TSTP Solution File: NUM463+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : NUM463+2 : TPTP v7.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : n068.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.625MB
% OS : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan 8 15:21:25 EST 2018
% Result : Theorem 0.53s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 20
% Syntax : Number of formulae : 178 ( 18 unt; 0 def)
% Number of atoms : 726 ( 144 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 955 ( 407 ~; 445 |; 79 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 259 ( 1 sgn 122 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( equal(sdtasdt0(X1,sz00),sz00)
& equal(sz00,sdtasdt0(sz00,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',m_MulZero) ).
fof(3,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( equal(sdtasdt0(X1,X2),sz00)
=> ( equal(X1,sz00)
| equal(X2,sz00) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',mZeroMul) ).
fof(6,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( ~ equal(X2,X1)
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',mLETotal) ).
fof(10,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( ~ equal(X1,sz00)
& ~ equal(X2,X3)
& sdtlseqdt0(X2,X3) )
=> ( ~ equal(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& ~ equal(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',mMonMul) ).
fof(11,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& equal(sdtpldt0(X1,X3),X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',mDefLE) ).
fof(12,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> equal(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(X1,sdtpldt0(X2,X3))) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',mAddAsso) ).
fof(13,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> equal(X1,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',mLEAsym) ).
fof(14,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( equal(X1,sz00)
| equal(X1,sz10)
| ( ~ equal(sz10,X1)
& sdtlseqdt0(sz10,X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',mLENTr) ).
fof(15,axiom,
( aNaturalNumber0(sz10)
& ~ equal(sz10,sz00) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',mSortsC_01) ).
fof(16,conjecture,
( ~ equal(xm,sz00)
=> ( ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtpldt0(xn,X1),sdtasdt0(xn,xm)) )
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',m__) ).
fof(17,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',m__987) ).
fof(18,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> equal(sdtasdt0(sdtasdt0(X1,X2),X3),sdtasdt0(X1,sdtasdt0(X2,X3))) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',mMulAsso) ).
fof(20,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',mLERefl) ).
fof(21,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( equal(X3,sdtmndt0(X2,X1))
<=> ( aNaturalNumber0(X3)
& equal(sdtpldt0(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',mDefDiff) ).
fof(22,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',mSortsB_02) ).
fof(23,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',mSortsC) ).
fof(24,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',mSortsB) ).
fof(26,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',mMulComm) ).
fof(27,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( equal(sdtpldt0(X1,sz00),X1)
& equal(X1,sdtpldt0(sz00,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',m_AddZero) ).
fof(28,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( equal(sdtasdt0(X1,sz10),X1)
& equal(X1,sdtasdt0(sz10,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1',m_MulUnit) ).
fof(29,negated_conjecture,
~ ( ~ equal(xm,sz00)
=> ( ? [X1] :
( aNaturalNumber0(X1)
& equal(sdtpldt0(xn,X1),sdtasdt0(xn,xm)) )
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ),
inference(assume_negation,[status(cth)],[16]) ).
fof(30,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| ( equal(sdtasdt0(X1,sz00),sz00)
& equal(sz00,sdtasdt0(sz00,X1)) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(31,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| ( equal(sdtasdt0(X2,sz00),sz00)
& equal(sz00,sdtasdt0(sz00,X2)) ) ),
inference(variable_rename,[status(thm)],[30]) ).
fof(32,plain,
! [X2] :
( ( equal(sdtasdt0(X2,sz00),sz00)
| ~ aNaturalNumber0(X2) )
& ( equal(sz00,sdtasdt0(sz00,X2))
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[31]) ).
cnf(34,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[32]) ).
fof(38,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ equal(sdtasdt0(X1,X2),sz00)
| equal(X1,sz00)
| equal(X2,sz00) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(39,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| ~ equal(sdtasdt0(X3,X4),sz00)
| equal(X3,sz00)
| equal(X4,sz00) ),
inference(variable_rename,[status(thm)],[38]) ).
cnf(40,plain,
( X1 = sz00
| X2 = sz00
| sdtasdt0(X2,X1) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[39]) ).
fof(52,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X1,X2)
| ( ~ equal(X2,X1)
& sdtlseqdt0(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(53,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| sdtlseqdt0(X3,X4)
| ( ~ equal(X4,X3)
& sdtlseqdt0(X4,X3) ) ),
inference(variable_rename,[status(thm)],[52]) ).
fof(54,plain,
! [X3,X4] :
( ( ~ equal(X4,X3)
| sdtlseqdt0(X3,X4)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4) )
& ( sdtlseqdt0(X4,X3)
| sdtlseqdt0(X3,X4)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4) ) ),
inference(distribute,[status(thm)],[53]) ).
cnf(55,plain,
( sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[54]) ).
fof(71,plain,
! [X1,X2,X3] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| equal(X1,sz00)
| equal(X2,X3)
| ~ sdtlseqdt0(X2,X3)
| ( ~ equal(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& ~ equal(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(72,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| equal(X4,sz00)
| equal(X5,X6)
| ~ sdtlseqdt0(X5,X6)
| ( ~ equal(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
& sdtlseqdt0(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
& ~ equal(sdtasdt0(X5,X4),sdtasdt0(X6,X4))
& sdtlseqdt0(sdtasdt0(X5,X4),sdtasdt0(X6,X4)) ) ),
inference(variable_rename,[status(thm)],[71]) ).
fof(73,plain,
! [X4,X5,X6] :
( ( ~ equal(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
| equal(X4,sz00)
| equal(X5,X6)
| ~ sdtlseqdt0(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( sdtlseqdt0(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
| equal(X4,sz00)
| equal(X5,X6)
| ~ sdtlseqdt0(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( ~ equal(sdtasdt0(X5,X4),sdtasdt0(X6,X4))
| equal(X4,sz00)
| equal(X5,X6)
| ~ sdtlseqdt0(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( sdtlseqdt0(sdtasdt0(X5,X4),sdtasdt0(X6,X4))
| equal(X4,sz00)
| equal(X5,X6)
| ~ sdtlseqdt0(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) ) ),
inference(distribute,[status(thm)],[72]) ).
cnf(76,plain,
( X2 = X1
| X3 = sz00
| sdtlseqdt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[73]) ).
fof(78,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ( ( ~ sdtlseqdt0(X1,X2)
| ? [X3] :
( aNaturalNumber0(X3)
& equal(sdtpldt0(X1,X3),X2) ) )
& ( ! [X3] :
( ~ aNaturalNumber0(X3)
| ~ equal(sdtpldt0(X1,X3),X2) )
| sdtlseqdt0(X1,X2) ) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(79,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ( ( ~ sdtlseqdt0(X4,X5)
| ? [X6] :
( aNaturalNumber0(X6)
& equal(sdtpldt0(X4,X6),X5) ) )
& ( ! [X7] :
( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5) )
| sdtlseqdt0(X4,X5) ) ) ),
inference(variable_rename,[status(thm)],[78]) ).
fof(80,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ( ( ~ sdtlseqdt0(X4,X5)
| ( aNaturalNumber0(esk1_2(X4,X5))
& equal(sdtpldt0(X4,esk1_2(X4,X5)),X5) ) )
& ( ! [X7] :
( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5) )
| sdtlseqdt0(X4,X5) ) ) ),
inference(skolemize,[status(esa)],[79]) ).
fof(81,plain,
! [X4,X5,X7] :
( ( ( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5)
| sdtlseqdt0(X4,X5) )
& ( ~ sdtlseqdt0(X4,X5)
| ( aNaturalNumber0(esk1_2(X4,X5))
& equal(sdtpldt0(X4,esk1_2(X4,X5)),X5) ) ) )
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[80]) ).
fof(82,plain,
! [X4,X5,X7] :
( ( ~ aNaturalNumber0(X7)
| ~ equal(sdtpldt0(X4,X7),X5)
| sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( aNaturalNumber0(esk1_2(X4,X5))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(sdtpldt0(X4,esk1_2(X4,X5)),X5)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[81]) ).
cnf(85,plain,
( sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[82]) ).
fof(86,plain,
! [X1,X2,X3] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| equal(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(X1,sdtpldt0(X2,X3))) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(87,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| equal(sdtpldt0(sdtpldt0(X4,X5),X6),sdtpldt0(X4,sdtpldt0(X5,X6))) ),
inference(variable_rename,[status(thm)],[86]) ).
cnf(88,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[87]) ).
fof(89,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1)
| equal(X1,X2) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(90,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| ~ sdtlseqdt0(X3,X4)
| ~ sdtlseqdt0(X4,X3)
| equal(X3,X4) ),
inference(variable_rename,[status(thm)],[89]) ).
cnf(91,plain,
( X1 = X2
| ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[90]) ).
fof(92,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| equal(X1,sz00)
| equal(X1,sz10)
| ( ~ equal(sz10,X1)
& sdtlseqdt0(sz10,X1) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(93,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| equal(X2,sz00)
| equal(X2,sz10)
| ( ~ equal(sz10,X2)
& sdtlseqdt0(sz10,X2) ) ),
inference(variable_rename,[status(thm)],[92]) ).
fof(94,plain,
! [X2] :
( ( ~ equal(sz10,X2)
| equal(X2,sz00)
| equal(X2,sz10)
| ~ aNaturalNumber0(X2) )
& ( sdtlseqdt0(sz10,X2)
| equal(X2,sz00)
| equal(X2,sz10)
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[93]) ).
cnf(95,plain,
( X1 = sz10
| X1 = sz00
| sdtlseqdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[94]) ).
cnf(97,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[15]) ).
cnf(98,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[15]) ).
fof(99,negated_conjecture,
( ~ equal(xm,sz00)
& ! [X1] :
( ~ aNaturalNumber0(X1)
| ~ equal(sdtpldt0(xn,X1),sdtasdt0(xn,xm)) )
& ~ sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(100,negated_conjecture,
( ~ equal(xm,sz00)
& ! [X2] :
( ~ aNaturalNumber0(X2)
| ~ equal(sdtpldt0(xn,X2),sdtasdt0(xn,xm)) )
& ~ sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(variable_rename,[status(thm)],[99]) ).
fof(101,negated_conjecture,
! [X2] :
( ( ~ aNaturalNumber0(X2)
| ~ equal(sdtpldt0(xn,X2),sdtasdt0(xn,xm)) )
& ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
& ~ equal(xm,sz00) ),
inference(shift_quantors,[status(thm)],[100]) ).
cnf(102,negated_conjecture,
xm != sz00,
inference(split_conjunct,[status(thm)],[101]) ).
cnf(103,negated_conjecture,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[101]) ).
cnf(104,negated_conjecture,
( sdtpldt0(xn,X1) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[101]) ).
cnf(105,plain,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(106,plain,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[17]) ).
fof(107,plain,
! [X1,X2,X3] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| equal(sdtasdt0(sdtasdt0(X1,X2),X3),sdtasdt0(X1,sdtasdt0(X2,X3))) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(108,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| equal(sdtasdt0(sdtasdt0(X4,X5),X6),sdtasdt0(X4,sdtasdt0(X5,X6))) ),
inference(variable_rename,[status(thm)],[107]) ).
cnf(109,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[108]) ).
fof(115,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X1) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(116,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X2) ),
inference(variable_rename,[status(thm)],[115]) ).
cnf(117,plain,
( sdtlseqdt0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[116]) ).
fof(118,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ! [X3] :
( ( ~ equal(X3,sdtmndt0(X2,X1))
| ( aNaturalNumber0(X3)
& equal(sdtpldt0(X1,X3),X2) ) )
& ( ~ aNaturalNumber0(X3)
| ~ equal(sdtpldt0(X1,X3),X2)
| equal(X3,sdtmndt0(X2,X1)) ) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(119,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ sdtlseqdt0(X4,X5)
| ! [X6] :
( ( ~ equal(X6,sdtmndt0(X5,X4))
| ( aNaturalNumber0(X6)
& equal(sdtpldt0(X4,X6),X5) ) )
& ( ~ aNaturalNumber0(X6)
| ~ equal(sdtpldt0(X4,X6),X5)
| equal(X6,sdtmndt0(X5,X4)) ) ) ),
inference(variable_rename,[status(thm)],[118]) ).
fof(120,plain,
! [X4,X5,X6] :
( ( ( ~ equal(X6,sdtmndt0(X5,X4))
| ( aNaturalNumber0(X6)
& equal(sdtpldt0(X4,X6),X5) ) )
& ( ~ aNaturalNumber0(X6)
| ~ equal(sdtpldt0(X4,X6),X5)
| equal(X6,sdtmndt0(X5,X4)) ) )
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ),
inference(shift_quantors,[status(thm)],[119]) ).
fof(121,plain,
! [X4,X5,X6] :
( ( aNaturalNumber0(X6)
| ~ equal(X6,sdtmndt0(X5,X4))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( equal(sdtpldt0(X4,X6),X5)
| ~ equal(X6,sdtmndt0(X5,X4))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X6)
| ~ equal(sdtpldt0(X4,X6),X5)
| equal(X6,sdtmndt0(X5,X4))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[120]) ).
cnf(122,plain,
( X3 = sdtmndt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[121]) ).
cnf(124,plain,
( aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| X3 != sdtmndt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[121]) ).
fof(125,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(126,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[125]) ).
cnf(127,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[126]) ).
cnf(128,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[23]) ).
fof(129,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(130,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtpldt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[129]) ).
cnf(131,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[130]) ).
fof(137,plain,
! [X1,X2] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(138,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| equal(sdtasdt0(X3,X4),sdtasdt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[137]) ).
cnf(139,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[138]) ).
fof(140,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| ( equal(sdtpldt0(X1,sz00),X1)
& equal(X1,sdtpldt0(sz00,X1)) ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(141,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| ( equal(sdtpldt0(X2,sz00),X2)
& equal(X2,sdtpldt0(sz00,X2)) ) ),
inference(variable_rename,[status(thm)],[140]) ).
fof(142,plain,
! [X2] :
( ( equal(sdtpldt0(X2,sz00),X2)
| ~ aNaturalNumber0(X2) )
& ( equal(X2,sdtpldt0(sz00,X2))
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[141]) ).
cnf(143,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[142]) ).
cnf(144,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[142]) ).
fof(145,plain,
! [X1] :
( ~ aNaturalNumber0(X1)
| ( equal(sdtasdt0(X1,sz10),X1)
& equal(X1,sdtasdt0(sz10,X1)) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(146,plain,
! [X2] :
( ~ aNaturalNumber0(X2)
| ( equal(sdtasdt0(X2,sz10),X2)
& equal(X2,sdtasdt0(sz10,X2)) ) ),
inference(variable_rename,[status(thm)],[145]) ).
fof(147,plain,
! [X2] :
( ( equal(sdtasdt0(X2,sz10),X2)
| ~ aNaturalNumber0(X2) )
& ( equal(X2,sdtasdt0(sz10,X2))
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[146]) ).
cnf(148,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[147]) ).
cnf(149,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[147]) ).
cnf(170,negated_conjecture,
( xn != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[104,144,theory(equality)]) ).
cnf(171,negated_conjecture,
( xn != sdtasdt0(xn,xm)
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[170,128,theory(equality)]) ).
cnf(172,negated_conjecture,
( xn != sdtasdt0(xn,xm)
| $false
| $false ),
inference(rw,[status(thm)],[171,105,theory(equality)]) ).
cnf(173,negated_conjecture,
xn != sdtasdt0(xn,xm),
inference(cn,[status(thm)],[172,theory(equality)]) ).
cnf(176,plain,
( sdtlseqdt0(X1,xm)
| sdtlseqdt0(xm,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[55,106,theory(equality)]) ).
cnf(257,plain,
( X1 = sz10
| sz00 = X1
| ~ sdtlseqdt0(X1,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[91,95,theory(equality)]) ).
cnf(258,plain,
( X1 = sz10
| sz00 = X1
| ~ sdtlseqdt0(X1,sz10)
| $false
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[257,98,theory(equality)]) ).
cnf(259,plain,
( X1 = sz10
| sz00 = X1
| ~ sdtlseqdt0(X1,sz10)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[258,theory(equality)]) ).
cnf(318,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2)
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[149,109,theory(equality)]) ).
cnf(320,plain,
( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[109,148,theory(equality)]) ).
cnf(325,plain,
( sz00 = X1
| sz00 = sdtasdt0(X2,X3)
| sdtasdt0(X2,sdtasdt0(X3,X1)) != sz00
| ~ aNaturalNumber0(sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[40,109,theory(equality)]) ).
cnf(334,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2)
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| $false
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[318,98,theory(equality)]) ).
cnf(335,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2)
| ~ aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[334,theory(equality)]) ).
cnf(338,plain,
( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[320,98,theory(equality)]) ).
cnf(339,plain,
( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[338,theory(equality)]) ).
cnf(395,plain,
( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
| ~ aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[144,88,theory(equality)]) ).
cnf(397,plain,
( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[88,143,theory(equality)]) ).
cnf(414,plain,
( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
| ~ aNaturalNumber0(sdtpldt0(X1,X2))
| $false
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[395,128,theory(equality)]) ).
cnf(415,plain,
( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
| ~ aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[414,theory(equality)]) ).
cnf(418,plain,
( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[397,128,theory(equality)]) ).
cnf(419,plain,
( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[418,theory(equality)]) ).
cnf(511,plain,
( sdtmndt0(X1,X2) = X3
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[122,85]) ).
cnf(513,plain,
( sdtmndt0(X1,X2) = sz00
| X2 != X1
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[511,144,theory(equality)]) ).
cnf(520,plain,
( sdtmndt0(X1,X2) = sz00
| X2 != X1
| $false
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[513,128,theory(equality)]) ).
cnf(521,plain,
( sdtmndt0(X1,X2) = sz00
| X2 != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[520,theory(equality)]) ).
cnf(522,plain,
( sdtmndt0(X1,X1) = sz00
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[521,theory(equality)]) ).
cnf(578,plain,
( sz00 = X1
| X2 = sz10
| sdtlseqdt0(X1,sdtasdt0(X1,X2))
| ~ sdtlseqdt0(sz10,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[76,149,theory(equality)]) ).
cnf(594,plain,
( sz00 = X1
| X2 = sz10
| sdtlseqdt0(X1,sdtasdt0(X1,X2))
| ~ sdtlseqdt0(sz10,X2)
| ~ aNaturalNumber0(X1)
| $false
| ~ aNaturalNumber0(X2) ),
inference(rw,[status(thm)],[578,98,theory(equality)]) ).
cnf(595,plain,
( sz00 = X1
| X2 = sz10
| sdtlseqdt0(X1,sdtasdt0(X1,X2))
| ~ sdtlseqdt0(sz10,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[594,theory(equality)]) ).
cnf(655,plain,
( sdtlseqdt0(xm,sz10)
| sdtlseqdt0(sz10,xm) ),
inference(spm,[status(thm)],[176,98,theory(equality)]) ).
cnf(965,plain,
( aNaturalNumber0(X1)
| sz00 != X1
| ~ sdtlseqdt0(X2,X2)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[124,522,theory(equality)]) ).
cnf(1151,plain,
( aNaturalNumber0(X1)
| sz00 != X1
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[965,117]) ).
cnf(1152,plain,
( aNaturalNumber0(X1)
| sz00 != X1 ),
inference(spm,[status(thm)],[1151,128,theory(equality)]) ).
cnf(1255,plain,
( sz00 = xm
| xm = sz10
| sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[259,655,theory(equality)]) ).
cnf(1259,plain,
( sz00 = xm
| xm = sz10
| sdtlseqdt0(sz10,xm)
| $false ),
inference(rw,[status(thm)],[1255,106,theory(equality)]) ).
cnf(1260,plain,
( sz00 = xm
| xm = sz10
| sdtlseqdt0(sz10,xm) ),
inference(cn,[status(thm)],[1259,theory(equality)]) ).
cnf(1261,plain,
( xm = sz10
| sdtlseqdt0(sz10,xm) ),
inference(sr,[status(thm)],[1260,102,theory(equality)]) ).
cnf(3239,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[335,127]) ).
cnf(3391,plain,
( sdtasdt0(X1,sz10) = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[3239,339,theory(equality)]) ).
cnf(3449,plain,
( sdtasdt0(X1,sz10) = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[3391,98,theory(equality)]) ).
cnf(3450,plain,
( sdtasdt0(X1,sz10) = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[3449,theory(equality)]) ).
cnf(4016,plain,
( sdtasdt0(X2,X3) = sz00
| sz00 = X1
| sdtasdt0(X2,sdtasdt0(X3,X1)) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[325,127]) ).
cnf(4361,plain,
( sdtasdt0(X1,X2) = sz00
| sz00 = sz10
| sdtasdt0(X1,sdtasdt0(sz10,X2)) != sz00
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[4016,3450,theory(equality)]) ).
cnf(4504,plain,
( sdtasdt0(X1,X2) = sz00
| sz00 = sz10
| sdtasdt0(X1,sdtasdt0(sz10,X2)) != sz00
| $false
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[4361,98,theory(equality)]) ).
cnf(4505,plain,
( sdtasdt0(X1,X2) = sz00
| sz00 = sz10
| sdtasdt0(X1,sdtasdt0(sz10,X2)) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[4504,theory(equality)]) ).
cnf(4506,plain,
( sdtasdt0(X1,X2) = sz00
| sdtasdt0(X1,sdtasdt0(sz10,X2)) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[4505,97,theory(equality)]) ).
cnf(6452,plain,
( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[415,131]) ).
cnf(6739,plain,
( sdtpldt0(X1,sz00) = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz00) ),
inference(spm,[status(thm)],[6452,419,theory(equality)]) ).
cnf(6784,plain,
( sdtpldt0(X1,sz00) = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[6739,128,theory(equality)]) ).
cnf(6785,plain,
( sdtpldt0(X1,sz00) = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[6784,theory(equality)]) ).
cnf(7020,plain,
( sdtasdt0(X1,X2) = sz00
| sdtasdt0(X1,sdtasdt0(X2,sz10)) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[4506,139,theory(equality)]) ).
cnf(7058,plain,
( sdtasdt0(X1,X2) = sz00
| sdtasdt0(X1,sdtasdt0(X2,sz10)) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[7020,98,theory(equality)]) ).
cnf(7059,plain,
( sdtasdt0(X1,X2) = sz00
| sdtasdt0(X1,sdtasdt0(X2,sz10)) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[7058,theory(equality)]) ).
cnf(7351,plain,
( sdtasdt0(sz10,X1) = sz00
| sdtasdt0(X1,sz10) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz10) ),
inference(spm,[status(thm)],[7059,339,theory(equality)]) ).
cnf(7391,plain,
( sdtasdt0(sz10,X1) = sz00
| sdtasdt0(X1,sz10) != sz00
| ~ aNaturalNumber0(X1)
| $false ),
inference(rw,[status(thm)],[7351,98,theory(equality)]) ).
cnf(7392,plain,
( sdtasdt0(sz10,X1) = sz00
| sdtasdt0(X1,sz10) != sz00
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[7391,theory(equality)]) ).
cnf(7491,plain,
( sdtasdt0(sz10,X1) = sz00
| X1 != sz00
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[7392,149,theory(equality)]) ).
cnf(7527,plain,
( sdtasdt0(sz10,X1) = sz00
| X1 != sz00 ),
inference(csr,[status(thm)],[7491,1152]) ).
cnf(7605,plain,
( sdtasdt0(X1,X2) = sz00
| sdtasdt0(X1,sz00) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X2 != sz00 ),
inference(spm,[status(thm)],[4506,7527,theory(equality)]) ).
cnf(8102,negated_conjecture,
( sdtpldt0(sz00,xn) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[104,6785,theory(equality)]) ).
cnf(8177,negated_conjecture,
( sdtpldt0(sz00,xn) != sdtasdt0(xn,xm)
| $false
| ~ aNaturalNumber0(xn) ),
inference(rw,[status(thm)],[8102,128,theory(equality)]) ).
cnf(8178,negated_conjecture,
( sdtpldt0(sz00,xn) != sdtasdt0(xn,xm)
| $false
| $false ),
inference(rw,[status(thm)],[8177,105,theory(equality)]) ).
cnf(8179,negated_conjecture,
sdtpldt0(sz00,xn) != sdtasdt0(xn,xm),
inference(cn,[status(thm)],[8178,theory(equality)]) ).
cnf(8407,negated_conjecture,
( xn != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(xn) ),
inference(spm,[status(thm)],[8179,143,theory(equality)]) ).
cnf(8408,negated_conjecture,
( xn != sdtasdt0(xn,xm)
| $false ),
inference(rw,[status(thm)],[8407,105,theory(equality)]) ).
cnf(8409,negated_conjecture,
xn != sdtasdt0(xn,xm),
inference(cn,[status(thm)],[8408,theory(equality)]) ).
cnf(11179,plain,
( sdtasdt0(X1,X2) = sz00
| sdtasdt0(X1,sz00) != sz00
| X2 != sz00
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[7605,1152]) ).
cnf(11180,plain,
( sdtasdt0(X1,X2) = sz00
| X2 != sz00
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[11179,34]) ).
cnf(11188,plain,
( sz00 = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X2 != sz00 ),
inference(spm,[status(thm)],[139,11180,theory(equality)]) ).
cnf(11430,plain,
( sdtasdt0(X2,X1) = sz00
| X2 != sz00
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[11188,1152]) ).
cnf(11433,negated_conjecture,
( sz00 != xn
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[173,11430,theory(equality)]) ).
cnf(11536,negated_conjecture,
( sz00 != xn
| $false ),
inference(rw,[status(thm)],[11433,106,theory(equality)]) ).
cnf(11537,negated_conjecture,
sz00 != xn,
inference(cn,[status(thm)],[11536,theory(equality)]) ).
cnf(35548,negated_conjecture,
( xm = sz10
| sz00 = xn
| ~ sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(spm,[status(thm)],[103,595,theory(equality)]) ).
cnf(35622,negated_conjecture,
( xm = sz10
| sz00 = xn
| ~ sdtlseqdt0(sz10,xm)
| $false
| ~ aNaturalNumber0(xm) ),
inference(rw,[status(thm)],[35548,105,theory(equality)]) ).
cnf(35623,negated_conjecture,
( xm = sz10
| sz00 = xn
| ~ sdtlseqdt0(sz10,xm)
| $false
| $false ),
inference(rw,[status(thm)],[35622,106,theory(equality)]) ).
cnf(35624,negated_conjecture,
( xm = sz10
| sz00 = xn
| ~ sdtlseqdt0(sz10,xm) ),
inference(cn,[status(thm)],[35623,theory(equality)]) ).
cnf(35625,negated_conjecture,
( xm = sz10
| ~ sdtlseqdt0(sz10,xm) ),
inference(sr,[status(thm)],[35624,11537,theory(equality)]) ).
cnf(35694,negated_conjecture,
xm = sz10,
inference(csr,[status(thm)],[35625,1261]) ).
cnf(35702,negated_conjecture,
sdtasdt0(xn,sz10) != xn,
inference(rw,[status(thm)],[8409,35694,theory(equality)]) ).
cnf(35922,negated_conjecture,
~ aNaturalNumber0(xn),
inference(spm,[status(thm)],[35702,149,theory(equality)]) ).
cnf(35929,negated_conjecture,
$false,
inference(rw,[status(thm)],[35922,105,theory(equality)]) ).
cnf(35930,negated_conjecture,
$false,
inference(cn,[status(thm)],[35929,theory(equality)]) ).
cnf(35931,negated_conjecture,
$false,
35930,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM463+2 : TPTP v7.0.0. Released v4.0.0.
% 0.00/0.04 % Command : Source/sine.py -e eprover -t %d %s
% 0.02/0.23 % Computer : n068.star.cs.uiowa.edu
% 0.02/0.23 % Model : x86_64 x86_64
% 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23 % Memory : 32218.625MB
% 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.23 % CPULimit : 300
% 0.02/0.23 % DateTime : Fri Jan 5 04:42:59 CST 2018
% 0.02/0.23 % CPUTime :
% 0.07/0.27 % SZS status Started for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.27 --creating new selector for []
% 0.53/0.95 -running prover on /export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1 with time limit 29
% 0.53/0.95 -running prover with command ['/export/starexec/sandbox2/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/export/starexec/sandbox2/tmp/tmpUQmY2A/sel_theBenchmark.p_1']
% 0.53/0.95 -prover status Theorem
% 0.53/0.95 Problem theBenchmark.p solved in phase 0.
% 0.53/0.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.53/0.95 % SZS status Ended for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.53/0.95 Solved 1 out of 1.
% 0.53/0.95 # Problem is unsatisfiable (or provable), constructing proof object
% 0.53/0.95 # SZS status Theorem
% 0.53/0.95 # SZS output start CNFRefutation.
% See solution above
% 0.53/0.95 # SZS output end CNFRefutation
%------------------------------------------------------------------------------