TSTP Solution File: NUM517+1 by E-SAT---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : NUM517+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n032.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:07:30 EDT 2023
% Result : Theorem 17.19s 2.62s
% Output : CNFRefutation 17.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 25
% Syntax : Number of formulae : 116 ( 30 unt; 0 def)
% Number of atoms : 377 ( 111 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 456 ( 195 ~; 196 |; 41 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 128 ( 0 sgn; 59 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',mSortsB_02) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',m_MulZero) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',mZeroMul) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',mSortsC) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',mSortsC_01) ).
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/tmp/tmp.ec57guSsS7/E---3.1_20644.p',mMulCanc) ).
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/tmp/tmp.ec57guSsS7/E---3.1_20644.p',mMulAsso) ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',m__2342) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',m_MulUnit) ).
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/tmp/tmp.ec57guSsS7/E---3.1_20644.p',mDivTrans) ).
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/tmp/tmp.ec57guSsS7/E---3.1_20644.p',mDefQuot) ).
fof(m__2315,hypothesis,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',m__2315) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',m__1837) ).
fof(m__2487,hypothesis,
doDivides0(xr,xn),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',m__2487) ).
fof(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',m__1860) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',m__2306) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',mMulComm) ).
fof(mIH_03,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> iLess0(X1,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',mIH_03) ).
fof(m__,conjecture,
( doDivides0(xp,sdtsldt0(xn,xr))
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',m__) ).
fof(m__2287,hypothesis,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',m__2287) ).
fof(m__1799,hypothesis,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( isPrime0(X3)
& doDivides0(X3,sdtasdt0(X1,X2)) )
=> ( iLess0(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(X3,X1)
| doDivides0(X3,X2) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',m__1799) ).
fof(m__2686,hypothesis,
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
& sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',m__2686) ).
fof(m__2529,hypothesis,
doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',m__2529) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p',mSortsB) ).
fof(c_0_25,plain,
! [X60,X61,X63] :
( ( aNaturalNumber0(esk2_2(X60,X61))
| ~ doDivides0(X60,X61)
| ~ aNaturalNumber0(X60)
| ~ aNaturalNumber0(X61) )
& ( X61 = sdtasdt0(X60,esk2_2(X60,X61))
| ~ doDivides0(X60,X61)
| ~ aNaturalNumber0(X60)
| ~ aNaturalNumber0(X61) )
& ( ~ aNaturalNumber0(X63)
| X61 != sdtasdt0(X60,X63)
| doDivides0(X60,X61)
| ~ aNaturalNumber0(X60)
| ~ aNaturalNumber0(X61) ) ),
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_26,plain,
! [X6,X7] :
( ~ aNaturalNumber0(X6)
| ~ aNaturalNumber0(X7)
| aNaturalNumber0(sdtasdt0(X6,X7)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_27,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_28,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_29,plain,
! [X20] :
( ( sdtasdt0(X20,sz00) = sz00
| ~ aNaturalNumber0(X20) )
& ( sz00 = sdtasdt0(sz00,X20)
| ~ aNaturalNumber0(X20) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
fof(c_0_30,plain,
! [X32,X33] :
( ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X33)
| sdtasdt0(X32,X33) != sz00
| X32 = sz00
| X33 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])]) ).
cnf(c_0_31,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_27]),c_0_28]) ).
cnf(c_0_32,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_34,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
( X1 = sdtasdt0(X2,esk2_2(X2,X1))
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,plain,
( doDivides0(X1,sz00)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_37,plain,
( esk2_2(X1,sz00) = sz00
| X1 = sz00
| ~ aNaturalNumber0(esk2_2(X1,sz00))
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35])]),c_0_33])]),c_0_36]) ).
cnf(c_0_38,plain,
( aNaturalNumber0(esk2_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_39,plain,
( esk2_2(X1,sz00) = sz00
| X1 = sz00
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_33])]),c_0_36]) ).
cnf(c_0_40,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_41,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
fof(c_0_42,plain,
! [X27,X28,X29] :
( ( sdtasdt0(X27,X28) != sdtasdt0(X27,X29)
| X28 = X29
| ~ aNaturalNumber0(X28)
| ~ aNaturalNumber0(X29)
| X27 = sz00
| ~ aNaturalNumber0(X27) )
& ( sdtasdt0(X28,X27) != sdtasdt0(X29,X27)
| X28 = X29
| ~ aNaturalNumber0(X28)
| ~ aNaturalNumber0(X29)
| X27 = sz00
| ~ aNaturalNumber0(X27) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
fof(c_0_43,plain,
! [X16,X17,X18] :
( ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X17)
| ~ aNaturalNumber0(X18)
| sdtasdt0(sdtasdt0(X16,X17),X18) = sdtasdt0(X16,sdtasdt0(X17,X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_44,plain,
esk2_2(sz10,sz00) = sz00,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_45,plain,
( X2 = X3
| X1 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_46,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
fof(c_0_47,plain,
! [X19] :
( ( sdtasdt0(X19,sz10) = X19
| ~ aNaturalNumber0(X19) )
& ( X19 = sdtasdt0(sz10,X19)
| ~ aNaturalNumber0(X19) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
cnf(c_0_48,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_49,plain,
( sdtasdt0(sz10,sz00) = sz00
| ~ doDivides0(sz10,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_44]),c_0_40]),c_0_33])]) ).
cnf(c_0_50,hypothesis,
( X1 = xr
| X2 = sz00
| sdtasdt0(X2,X1) != sdtasdt0(X2,xr)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_48]),c_0_28]) ).
cnf(c_0_53,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_36]),c_0_40])]) ).
cnf(c_0_54,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_55,plain,
! [X67,X68,X69] :
( ~ aNaturalNumber0(X67)
| ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X69)
| ~ doDivides0(X67,X68)
| ~ doDivides0(X68,X69)
| doDivides0(X67,X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])]) ).
fof(c_0_56,plain,
! [X64,X65,X66] :
( ( aNaturalNumber0(X66)
| X66 != sdtsldt0(X65,X64)
| X64 = sz00
| ~ doDivides0(X64,X65)
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X65) )
& ( X65 = sdtasdt0(X64,X66)
| X66 != sdtsldt0(X65,X64)
| X64 = sz00
| ~ doDivides0(X64,X65)
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X65) )
& ( ~ aNaturalNumber0(X66)
| X65 != sdtasdt0(X64,X66)
| X66 = sdtsldt0(X65,X64)
| X64 = sz00
| ~ doDivides0(X64,X65)
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X65) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_57,hypothesis,
( X1 = xr
| sdtasdt0(sz10,X1) != xr
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_40]),c_0_46])]),c_0_41]) ).
cnf(c_0_58,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_32,c_0_48]),c_0_33])]),c_0_28]) ).
cnf(c_0_59,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_52,c_0_53]),c_0_33]),c_0_40])]) ).
cnf(c_0_60,plain,
( X1 = sz00
| ~ doDivides0(sz00,X1)
| ~ aNaturalNumber0(esk2_2(sz00,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_35]),c_0_33])]) ).
cnf(c_0_61,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_62,hypothesis,
doDivides0(xr,xk),
inference(split_conjunct,[status(thm)],[m__2342]) ).
fof(c_0_63,hypothesis,
( xk != sz00
& xk != sz10 ),
inference(fof_nnf,[status(thm)],[m__2315]) ).
cnf(c_0_64,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_65,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_66,hypothesis,
doDivides0(xr,xn),
inference(split_conjunct,[status(thm)],[m__2487]) ).
cnf(c_0_67,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_68,hypothesis,
( sdtasdt0(X1,sz00) = xr
| xr != sz00
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_40])]),c_0_59]) ).
cnf(c_0_69,plain,
( X1 = sz00
| ~ doDivides0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_38]),c_0_33])]) ).
cnf(c_0_70,hypothesis,
( doDivides0(X1,xk)
| ~ doDivides0(X1,xr)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_46])]) ).
cnf(c_0_71,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_72,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_64]) ).
cnf(c_0_73,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_74,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_75,hypothesis,
( X1 = xp
| X2 = sz00
| sdtasdt0(X2,X1) != sdtasdt0(X2,xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_45,c_0_65]) ).
fof(c_0_76,plain,
! [X14,X15] :
( ~ aNaturalNumber0(X14)
| ~ aNaturalNumber0(X15)
| sdtasdt0(X14,X15) = sdtasdt0(X15,X14) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_77,plain,
( doDivides0(X1,sdtasdt0(X2,X3))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_31]),c_0_28]) ).
cnf(c_0_78,hypothesis,
( doDivides0(X1,xn)
| ~ doDivides0(X1,xr)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_66]),c_0_67]),c_0_46])]) ).
cnf(c_0_79,hypothesis,
( doDivides0(X1,xr)
| xr != sz00
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_68]),c_0_33])]) ).
cnf(c_0_80,hypothesis,
( ~ doDivides0(sz00,xr)
| ~ aNaturalNumber0(xk) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_33])]),c_0_71]) ).
cnf(c_0_81,hypothesis,
( xp = sz00
| aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]),c_0_65])]) ).
cnf(c_0_82,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_83,hypothesis,
( X1 = xp
| sdtasdt0(sz10,X1) != xp
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_51]),c_0_40]),c_0_65])]),c_0_41]) ).
cnf(c_0_84,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_85,plain,
( sdtasdt0(X1,X2) = sz00
| ~ doDivides0(sz00,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_77]),c_0_33])]),c_0_28]) ).
cnf(c_0_86,hypothesis,
( doDivides0(X1,xn)
| xr != sz00
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_87,hypothesis,
( xr != sz00
| ~ aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_79]),c_0_33])]) ).
cnf(c_0_88,hypothesis,
( xp = sz00
| aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_28]),c_0_82]),c_0_67])]) ).
fof(c_0_89,plain,
! [X58,X59] :
( ~ aNaturalNumber0(X58)
| ~ aNaturalNumber0(X59)
| X58 = X59
| ~ sdtlseqdt0(X58,X59)
| iLess0(X58,X59) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH_03])]) ).
fof(c_0_90,negated_conjecture,
~ ( doDivides0(xp,sdtsldt0(xn,xr))
| doDivides0(xp,xm) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_91,hypothesis,
( X1 = xp
| sdtasdt0(X1,sz10) != xp
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_40])]) ).
cnf(c_0_92,hypothesis,
( sdtasdt0(xn,X1) = sz00
| xr != sz00
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_67]),c_0_33])]) ).
cnf(c_0_93,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[m__2287]) ).
cnf(c_0_94,hypothesis,
( xp = sz00
| xr != sz00 ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
fof(c_0_95,hypothesis,
! [X86,X87,X88] :
( ~ aNaturalNumber0(X86)
| ~ aNaturalNumber0(X87)
| ~ aNaturalNumber0(X88)
| ~ isPrime0(X88)
| ~ doDivides0(X88,sdtasdt0(X86,X87))
| ~ iLess0(sdtpldt0(sdtpldt0(X86,X87),X88),sdtpldt0(sdtpldt0(xn,xm),xp))
| doDivides0(X88,X86)
| doDivides0(X88,X87) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1799])]) ).
cnf(c_0_96,plain,
( X1 = X2
| iLess0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_97,hypothesis,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(split_conjunct,[status(thm)],[m__2686]) ).
cnf(c_0_98,hypothesis,
sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2686]) ).
fof(c_0_99,negated_conjecture,
( ~ doDivides0(xp,sdtsldt0(xn,xr))
& ~ doDivides0(xp,xm) ),
inference(fof_nnf,[status(thm)],[c_0_90]) ).
cnf(c_0_100,hypothesis,
( xr = sz00
| aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_66]),c_0_46]),c_0_67])]) ).
cnf(c_0_101,hypothesis,
xr != sz00,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_67]),c_0_40])]),c_0_93]),c_0_94]) ).
cnf(c_0_102,hypothesis,
( doDivides0(X3,X1)
| doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ isPrime0(X3)
| ~ doDivides0(X3,sdtasdt0(X1,X2))
| ~ iLess0(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_103,hypothesis,
( iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98]) ).
cnf(c_0_104,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_105,hypothesis,
doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(split_conjunct,[status(thm)],[m__2529]) ).
cnf(c_0_106,negated_conjecture,
~ doDivides0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_107,negated_conjecture,
~ doDivides0(xp,sdtsldt0(xn,xr)),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_108,hypothesis,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(sr,[status(thm)],[c_0_100,c_0_101]) ).
fof(c_0_109,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| aNaturalNumber0(sdtpldt0(X4,X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_110,hypothesis,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]),c_0_105]),c_0_65]),c_0_82])]),c_0_106]),c_0_107]),c_0_108])]) ).
cnf(c_0_111,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_112,hypothesis,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_65])]) ).
cnf(c_0_113,hypothesis,
~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_111]),c_0_82]),c_0_108])]) ).
cnf(c_0_114,hypothesis,
~ aNaturalNumber0(sdtpldt0(xn,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_111]),c_0_65])]) ).
cnf(c_0_115,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_111]),c_0_82]),c_0_67])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : NUM517+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 2400
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Oct 2 14:57:49 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.16/0.43 Running first-order model finding
% 0.16/0.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.ec57guSsS7/E---3.1_20644.p
% 17.19/2.62 # Version: 3.1pre001
% 17.19/2.62 # Preprocessing class: FSLSSMSSSSSNFFN.
% 17.19/2.62 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.19/2.62 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 17.19/2.62 # Starting new_bool_3 with 300s (1) cores
% 17.19/2.62 # Starting new_bool_1 with 300s (1) cores
% 17.19/2.62 # Starting sh5l with 300s (1) cores
% 17.19/2.62 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 20722 completed with status 0
% 17.19/2.62 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 17.19/2.62 # Preprocessing class: FSLSSMSSSSSNFFN.
% 17.19/2.62 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.19/2.62 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 17.19/2.62 # No SInE strategy applied
% 17.19/2.62 # Search class: FGHSF-FFMM21-MFFFFFNN
% 17.19/2.62 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 17.19/2.62 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 17.19/2.62 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 17.19/2.62 # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 17.19/2.62 # Starting new_bool_3 with 136s (1) cores
% 17.19/2.62 # Starting new_bool_1 with 136s (1) cores
% 17.19/2.62 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 20726 completed with status 0
% 17.19/2.62 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 17.19/2.62 # Preprocessing class: FSLSSMSSSSSNFFN.
% 17.19/2.62 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.19/2.62 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 17.19/2.62 # No SInE strategy applied
% 17.19/2.62 # Search class: FGHSF-FFMM21-MFFFFFNN
% 17.19/2.62 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 17.19/2.62 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 17.19/2.62 # Preprocessing time : 0.002 s
% 17.19/2.62 # Presaturation interreduction done
% 17.19/2.62
% 17.19/2.62 # Proof found!
% 17.19/2.62 # SZS status Theorem
% 17.19/2.62 # SZS output start CNFRefutation
% See solution above
% 17.19/2.62 # Parsed axioms : 56
% 17.19/2.62 # Removed by relevancy pruning/SinE : 0
% 17.19/2.62 # Initial clauses : 103
% 17.19/2.62 # Removed in clause preprocessing : 3
% 17.19/2.62 # Initial clauses in saturation : 100
% 17.19/2.62 # Processed clauses : 10085
% 17.19/2.62 # ...of these trivial : 409
% 17.19/2.62 # ...subsumed : 5798
% 17.19/2.62 # ...remaining for further processing : 3878
% 17.19/2.62 # Other redundant clauses eliminated : 386
% 17.19/2.62 # Clauses deleted for lack of memory : 0
% 17.19/2.62 # Backward-subsumed : 445
% 17.19/2.62 # Backward-rewritten : 350
% 17.19/2.62 # Generated clauses : 106560
% 17.19/2.62 # ...of the previous two non-redundant : 100008
% 17.19/2.62 # ...aggressively subsumed : 0
% 17.19/2.62 # Contextual simplify-reflections : 475
% 17.19/2.62 # Paramodulations : 105824
% 17.19/2.62 # Factorizations : 9
% 17.19/2.62 # NegExts : 0
% 17.19/2.62 # Equation resolutions : 425
% 17.19/2.62 # Total rewrite steps : 71413
% 17.19/2.62 # Propositional unsat checks : 0
% 17.19/2.62 # Propositional check models : 0
% 17.19/2.62 # Propositional check unsatisfiable : 0
% 17.19/2.62 # Propositional clauses : 0
% 17.19/2.62 # Propositional clauses after purity: 0
% 17.19/2.62 # Propositional unsat core size : 0
% 17.19/2.62 # Propositional preprocessing time : 0.000
% 17.19/2.62 # Propositional encoding time : 0.000
% 17.19/2.62 # Propositional solver time : 0.000
% 17.19/2.62 # Success case prop preproc time : 0.000
% 17.19/2.62 # Success case prop encoding time : 0.000
% 17.19/2.62 # Success case prop solver time : 0.000
% 17.19/2.62 # Current number of processed clauses : 2678
% 17.19/2.62 # Positive orientable unit clauses : 392
% 17.19/2.62 # Positive unorientable unit clauses: 0
% 17.19/2.62 # Negative unit clauses : 202
% 17.19/2.62 # Non-unit-clauses : 2084
% 17.19/2.62 # Current number of unprocessed clauses: 88437
% 17.19/2.62 # ...number of literals in the above : 435266
% 17.19/2.62 # Current number of archived formulas : 0
% 17.19/2.62 # Current number of archived clauses : 1189
% 17.19/2.62 # Clause-clause subsumption calls (NU) : 453686
% 17.19/2.62 # Rec. Clause-clause subsumption calls : 169973
% 17.19/2.62 # Non-unit clause-clause subsumptions : 4934
% 17.19/2.62 # Unit Clause-clause subsumption calls : 66327
% 17.19/2.62 # Rewrite failures with RHS unbound : 0
% 17.19/2.62 # BW rewrite match attempts : 197
% 17.19/2.62 # BW rewrite match successes : 104
% 17.19/2.62 # Condensation attempts : 0
% 17.19/2.62 # Condensation successes : 0
% 17.19/2.62 # Termbank termtop insertions : 2392613
% 17.19/2.62
% 17.19/2.62 # -------------------------------------------------
% 17.19/2.62 # User time : 2.080 s
% 17.19/2.62 # System time : 0.064 s
% 17.19/2.62 # Total time : 2.145 s
% 17.19/2.62 # Maximum resident set size: 1984 pages
% 17.19/2.62
% 17.19/2.62 # -------------------------------------------------
% 17.19/2.62 # User time : 10.566 s
% 17.19/2.62 # System time : 0.173 s
% 17.19/2.62 # Total time : 10.740 s
% 17.19/2.62 # Maximum resident set size: 1736 pages
% 17.19/2.62 % E---3.1 exiting
%------------------------------------------------------------------------------