1 )
=> iLess0(W0,W1) ) ),
file('theBenchmark.p',mIH_03) ).
fof(mDefDiv,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ),
file('theBenchmark.p',mDefDiv) ).
fof(mDefQuot,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W1)
& W0 != sz00 )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ) ),
file('theBenchmark.p',mDefQuot) ).
fof(mDivTrans,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W1,W2)
& doDivides0(W0,W1) )
=> doDivides0(W0,W2) ) ),
file('theBenchmark.p',mDivTrans) ).
fof(mDivSum,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W2)
& doDivides0(W0,W1) )
=> doDivides0(W0,sdtpldt0(W1,W2)) ) ),
file('theBenchmark.p',mDivSum) ).
fof(m__1324,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('theBenchmark.p',m__1324) ).
fof(m__1324_04,hypothesis,
( doDivides0(xl,sdtpldt0(xm,xn))
& ? [W0] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) )
& doDivides0(xl,xm)
& ? [W0] :
( xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ),
file('theBenchmark.p',m__1324_04) ).
fof(m__1347,hypothesis,
xl != sz00,
file('theBenchmark.p',m__1347) ).
fof(m__1360,hypothesis,
( xp = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,xp)
& aNaturalNumber0(xp) ),
file('theBenchmark.p',m__1360) ).
fof(m__1379,hypothesis,
( xq = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
& aNaturalNumber0(xq) ),
file('theBenchmark.p',m__1379) ).
fof(m__1395,hypothesis,
( sdtlseqdt0(xp,xq)
& ? [W0] :
( sdtpldt0(xp,W0) = xq
& aNaturalNumber0(W0) ) ),
file('theBenchmark.p',m__1395) ).
fof(m__1422,hypothesis,
( xr = sdtmndt0(xq,xp)
& sdtpldt0(xp,xr) = xq
& aNaturalNumber0(xr) ),
file('theBenchmark.p',m__1422) ).
fof(m__1459,hypothesis,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
file('theBenchmark.p',m__1459) ).
fof(m__,conjecture,
xn = sdtasdt0(xl,xr),
file('theBenchmark.p',m__) ).
fof(f_1_1,plain,
! [W0] :
( $true
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mNatSort]) ).
fof(f_1_2,plain,
! [U_0] :
( $true
| ~ aNaturalNumber0(U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_0] : ~ aNaturalNumber0(U_0)
| $true ),
inference(miniscope,[status(thm)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ aNaturalNumber0(U_0)
| $true ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
aNaturalNumber0(sz00),
inference(fof_nnf,[status(thm)],[mSortsC]) ).
cnf(f_2_2,plain,
aNaturalNumber0(sz00),
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[mSortsC_01]) ).
cnf(f_3_2,plain,
aNaturalNumber0(sz10),
inference(clausify,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
sz10 != sz00,
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
! [W0,W1] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mSortsB]) ).
fof(f_4_2,plain,
! [U_2,U_1] :
( aNaturalNumber0(sdtpldt0(U_2,U_1))
| ~ aNaturalNumber0(U_1)
| ~ aNaturalNumber0(U_2) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( aNaturalNumber0(sdtpldt0(U_2,U_1))
| ~ aNaturalNumber0(U_1)
| ~ aNaturalNumber0(U_2) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mSortsB_02]) ).
fof(f_5_2,plain,
! [U_4,U_3] :
( aNaturalNumber0(sdtasdt0(U_4,U_3))
| ~ aNaturalNumber0(U_3)
| ~ aNaturalNumber0(U_4) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( aNaturalNumber0(sdtasdt0(U_4,U_3))
| ~ aNaturalNumber0(U_3)
| ~ aNaturalNumber0(U_4) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mAddComm]) ).
fof(f_6_2,plain,
! [U_6,U_5] :
( sdtpldt0(U_6,U_5) = sdtpldt0(U_5,U_6)
| ~ aNaturalNumber0(U_5)
| ~ aNaturalNumber0(U_6) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( sdtpldt0(U_6,U_5) = sdtpldt0(U_5,U_6)
| ~ aNaturalNumber0(U_5)
| ~ aNaturalNumber0(U_6) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [W0,W1,W2] :
( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mAddAsso]) ).
fof(f_7_2,plain,
! [U_9,U_8,U_7] :
( sdtpldt0(sdtpldt0(U_9,U_8),U_7) = sdtpldt0(U_9,sdtpldt0(U_8,U_7))
| ~ aNaturalNumber0(U_7)
| ~ aNaturalNumber0(U_8)
| ~ aNaturalNumber0(U_9) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( sdtpldt0(sdtpldt0(U_9,U_8),U_7) = sdtpldt0(U_9,sdtpldt0(U_8,U_7))
| ~ aNaturalNumber0(U_7)
| ~ aNaturalNumber0(U_8)
| ~ aNaturalNumber0(U_9) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[m_AddZero]) ).
fof(f_8_2,plain,
! [U_10] :
( ( U_10 = sdtpldt0(sz00,U_10)
& sdtpldt0(U_10,sz00) = U_10 )
| ~ aNaturalNumber0(U_10) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( sdtpldt0(U_10,sz00) = U_10
| ~ aNaturalNumber0(U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( U_10 = sdtpldt0(sz00,U_10)
| ~ aNaturalNumber0(U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mMulComm]) ).
fof(f_9_2,plain,
! [U_12,U_11] :
( sdtasdt0(U_12,U_11) = sdtasdt0(U_11,U_12)
| ~ aNaturalNumber0(U_11)
| ~ aNaturalNumber0(U_12) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( sdtasdt0(U_12,U_11) = sdtasdt0(U_11,U_12)
| ~ aNaturalNumber0(U_11)
| ~ aNaturalNumber0(U_12) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [W0,W1,W2] :
( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mMulAsso]) ).
fof(f_10_2,plain,
! [U_15,U_14,U_13] :
( sdtasdt0(sdtasdt0(U_15,U_14),U_13) = sdtasdt0(U_15,sdtasdt0(U_14,U_13))
| ~ aNaturalNumber0(U_13)
| ~ aNaturalNumber0(U_14)
| ~ aNaturalNumber0(U_15) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( sdtasdt0(sdtasdt0(U_15,U_14),U_13) = sdtasdt0(U_15,sdtasdt0(U_14,U_13))
| ~ aNaturalNumber0(U_13)
| ~ aNaturalNumber0(U_14)
| ~ aNaturalNumber0(U_15) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[m_MulUnit]) ).
fof(f_11_2,plain,
! [U_16] :
( ( U_16 = sdtasdt0(sz10,U_16)
& sdtasdt0(U_16,sz10) = U_16 )
| ~ aNaturalNumber0(U_16) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( sdtasdt0(U_16,sz10) = U_16
| ~ aNaturalNumber0(U_16) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( U_16 = sdtasdt0(sz10,U_16)
| ~ aNaturalNumber0(U_16) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[m_MulZero]) ).
fof(f_12_2,plain,
! [U_17] :
( ( sz00 = sdtasdt0(sz00,U_17)
& sdtasdt0(U_17,sz00) = sz00 )
| ~ aNaturalNumber0(U_17) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( sdtasdt0(U_17,sz00) = sz00
| ~ aNaturalNumber0(U_17) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( sz00 = sdtasdt0(sz00,U_17)
| ~ aNaturalNumber0(U_17) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [W0,W1,W2] :
( ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mAMDistr]) ).
fof(f_13_2,plain,
! [U_20,U_19,U_18] :
( ( sdtasdt0(sdtpldt0(U_19,U_18),U_20) = sdtpldt0(sdtasdt0(U_19,U_20),sdtasdt0(U_18,U_20))
& sdtasdt0(U_20,sdtpldt0(U_19,U_18)) = sdtpldt0(sdtasdt0(U_20,U_19),sdtasdt0(U_20,U_18)) )
| ~ aNaturalNumber0(U_18)
| ~ aNaturalNumber0(U_19)
| ~ aNaturalNumber0(U_20) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( sdtasdt0(U_20,sdtpldt0(U_19,U_18)) = sdtpldt0(sdtasdt0(U_20,U_19),sdtasdt0(U_20,U_18))
| ~ aNaturalNumber0(U_18)
| ~ aNaturalNumber0(U_19)
| ~ aNaturalNumber0(U_20) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( sdtasdt0(sdtpldt0(U_19,U_18),U_20) = sdtpldt0(sdtasdt0(U_19,U_20),sdtasdt0(U_18,U_20))
| ~ aNaturalNumber0(U_18)
| ~ aNaturalNumber0(U_19)
| ~ aNaturalNumber0(U_20) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [W0,W1,W2] :
( W1 = W2
| ( sdtpldt0(W1,W0) != sdtpldt0(W2,W0)
& sdtpldt0(W0,W1) != sdtpldt0(W0,W2) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mAddCanc]) ).
fof(f_14_2,plain,
! [U_23,U_22,U_21] :
( U_22 = U_21
| ( sdtpldt0(U_22,U_23) != sdtpldt0(U_21,U_23)
& sdtpldt0(U_23,U_22) != sdtpldt0(U_23,U_21) )
| ~ aNaturalNumber0(U_21)
| ~ aNaturalNumber0(U_22)
| ~ aNaturalNumber0(U_23) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( sdtpldt0(U_23,U_22) != sdtpldt0(U_23,U_21)
| U_22 = U_21
| ~ aNaturalNumber0(U_21)
| ~ aNaturalNumber0(U_22)
| ~ aNaturalNumber0(U_23) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( sdtpldt0(U_22,U_23) != sdtpldt0(U_21,U_23)
| U_22 = U_21
| ~ aNaturalNumber0(U_21)
| ~ aNaturalNumber0(U_22)
| ~ aNaturalNumber0(U_23) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [W0] :
( ! [W1,W2] :
( W1 = W2
| ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
& sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) )
| W0 = sz00
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mMulCanc]) ).
fof(f_15_2,plain,
! [U_26] :
( ! [U_25,U_24] :
( U_25 = U_24
| ( sdtasdt0(U_25,U_26) != sdtasdt0(U_24,U_26)
& sdtasdt0(U_26,U_25) != sdtasdt0(U_26,U_24) )
| ~ aNaturalNumber0(U_24)
| ~ aNaturalNumber0(U_25) )
| U_26 = sz00
| ~ aNaturalNumber0(U_26) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( sdtasdt0(U_26,U_25) != sdtasdt0(U_26,U_24)
| U_25 = U_24
| ~ aNaturalNumber0(U_24)
| ~ aNaturalNumber0(U_25)
| U_26 = sz00
| ~ aNaturalNumber0(U_26) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( sdtasdt0(U_25,U_26) != sdtasdt0(U_24,U_26)
| U_25 = U_24
| ~ aNaturalNumber0(U_24)
| ~ aNaturalNumber0(U_25)
| U_26 = sz00
| ~ aNaturalNumber0(U_26) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [W0,W1] :
( ( W1 = sz00
& W0 = sz00 )
| sdtpldt0(W0,W1) != sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mZeroAdd]) ).
fof(f_16_2,plain,
! [U_28,U_27] :
( ( U_27 = sz00
& U_28 = sz00 )
| sdtpldt0(U_28,U_27) != sz00
| ~ aNaturalNumber0(U_27)
| ~ aNaturalNumber0(U_28) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( U_28 = sz00
| sdtpldt0(U_28,U_27) != sz00
| ~ aNaturalNumber0(U_27)
| ~ aNaturalNumber0(U_28) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( U_27 = sz00
| sdtpldt0(U_28,U_27) != sz00
| ~ aNaturalNumber0(U_27)
| ~ aNaturalNumber0(U_28) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [W0,W1] :
( W1 = sz00
| W0 = sz00
| sdtasdt0(W0,W1) != sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mZeroMul]) ).
fof(f_17_2,plain,
! [U_30,U_29] :
( U_29 = sz00
| U_30 = sz00
| sdtasdt0(U_30,U_29) != sz00
| ~ aNaturalNumber0(U_29)
| ~ aNaturalNumber0(U_30) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( U_29 = sz00
| U_30 = sz00
| sdtasdt0(U_30,U_29) != sz00
| ~ aNaturalNumber0(U_29)
| ~ aNaturalNumber0(U_30) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [W0,W1] :
( ( ( sdtlseqdt0(W0,W1)
| ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) ) )
& ( ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mDefLE]) ).
fof(f_18_2,plain,
! [U_34,U_33] :
( ( ( sdtlseqdt0(U_34,U_33)
| ! [U_32] :
( sdtpldt0(U_34,U_32) != U_33
| ~ aNaturalNumber0(U_32) ) )
& ( ? [U_31] :
( sdtpldt0(U_34,U_31) = U_33
& aNaturalNumber0(U_31) )
| ~ sdtlseqdt0(U_34,U_33) ) )
| ~ aNaturalNumber0(U_33)
| ~ aNaturalNumber0(U_34) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_34,U_33] :
( ( ( sdtlseqdt0(U_34,U_33)
| ! [U_32] :
( sdtpldt0(U_34,U_32) != U_33
| ~ aNaturalNumber0(U_32) ) )
& ( ( sdtpldt0(U_34,sK1(U_34,U_33)) = U_33
& aNaturalNumber0(sK1(U_34,U_33)) )
| ~ sdtlseqdt0(U_34,U_33) ) )
| ~ aNaturalNumber0(U_33)
| ~ aNaturalNumber0(U_34) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_31,sK1(U_34,U_33))],[f_18_2]) ).
cnf(f_18_4,plain,
( aNaturalNumber0(sK1(U_34,U_33))
| ~ sdtlseqdt0(U_34,U_33)
| ~ aNaturalNumber0(U_33)
| ~ aNaturalNumber0(U_34) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
( sdtpldt0(U_34,sK1(U_34,U_33)) = U_33
| ~ sdtlseqdt0(U_34,U_33)
| ~ aNaturalNumber0(U_33)
| ~ aNaturalNumber0(U_34) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_6,plain,
( sdtlseqdt0(U_34,U_33)
| sdtpldt0(U_34,U_32) != U_33
| ~ aNaturalNumber0(U_32)
| ~ aNaturalNumber0(U_33)
| ~ aNaturalNumber0(U_34) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = sdtmndt0(W1,W0)
| sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
& ( ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| W2 != sdtmndt0(W1,W0) ) )
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mDefDiff]) ).
fof(f_19_2,plain,
! [U_37,U_36] :
( ! [U_35] :
( ( U_35 = sdtmndt0(U_36,U_37)
| sdtpldt0(U_37,U_35) != U_36
| ~ aNaturalNumber0(U_35) )
& ( ( sdtpldt0(U_37,U_35) = U_36
& aNaturalNumber0(U_35) )
| U_35 != sdtmndt0(U_36,U_37) ) )
| ~ sdtlseqdt0(U_37,U_36)
| ~ aNaturalNumber0(U_36)
| ~ aNaturalNumber0(U_37) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_37,U_36] :
( ( ! [U_39] :
( U_39 = sdtmndt0(U_36,U_37)
| sdtpldt0(U_37,U_39) != U_36
| ~ aNaturalNumber0(U_39) )
& ! [U_38] :
( ( sdtpldt0(U_37,U_38) = U_36
& aNaturalNumber0(U_38) )
| U_38 != sdtmndt0(U_36,U_37) ) )
| ~ sdtlseqdt0(U_37,U_36)
| ~ aNaturalNumber0(U_36)
| ~ aNaturalNumber0(U_37) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( aNaturalNumber0(U_38)
| U_38 != sdtmndt0(U_36,U_37)
| ~ sdtlseqdt0(U_37,U_36)
| ~ aNaturalNumber0(U_36)
| ~ aNaturalNumber0(U_37) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
( sdtpldt0(U_37,U_38) = U_36
| U_38 != sdtmndt0(U_36,U_37)
| ~ sdtlseqdt0(U_37,U_36)
| ~ aNaturalNumber0(U_36)
| ~ aNaturalNumber0(U_37) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_6,plain,
( U_39 = sdtmndt0(U_36,U_37)
| sdtpldt0(U_37,U_39) != U_36
| ~ aNaturalNumber0(U_39)
| ~ sdtlseqdt0(U_37,U_36)
| ~ aNaturalNumber0(U_36)
| ~ aNaturalNumber0(U_37) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [W0] :
( sdtlseqdt0(W0,W0)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mLERefl]) ).
fof(f_20_2,plain,
! [U_40] :
( sdtlseqdt0(U_40,U_40)
| ~ aNaturalNumber0(U_40) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( sdtlseqdt0(U_40,U_40)
| ~ aNaturalNumber0(U_40) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mLEAsym]) ).
fof(f_21_2,plain,
! [U_42,U_41] :
( U_42 = U_41
| ~ sdtlseqdt0(U_41,U_42)
| ~ sdtlseqdt0(U_42,U_41)
| ~ aNaturalNumber0(U_41)
| ~ aNaturalNumber0(U_42) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( U_42 = U_41
| ~ sdtlseqdt0(U_41,U_42)
| ~ sdtlseqdt0(U_42,U_41)
| ~ aNaturalNumber0(U_41)
| ~ aNaturalNumber0(U_42) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [W0,W1,W2] :
( sdtlseqdt0(W0,W2)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mLETran]) ).
fof(f_22_2,plain,
! [U_45,U_44,U_43] :
( sdtlseqdt0(U_45,U_43)
| ~ sdtlseqdt0(U_44,U_43)
| ~ sdtlseqdt0(U_45,U_44)
| ~ aNaturalNumber0(U_43)
| ~ aNaturalNumber0(U_44)
| ~ aNaturalNumber0(U_45) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( sdtlseqdt0(U_45,U_43)
| ~ sdtlseqdt0(U_44,U_43)
| ~ sdtlseqdt0(U_45,U_44)
| ~ aNaturalNumber0(U_43)
| ~ aNaturalNumber0(U_44)
| ~ aNaturalNumber0(U_45) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [W0,W1] :
( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mLETotal]) ).
fof(f_23_2,plain,
! [U_47,U_46] :
( ( sdtlseqdt0(U_46,U_47)
& U_46 != U_47 )
| sdtlseqdt0(U_47,U_46)
| ~ aNaturalNumber0(U_46)
| ~ aNaturalNumber0(U_47) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( U_46 != U_47
| sdtlseqdt0(U_47,U_46)
| ~ aNaturalNumber0(U_46)
| ~ aNaturalNumber0(U_47) ),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( sdtlseqdt0(U_46,U_47)
| sdtlseqdt0(U_47,U_46)
| ~ aNaturalNumber0(U_46)
| ~ aNaturalNumber0(U_47) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [W0,W1] :
( ! [W2] :
( ( sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2))
& sdtpldt0(W0,W2) != sdtpldt0(W1,W2)
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
| ~ aNaturalNumber0(W2) )
| ~ sdtlseqdt0(W0,W1)
| W0 = W1
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mMonAdd]) ).
fof(f_24_2,plain,
! [U_50,U_49] :
( ! [U_48] :
( ( sdtlseqdt0(sdtpldt0(U_50,U_48),sdtpldt0(U_49,U_48))
& sdtpldt0(U_50,U_48) != sdtpldt0(U_49,U_48)
& sdtlseqdt0(sdtpldt0(U_48,U_50),sdtpldt0(U_48,U_49))
& sdtpldt0(U_48,U_50) != sdtpldt0(U_48,U_49) )
| ~ aNaturalNumber0(U_48) )
| ~ sdtlseqdt0(U_50,U_49)
| U_50 = U_49
| ~ aNaturalNumber0(U_49)
| ~ aNaturalNumber0(U_50) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( sdtpldt0(U_48,U_50) != sdtpldt0(U_48,U_49)
| ~ aNaturalNumber0(U_48)
| ~ sdtlseqdt0(U_50,U_49)
| U_50 = U_49
| ~ aNaturalNumber0(U_49)
| ~ aNaturalNumber0(U_50) ),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
( sdtlseqdt0(sdtpldt0(U_48,U_50),sdtpldt0(U_48,U_49))
| ~ aNaturalNumber0(U_48)
| ~ sdtlseqdt0(U_50,U_49)
| U_50 = U_49
| ~ aNaturalNumber0(U_49)
| ~ aNaturalNumber0(U_50) ),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_5,plain,
( sdtpldt0(U_50,U_48) != sdtpldt0(U_49,U_48)
| ~ aNaturalNumber0(U_48)
| ~ sdtlseqdt0(U_50,U_49)
| U_50 = U_49
| ~ aNaturalNumber0(U_49)
| ~ aNaturalNumber0(U_50) ),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_6,plain,
( sdtlseqdt0(sdtpldt0(U_50,U_48),sdtpldt0(U_49,U_48))
| ~ aNaturalNumber0(U_48)
| ~ sdtlseqdt0(U_50,U_49)
| U_50 = U_49
| ~ aNaturalNumber0(U_49)
| ~ aNaturalNumber0(U_50) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [W0,W1,W2] :
( ( sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
| ~ sdtlseqdt0(W1,W2)
| W1 = W2
| W0 = sz00
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mMonMul]) ).
fof(f_25_2,plain,
! [U_53,U_52,U_51] :
( ( sdtlseqdt0(sdtasdt0(U_52,U_53),sdtasdt0(U_51,U_53))
& sdtasdt0(U_52,U_53) != sdtasdt0(U_51,U_53)
& sdtlseqdt0(sdtasdt0(U_53,U_52),sdtasdt0(U_53,U_51))
& sdtasdt0(U_53,U_52) != sdtasdt0(U_53,U_51) )
| ~ sdtlseqdt0(U_52,U_51)
| U_52 = U_51
| U_53 = sz00
| ~ aNaturalNumber0(U_51)
| ~ aNaturalNumber0(U_52)
| ~ aNaturalNumber0(U_53) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( sdtasdt0(U_53,U_52) != sdtasdt0(U_53,U_51)
| ~ sdtlseqdt0(U_52,U_51)
| U_52 = U_51
| U_53 = sz00
| ~ aNaturalNumber0(U_51)
| ~ aNaturalNumber0(U_52)
| ~ aNaturalNumber0(U_53) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_4,plain,
( sdtlseqdt0(sdtasdt0(U_53,U_52),sdtasdt0(U_53,U_51))
| ~ sdtlseqdt0(U_52,U_51)
| U_52 = U_51
| U_53 = sz00
| ~ aNaturalNumber0(U_51)
| ~ aNaturalNumber0(U_52)
| ~ aNaturalNumber0(U_53) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_5,plain,
( sdtasdt0(U_52,U_53) != sdtasdt0(U_51,U_53)
| ~ sdtlseqdt0(U_52,U_51)
| U_52 = U_51
| U_53 = sz00
| ~ aNaturalNumber0(U_51)
| ~ aNaturalNumber0(U_52)
| ~ aNaturalNumber0(U_53) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_6,plain,
( sdtlseqdt0(sdtasdt0(U_52,U_53),sdtasdt0(U_51,U_53))
| ~ sdtlseqdt0(U_52,U_51)
| U_52 = U_51
| U_53 = sz00
| ~ aNaturalNumber0(U_51)
| ~ aNaturalNumber0(U_52)
| ~ aNaturalNumber0(U_53) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [W0] :
( ( sdtlseqdt0(sz10,W0)
& sz10 != W0 )
| W0 = sz10
| W0 = sz00
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mLENTr]) ).
fof(f_26_2,plain,
! [U_54] :
( ( sdtlseqdt0(sz10,U_54)
& sz10 != U_54 )
| U_54 = sz10
| U_54 = sz00
| ~ aNaturalNumber0(U_54) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( sz10 != U_54
| U_54 = sz10
| U_54 = sz00
| ~ aNaturalNumber0(U_54) ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
( sdtlseqdt0(sz10,U_54)
| U_54 = sz10
| U_54 = sz00
| ~ aNaturalNumber0(U_54) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [W0,W1] :
( sdtlseqdt0(W1,sdtasdt0(W1,W0))
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mMonMul2]) ).
fof(f_27_2,plain,
! [U_56,U_55] :
( sdtlseqdt0(U_55,sdtasdt0(U_55,U_56))
| U_56 = sz00
| ~ aNaturalNumber0(U_55)
| ~ aNaturalNumber0(U_56) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( sdtlseqdt0(U_55,sdtasdt0(U_55,U_56))
| U_56 = sz00
| ~ aNaturalNumber0(U_55)
| ~ aNaturalNumber0(U_56) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [W0,W1] :
( $true
| ~ iLess0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mIH]) ).
fof(f_28_2,plain,
! [U_58,U_57] :
( $true
| ~ iLess0(U_58,U_57)
| ~ aNaturalNumber0(U_57)
| ~ aNaturalNumber0(U_58) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( $true
| ~ iLess0(U_58,U_57)
| ~ aNaturalNumber0(U_57)
| ~ aNaturalNumber0(U_58) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [W0,W1] :
( iLess0(W0,W1)
| ~ sdtlseqdt0(W0,W1)
| W0 = W1
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mIH_03]) ).
fof(f_29_2,plain,
! [U_60,U_59] :
( iLess0(U_60,U_59)
| ~ sdtlseqdt0(U_60,U_59)
| U_60 = U_59
| ~ aNaturalNumber0(U_59)
| ~ aNaturalNumber0(U_60) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( iLess0(U_60,U_59)
| ~ sdtlseqdt0(U_60,U_59)
| U_60 = U_59
| ~ aNaturalNumber0(U_59)
| ~ aNaturalNumber0(U_60) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [W0,W1] :
( ( ( doDivides0(W0,W1)
| ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) ) )
& ( ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mDefDiv]) ).
fof(f_30_2,plain,
! [U_64,U_63] :
( ( ( doDivides0(U_64,U_63)
| ! [U_62] :
( U_63 != sdtasdt0(U_64,U_62)
| ~ aNaturalNumber0(U_62) ) )
& ( ? [U_61] :
( U_63 = sdtasdt0(U_64,U_61)
& aNaturalNumber0(U_61) )
| ~ doDivides0(U_64,U_63) ) )
| ~ aNaturalNumber0(U_63)
| ~ aNaturalNumber0(U_64) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_64,U_63] :
( ( ( doDivides0(U_64,U_63)
| ! [U_62] :
( U_63 != sdtasdt0(U_64,U_62)
| ~ aNaturalNumber0(U_62) ) )
& ( ( U_63 = sdtasdt0(U_64,sK2(U_64,U_63))
& aNaturalNumber0(sK2(U_64,U_63)) )
| ~ doDivides0(U_64,U_63) ) )
| ~ aNaturalNumber0(U_63)
| ~ aNaturalNumber0(U_64) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_61,sK2(U_64,U_63))],[f_30_2]) ).
cnf(f_30_4,plain,
( aNaturalNumber0(sK2(U_64,U_63))
| ~ doDivides0(U_64,U_63)
| ~ aNaturalNumber0(U_63)
| ~ aNaturalNumber0(U_64) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
( U_63 = sdtasdt0(U_64,sK2(U_64,U_63))
| ~ doDivides0(U_64,U_63)
| ~ aNaturalNumber0(U_63)
| ~ aNaturalNumber0(U_64) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_6,plain,
( doDivides0(U_64,U_63)
| U_63 != sdtasdt0(U_64,U_62)
| ~ aNaturalNumber0(U_62)
| ~ aNaturalNumber0(U_63)
| ~ aNaturalNumber0(U_64) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = sdtsldt0(W1,W0)
| W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) )
& ( ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| W2 != sdtsldt0(W1,W0) ) )
| ~ doDivides0(W0,W1)
| W0 = sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mDefQuot]) ).
fof(f_31_2,plain,
! [U_67,U_66] :
( ! [U_65] :
( ( U_65 = sdtsldt0(U_66,U_67)
| U_66 != sdtasdt0(U_67,U_65)
| ~ aNaturalNumber0(U_65) )
& ( ( U_66 = sdtasdt0(U_67,U_65)
& aNaturalNumber0(U_65) )
| U_65 != sdtsldt0(U_66,U_67) ) )
| ~ doDivides0(U_67,U_66)
| U_67 = sz00
| ~ aNaturalNumber0(U_66)
| ~ aNaturalNumber0(U_67) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_67,U_66] :
( ( ! [U_69] :
( U_69 = sdtsldt0(U_66,U_67)
| U_66 != sdtasdt0(U_67,U_69)
| ~ aNaturalNumber0(U_69) )
& ! [U_68] :
( ( U_66 = sdtasdt0(U_67,U_68)
& aNaturalNumber0(U_68) )
| U_68 != sdtsldt0(U_66,U_67) ) )
| ~ doDivides0(U_67,U_66)
| U_67 = sz00
| ~ aNaturalNumber0(U_66)
| ~ aNaturalNumber0(U_67) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( aNaturalNumber0(U_68)
| U_68 != sdtsldt0(U_66,U_67)
| ~ doDivides0(U_67,U_66)
| U_67 = sz00
| ~ aNaturalNumber0(U_66)
| ~ aNaturalNumber0(U_67) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
( U_66 = sdtasdt0(U_67,U_68)
| U_68 != sdtsldt0(U_66,U_67)
| ~ doDivides0(U_67,U_66)
| U_67 = sz00
| ~ aNaturalNumber0(U_66)
| ~ aNaturalNumber0(U_67) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_6,plain,
( U_69 = sdtsldt0(U_66,U_67)
| U_66 != sdtasdt0(U_67,U_69)
| ~ aNaturalNumber0(U_69)
| ~ doDivides0(U_67,U_66)
| U_67 = sz00
| ~ aNaturalNumber0(U_66)
| ~ aNaturalNumber0(U_67) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [W0,W1,W2] :
( doDivides0(W0,W2)
| ~ doDivides0(W1,W2)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mDivTrans]) ).
fof(f_32_2,plain,
! [U_72,U_71,U_70] :
( doDivides0(U_72,U_70)
| ~ doDivides0(U_71,U_70)
| ~ doDivides0(U_72,U_71)
| ~ aNaturalNumber0(U_70)
| ~ aNaturalNumber0(U_71)
| ~ aNaturalNumber0(U_72) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( doDivides0(U_72,U_70)
| ~ doDivides0(U_71,U_70)
| ~ doDivides0(U_72,U_71)
| ~ aNaturalNumber0(U_70)
| ~ aNaturalNumber0(U_71)
| ~ aNaturalNumber0(U_72) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [W0,W1,W2] :
( doDivides0(W0,sdtpldt0(W1,W2))
| ~ doDivides0(W0,W2)
| ~ doDivides0(W0,W1)
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mDivSum]) ).
fof(f_33_2,plain,
! [U_75,U_74,U_73] :
( doDivides0(U_75,sdtpldt0(U_74,U_73))
| ~ doDivides0(U_75,U_73)
| ~ doDivides0(U_75,U_74)
| ~ aNaturalNumber0(U_73)
| ~ aNaturalNumber0(U_74)
| ~ aNaturalNumber0(U_75) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( doDivides0(U_75,sdtpldt0(U_74,U_73))
| ~ doDivides0(U_75,U_73)
| ~ doDivides0(U_75,U_74)
| ~ aNaturalNumber0(U_73)
| ~ aNaturalNumber0(U_74)
| ~ aNaturalNumber0(U_75) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
inference(fof_nnf,[status(thm)],[m__1324]) ).
cnf(f_34_2,plain,
aNaturalNumber0(xl),
inference(clausify,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[f_34_1]) ).
cnf(f_34_4,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[f_34_1]) ).
fof(f_35_1,plain,
( doDivides0(xl,sdtpldt0(xm,xn))
& ? [W0] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) )
& doDivides0(xl,xm)
& ? [W0] :
( xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ),
inference(fof_nnf,[status(thm)],[m__1324_04]) ).
fof(f_35_2,plain,
( doDivides0(xl,sdtpldt0(xm,xn))
& ? [U_77] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,U_77)
& aNaturalNumber0(U_77) )
& doDivides0(xl,xm)
& ? [U_76] :
( xm = sdtasdt0(xl,U_76)
& aNaturalNumber0(U_76) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( doDivides0(xl,sdtpldt0(xm,xn))
& ? [U_77] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,U_77)
& aNaturalNumber0(U_77) )
& doDivides0(xl,xm)
& xm = sdtasdt0(xl,sK3)
& aNaturalNumber0(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_76,sK3)],[f_35_2]) ).
fof(f_35_4,plain,
( doDivides0(xl,sdtpldt0(xm,xn))
& sdtpldt0(xm,xn) = sdtasdt0(xl,sK4)
& aNaturalNumber0(sK4)
& doDivides0(xl,xm)
& xm = sdtasdt0(xl,sK3)
& aNaturalNumber0(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_77,sK4)],[f_35_3]) ).
cnf(f_35_5,plain,
aNaturalNumber0(sK3),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_6,plain,
xm = sdtasdt0(xl,sK3),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_7,plain,
doDivides0(xl,xm),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_8,plain,
aNaturalNumber0(sK4),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_9,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,sK4),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_10,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(clausify,[status(thm)],[f_35_4]) ).
fof(f_36_1,plain,
xl != sz00,
inference(fof_nnf,[status(thm)],[m__1347]) ).
cnf(f_36_2,plain,
xl != sz00,
inference(clausify,[status(thm)],[f_36_1]) ).
fof(f_37_1,plain,
( xp = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,xp)
& aNaturalNumber0(xp) ),
inference(fof_nnf,[status(thm)],[m__1360]) ).
cnf(f_37_2,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
xm = sdtasdt0(xl,xp),
inference(clausify,[status(thm)],[f_37_1]) ).
cnf(f_37_4,plain,
xp = sdtsldt0(xm,xl),
inference(clausify,[status(thm)],[f_37_1]) ).
fof(f_38_1,plain,
( xq = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
& aNaturalNumber0(xq) ),
inference(fof_nnf,[status(thm)],[m__1379]) ).
cnf(f_38_2,plain,
aNaturalNumber0(xq),
inference(clausify,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(clausify,[status(thm)],[f_38_1]) ).
cnf(f_38_4,plain,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(clausify,[status(thm)],[f_38_1]) ).
fof(f_39_1,plain,
( sdtlseqdt0(xp,xq)
& ? [W0] :
( sdtpldt0(xp,W0) = xq
& aNaturalNumber0(W0) ) ),
inference(fof_nnf,[status(thm)],[m__1395]) ).
fof(f_39_2,plain,
( sdtlseqdt0(xp,xq)
& ? [U_78] :
( sdtpldt0(xp,U_78) = xq
& aNaturalNumber0(U_78) ) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( sdtlseqdt0(xp,xq)
& sdtpldt0(xp,sK5) = xq
& aNaturalNumber0(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_78,sK5)],[f_39_2]) ).
cnf(f_39_4,plain,
aNaturalNumber0(sK5),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_5,plain,
sdtpldt0(xp,sK5) = xq,
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_6,plain,
sdtlseqdt0(xp,xq),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
( xr = sdtmndt0(xq,xp)
& sdtpldt0(xp,xr) = xq
& aNaturalNumber0(xr) ),
inference(fof_nnf,[status(thm)],[m__1422]) ).
cnf(f_40_2,plain,
aNaturalNumber0(xr),
inference(clausify,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
sdtpldt0(xp,xr) = xq,
inference(clausify,[status(thm)],[f_40_1]) ).
cnf(f_40_4,plain,
xr = sdtmndt0(xq,xp),
inference(clausify,[status(thm)],[f_40_1]) ).
fof(f_41_1,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(fof_nnf,[status(thm)],[m__1459]) ).
cnf(f_41_2,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(clausify,[status(thm)],[f_41_1]) ).
fof(f_42_1,negated_conjecture,
xn != sdtasdt0(xl,xr),
inference(negate,[status(cth)],[m__]) ).
cnf(f_42_2,negated_conjecture,
xn != sdtasdt0(xl,xr),
inference(clausify,[status(thm)],[f_42_1]) ).
cnf(f_1_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_4]) ).
cnf(f_28_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_28_3]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( sdtpldt0(Eq_x_0,Eq_x_1) = sdtpldt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( sdtasdt0(Eq_x_0,Eq_x_1) = sdtasdt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( sdtmndt0(Eq_x_0,Eq_x_1) = sdtmndt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sdtsldt0(Eq_x_0,Eq_x_1) = sdtsldt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( aNaturalNumber0(Eq_y_0)
| ~ aNaturalNumber0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_11,axiom,
( sdtlseqdt0(Eq_y_0,Eq_y_1)
| ~ sdtlseqdt0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,axiom,
( iLess0(Eq_y_0,Eq_y_1)
| ~ iLess0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,axiom,
( doDivides0(Eq_y_0,Eq_y_1)
| ~ doDivides0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM475+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 18:31:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 199.39/199.71 % SZS status Theorem for theBenchmark
% 199.39/199.71 % SZS output start Proof for theBenchmark
% See solution above
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