TSTP Solution File: NUM463+2 by E-SAT---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : NUM463+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n007.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 19:07:15 EDT 2023
% Result : Theorem 1.79s 0.70s
% Output : CNFRefutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of formulae : 102 ( 17 unt; 0 def)
% Number of atoms : 370 ( 143 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 479 ( 211 ~; 208 |; 40 &)
% ( 1 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 138 ( 0 sgn; 52 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X1 = sz00
& X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zajk6Fobz0/E---3.1_12637.p',mZeroAdd) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zajk6Fobz0/E---3.1_12637.p',mDefLE) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/tmp/tmp.zajk6Fobz0/E---3.1_12637.p',mSortsC) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.zajk6Fobz0/E---3.1_12637.p',mSortsB) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zajk6Fobz0/E---3.1_12637.p',m_AddZero) ).
fof(m__,conjecture,
( xm != sz00
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = sdtasdt0(xn,xm) )
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zajk6Fobz0/E---3.1_12637.p',m__) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.zajk6Fobz0/E---3.1_12637.p',mAddComm) ).
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/tmp/tmp.zajk6Fobz0/E---3.1_12637.p',mAddAsso) ).
fof(m__987,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/tmp/tmp.zajk6Fobz0/E---3.1_12637.p',m__987) ).
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.zajk6Fobz0/E---3.1_12637.p',mMulCanc) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zajk6Fobz0/E---3.1_12637.p',m_MulUnit) ).
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/tmp/tmp.zajk6Fobz0/E---3.1_12637.p',mAMDistr) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/tmp/tmp.zajk6Fobz0/E---3.1_12637.p',mSortsC_01) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.zajk6Fobz0/E---3.1_12637.p',mSortsB_02) ).
fof(mLENTr,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sz00
| X1 = sz10
| ( sz10 != X1
& sdtlseqdt0(sz10,X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zajk6Fobz0/E---3.1_12637.p',mLENTr) ).
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/tmp/tmp.zajk6Fobz0/E---3.1_12637.p',mMonMul) ).
fof(c_0_16,plain,
! [X30,X31] :
( ( X30 = sz00
| sdtpldt0(X30,X31) != sz00
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X31) )
& ( X31 = sz00
| sdtpldt0(X30,X31) != sz00
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X31) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])]) ).
fof(c_0_17,plain,
! [X34,X35,X37] :
( ( aNaturalNumber0(esk1_2(X34,X35))
| ~ sdtlseqdt0(X34,X35)
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X35) )
& ( sdtpldt0(X34,esk1_2(X34,X35)) = X35
| ~ sdtlseqdt0(X34,X35)
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X35) )
& ( ~ aNaturalNumber0(X37)
| sdtpldt0(X34,X37) != X35
| sdtlseqdt0(X34,X35)
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X35) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])]) ).
cnf(c_0_18,plain,
( X1 = sz00
| sdtpldt0(X2,X1) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_21,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_22,plain,
( esk1_2(X1,sz00) = sz00
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(esk1_2(X1,sz00))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19])]),c_0_20])]) ).
cnf(c_0_23,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_26,plain,
! [X13] :
( ( sdtpldt0(X13,sz00) = X13
| ~ aNaturalNumber0(X13) )
& ( X13 = sdtpldt0(sz00,X13)
| ~ aNaturalNumber0(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
fof(c_0_27,negated_conjecture,
~ ( xm != sz00
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = sdtasdt0(xn,xm) )
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_28,plain,
( esk1_2(X1,sz00) = sz00
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_20])]) ).
cnf(c_0_29,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_24]),c_0_25]) ).
cnf(c_0_30,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_31,negated_conjecture,
! [X56] :
( xm != sz00
& ( ~ aNaturalNumber0(X56)
| sdtpldt0(xn,X56) != sdtasdt0(xn,xm) )
& ~ sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
fof(c_0_32,plain,
! [X8,X9] :
( ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X9)
| sdtpldt0(X8,X9) = sdtpldt0(X9,X8) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(c_0_33,plain,
! [X10,X11,X12] :
( ~ aNaturalNumber0(X10)
| ~ aNaturalNumber0(X11)
| ~ aNaturalNumber0(X12)
| sdtpldt0(sdtpldt0(X10,X11),X12) = sdtpldt0(X10,sdtpldt0(X11,X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_34,plain,
( sdtpldt0(X1,sz00) = sz00
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_28]),c_0_20])]) ).
cnf(c_0_35,plain,
( sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_20])]) ).
cnf(c_0_36,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(xn,X1) != sdtasdt0(xn,xm) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__987]) ).
cnf(c_0_39,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_20])]) ).
cnf(c_0_41,negated_conjecture,
( sdtpldt0(X1,xn) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_42,plain,
( sdtpldt0(sz00,sdtpldt0(sz00,X1)) = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_20])]) ).
cnf(c_0_43,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_44,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])])])]) ).
cnf(c_0_45,negated_conjecture,
( sdtpldt0(X1,sdtpldt0(X2,xn)) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_39]),c_0_38])]),c_0_25]) ).
cnf(c_0_46,plain,
( sdtpldt0(sz00,sdtpldt0(X1,sz00)) = sdtpldt0(X1,sz00)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_37]),c_0_20])]) ).
cnf(c_0_47,plain,
( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_39]),c_0_20])]),c_0_25]) ).
cnf(c_0_48,plain,
( X2 = X3
| X1 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_49,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_50,negated_conjecture,
( sdtpldt0(X1,sdtpldt0(xn,X2)) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_37]),c_0_38])]) ).
cnf(c_0_51,plain,
( sdtpldt0(sz00,X1) = sdtpldt0(X1,sz00)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_20])]) ).
fof(c_0_52,plain,
! [X21,X22,X23] :
( ( sdtasdt0(X21,sdtpldt0(X22,X23)) = sdtpldt0(sdtasdt0(X21,X22),sdtasdt0(X21,X23))
| ~ aNaturalNumber0(X21)
| ~ aNaturalNumber0(X22)
| ~ aNaturalNumber0(X23) )
& ( sdtasdt0(sdtpldt0(X22,X23),X21) = sdtpldt0(sdtasdt0(X22,X21),sdtasdt0(X23,X21))
| ~ aNaturalNumber0(X21)
| ~ aNaturalNumber0(X22)
| ~ aNaturalNumber0(X23) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
cnf(c_0_53,plain,
( X1 = sz00
| X2 = sz00
| sdtasdt0(X2,X1) != sdtasdt0(X2,sz00)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_20]) ).
cnf(c_0_54,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_55,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_56,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
fof(c_0_57,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_58,negated_conjecture,
( sdtpldt0(X1,sdtpldt0(sz00,xn)) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_20]),c_0_38])]) ).
cnf(c_0_59,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_39]),c_0_25]) ).
cnf(c_0_60,plain,
( X1 = sz00
| sdtpldt0(X1,X2) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_61,hypothesis,
( X1 = xn
| X2 = sz00
| sdtasdt0(X2,X1) != sdtasdt0(X2,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_38]) ).
cnf(c_0_62,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_63,plain,
( sdtasdt0(sz10,sz00) = sz00
| ~ aNaturalNumber0(sdtasdt0(sz10,sz00)) ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]),c_0_56])]) ).
cnf(c_0_64,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_65,negated_conjecture,
( sdtpldt0(xn,sdtpldt0(X1,sz00)) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_38]),c_0_20])]) ).
cnf(c_0_66,plain,
( sdtpldt0(X1,X2) = sz00
| sdtpldt0(X1,sdtpldt0(X2,X3)) != sz00
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_39]),c_0_25]) ).
cnf(c_0_67,hypothesis,
( sdtasdt0(sz10,xn) = xn
| ~ aNaturalNumber0(sdtasdt0(sz10,xn)) ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_54]),c_0_55])]),c_0_56])]) ).
cnf(c_0_68,plain,
( sdtasdt0(sz10,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(sz10,X1),X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_54]),c_0_55])]) ).
cnf(c_0_69,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_20]),c_0_55])]) ).
cnf(c_0_70,negated_conjecture,
( sdtpldt0(xn,sdtpldt0(sz00,X1)) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_37]),c_0_20])]) ).
cnf(c_0_71,plain,
( sdtpldt0(X1,sdtpldt0(X2,esk1_2(sdtpldt0(X1,X2),X3))) = X3
| ~ sdtlseqdt0(sdtpldt0(X1,X2),X3)
| ~ aNaturalNumber0(esk1_2(sdtpldt0(X1,X2),X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_39]),c_0_25]) ).
cnf(c_0_72,plain,
( sdtpldt0(X1,sz00) = sz00
| sdtpldt0(X1,X2) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_30]),c_0_20])]) ).
cnf(c_0_73,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_64]),c_0_38]),c_0_55])]) ).
cnf(c_0_74,plain,
( sdtasdt0(sz10,X1) = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_30]),c_0_69]),c_0_20])]) ).
fof(c_0_75,plain,
! [X55] :
( ( sz10 != X55
| X55 = sz00
| X55 = sz10
| ~ aNaturalNumber0(X55) )
& ( sdtlseqdt0(sz10,X55)
| X55 = sz00
| X55 = sz10
| ~ aNaturalNumber0(X55) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLENTr])])]) ).
cnf(c_0_76,plain,
( X1 = X3
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_77,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(xn,sz00),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(esk1_2(sdtpldt0(xn,sz00),sdtasdt0(xn,xm)))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_20]),c_0_38])])]) ).
cnf(c_0_78,plain,
( sdtpldt0(X1,sz00) = sz00
| sdtpldt0(sz00,X1) != sz00
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_51]),c_0_20])]) ).
cnf(c_0_79,hypothesis,
sdtpldt0(sz00,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_38])]) ).
cnf(c_0_80,negated_conjecture,
( sdtpldt0(sdtpldt0(xn,X1),X2) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_37]) ).
fof(c_0_81,plain,
! [X52,X53,X54] :
( ( sdtasdt0(X52,X53) != sdtasdt0(X52,X54)
| X52 = sz00
| X53 = X54
| ~ sdtlseqdt0(X53,X54)
| ~ aNaturalNumber0(X52)
| ~ aNaturalNumber0(X53)
| ~ aNaturalNumber0(X54) )
& ( sdtlseqdt0(sdtasdt0(X52,X53),sdtasdt0(X52,X54))
| X52 = sz00
| X53 = X54
| ~ sdtlseqdt0(X53,X54)
| ~ aNaturalNumber0(X52)
| ~ aNaturalNumber0(X53)
| ~ aNaturalNumber0(X54) )
& ( sdtasdt0(X53,X52) != sdtasdt0(X54,X52)
| X52 = sz00
| X53 = X54
| ~ sdtlseqdt0(X53,X54)
| ~ aNaturalNumber0(X52)
| ~ aNaturalNumber0(X53)
| ~ aNaturalNumber0(X54) )
& ( sdtlseqdt0(sdtasdt0(X53,X52),sdtasdt0(X54,X52))
| X52 = sz00
| X53 = X54
| ~ sdtlseqdt0(X53,X54)
| ~ aNaturalNumber0(X52)
| ~ aNaturalNumber0(X53)
| ~ aNaturalNumber0(X54) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).
cnf(c_0_82,plain,
( sdtlseqdt0(sz10,X1)
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_83,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__987]) ).
cnf(c_0_84,negated_conjecture,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_85,hypothesis,
( X1 = xn
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(xn,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_38]) ).
cnf(c_0_86,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_87,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(xn,sz00),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,sz00)) ),
inference(spm,[status(thm)],[c_0_77,c_0_23]) ).
cnf(c_0_88,hypothesis,
( sdtpldt0(xn,sz00) = sz00
| xn != sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_38])]) ).
cnf(c_0_89,negated_conjecture,
( sdtpldt0(xn,sdtpldt0(X1,X2)) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtpldt0(xn,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_39]),c_0_38])]) ).
cnf(c_0_90,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| X1 = sz00
| X2 = X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_91,hypothesis,
( xm = sz10
| sdtlseqdt0(sz10,xm) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]) ).
cnf(c_0_92,hypothesis,
( sdtasdt0(xn,sz10) = xn
| ~ aNaturalNumber0(sdtasdt0(xn,sz10)) ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_55])]),c_0_56])]) ).
cnf(c_0_93,negated_conjecture,
( xn != sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_20])]),c_0_35]) ).
cnf(c_0_94,negated_conjecture,
( sdtasdt0(xn,xm) != sdtpldt0(xn,sz00)
| ~ aNaturalNumber0(sdtpldt0(xn,sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_40]),c_0_20])]) ).
cnf(c_0_95,hypothesis,
( xm = sz10
| X1 = sz00
| sdtlseqdt0(sdtasdt0(X1,sz10),sdtasdt0(X1,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_83]),c_0_55])]) ).
cnf(c_0_96,hypothesis,
sdtasdt0(xn,sz10) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_64]),c_0_55]),c_0_38])]) ).
cnf(c_0_97,negated_conjecture,
xn != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_64]),c_0_83]),c_0_38])]) ).
cnf(c_0_98,negated_conjecture,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_99,negated_conjecture,
sdtasdt0(xn,xm) != xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_43]),c_0_38])]) ).
cnf(c_0_100,hypothesis,
xm = sz10,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_38]),c_0_96]),c_0_97]),c_0_98]) ).
cnf(c_0_101,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_100]),c_0_96])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM463+2 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 2400
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Oct 2 14:04:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.47 Running first-order model finding
% 0.19/0.47 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.zajk6Fobz0/E---3.1_12637.p
% 1.79/0.70 # Version: 3.1pre001
% 1.79/0.70 # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.79/0.70 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.79/0.70 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.79/0.70 # Starting new_bool_3 with 300s (1) cores
% 1.79/0.70 # Starting new_bool_1 with 300s (1) cores
% 1.79/0.70 # Starting sh5l with 300s (1) cores
% 1.79/0.70 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 12714 completed with status 0
% 1.79/0.70 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.79/0.70 # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.79/0.70 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.79/0.70 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.79/0.70 # No SInE strategy applied
% 1.79/0.70 # Search class: FGHSF-FFMS22-SFFFFFNN
% 1.79/0.70 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.79/0.70 # Starting SAT001_MinMin_p005000_rr_RG with 811s (1) cores
% 1.79/0.70 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.79/0.70 # Starting new_bool_3 with 136s (1) cores
% 1.79/0.70 # Starting new_bool_1 with 136s (1) cores
% 1.79/0.70 # Starting sh5l with 136s (1) cores
% 1.79/0.70 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 12719 completed with status 0
% 1.79/0.70 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.79/0.70 # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.79/0.70 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.79/0.70 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.79/0.70 # No SInE strategy applied
% 1.79/0.70 # Search class: FGHSF-FFMS22-SFFFFFNN
% 1.79/0.70 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.79/0.70 # Starting SAT001_MinMin_p005000_rr_RG with 811s (1) cores
% 1.79/0.70 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.79/0.70 # Preprocessing time : 0.001 s
% 1.79/0.70 # Presaturation interreduction done
% 1.79/0.70
% 1.79/0.70 # Proof found!
% 1.79/0.70 # SZS status Theorem
% 1.79/0.70 # SZS output start CNFRefutation
% See solution above
% 1.79/0.70 # Parsed axioms : 28
% 1.79/0.70 # Removed by relevancy pruning/SinE : 0
% 1.79/0.70 # Initial clauses : 51
% 1.79/0.70 # Removed in clause preprocessing : 2
% 1.79/0.70 # Initial clauses in saturation : 49
% 1.79/0.70 # Processed clauses : 1932
% 1.79/0.70 # ...of these trivial : 34
% 1.79/0.70 # ...subsumed : 1264
% 1.79/0.70 # ...remaining for further processing : 634
% 1.79/0.70 # Other redundant clauses eliminated : 167
% 1.79/0.70 # Clauses deleted for lack of memory : 0
% 1.79/0.70 # Backward-subsumed : 75
% 1.79/0.70 # Backward-rewritten : 204
% 1.79/0.70 # Generated clauses : 12903
% 1.79/0.70 # ...of the previous two non-redundant : 11738
% 1.79/0.70 # ...aggressively subsumed : 0
% 1.79/0.70 # Contextual simplify-reflections : 71
% 1.79/0.70 # Paramodulations : 12701
% 1.79/0.70 # Factorizations : 0
% 1.79/0.70 # NegExts : 0
% 1.79/0.70 # Equation resolutions : 186
% 1.79/0.70 # Total rewrite steps : 10267
% 1.79/0.70 # Propositional unsat checks : 0
% 1.79/0.70 # Propositional check models : 0
% 1.79/0.70 # Propositional check unsatisfiable : 0
% 1.79/0.70 # Propositional clauses : 0
% 1.79/0.70 # Propositional clauses after purity: 0
% 1.79/0.70 # Propositional unsat core size : 0
% 1.79/0.70 # Propositional preprocessing time : 0.000
% 1.79/0.70 # Propositional encoding time : 0.000
% 1.79/0.70 # Propositional solver time : 0.000
% 1.79/0.70 # Success case prop preproc time : 0.000
% 1.79/0.70 # Success case prop encoding time : 0.000
% 1.79/0.70 # Success case prop solver time : 0.000
% 1.79/0.70 # Current number of processed clauses : 290
% 1.79/0.70 # Positive orientable unit clauses : 36
% 1.79/0.70 # Positive unorientable unit clauses: 0
% 1.79/0.70 # Negative unit clauses : 5
% 1.79/0.70 # Non-unit-clauses : 249
% 1.79/0.70 # Current number of unprocessed clauses: 9689
% 1.79/0.70 # ...number of literals in the above : 52304
% 1.79/0.70 # Current number of archived formulas : 0
% 1.79/0.70 # Current number of archived clauses : 339
% 1.79/0.70 # Clause-clause subsumption calls (NU) : 21879
% 1.79/0.70 # Rec. Clause-clause subsumption calls : 11360
% 1.79/0.70 # Non-unit clause-clause subsumptions : 1215
% 1.79/0.70 # Unit Clause-clause subsumption calls : 1902
% 1.79/0.70 # Rewrite failures with RHS unbound : 0
% 1.79/0.70 # BW rewrite match attempts : 30
% 1.79/0.70 # BW rewrite match successes : 30
% 1.79/0.70 # Condensation attempts : 0
% 1.79/0.70 # Condensation successes : 0
% 1.79/0.70 # Termbank termtop insertions : 224664
% 1.79/0.70
% 1.79/0.70 # -------------------------------------------------
% 1.79/0.70 # User time : 0.205 s
% 1.79/0.70 # System time : 0.012 s
% 1.79/0.70 # Total time : 0.217 s
% 1.79/0.70 # Maximum resident set size: 1860 pages
% 1.79/0.70
% 1.79/0.70 # -------------------------------------------------
% 1.79/0.70 # User time : 1.035 s
% 1.79/0.70 # System time : 0.021 s
% 1.79/0.70 # Total time : 1.056 s
% 1.79/0.70 # Maximum resident set size: 1732 pages
% 1.79/0.70 % E---3.1 exiting
%------------------------------------------------------------------------------