TSTP Solution File: NUM462+2 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM462+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 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 : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 10:37:44 EDT 2023
% Result : Theorem 77.42s 77.47s
% Output : CNFRefutation 77.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 36
% Syntax : Number of formulae : 187 ( 59 unt; 12 typ; 0 def)
% Number of atoms : 589 ( 209 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 708 ( 294 ~; 309 |; 74 &)
% ( 2 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 209 ( 1 sgn; 89 !; 6 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
aNaturalNumber0: $i > $o ).
tff(decl_23,type,
sz00: $i ).
tff(decl_24,type,
sz10: $i ).
tff(decl_25,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(decl_26,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(decl_27,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(decl_28,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(decl_29,type,
xm: $i ).
tff(decl_30,type,
xl: $i ).
tff(decl_31,type,
xn: $i ).
tff(decl_32,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_33,type,
esk2_0: $i ).
fof(mMonAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> ( sdtpldt0(X3,X1) != sdtpldt0(X3,X2)
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtpldt0(X1,X3) != sdtpldt0(X2,X3)
& sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
fof(m__897_03,hypothesis,
( xm != sz00
& xl != xn
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xl,X1) = xn )
& sdtlseqdt0(xl,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__897_03) ).
fof(m__897,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xl)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__897) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
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/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(mAddCanc,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtpldt0(X1,X2) = sdtpldt0(X1,X3)
| sdtpldt0(X2,X1) = sdtpldt0(X3,X1) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
fof(m__,conjecture,
( sdtasdt0(xm,xl) != sdtasdt0(xm,xn)
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtasdt0(xm,xl),X1) = sdtasdt0(xm,xn) )
| sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn)) )
& sdtasdt0(xl,xm) != sdtasdt0(xn,xm)
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtasdt0(xl,xm),X1) = sdtasdt0(xn,xm) )
| sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
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/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X1 = sz00
& X2 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( X3 = sdtmndt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
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/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(c_0_24,plain,
! [X49,X50,X51] :
( ( sdtpldt0(X51,X49) != sdtpldt0(X51,X50)
| ~ aNaturalNumber0(X51)
| X49 = X50
| ~ sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) )
& ( sdtlseqdt0(sdtpldt0(X51,X49),sdtpldt0(X51,X50))
| ~ aNaturalNumber0(X51)
| X49 = X50
| ~ sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) )
& ( sdtpldt0(X49,X51) != sdtpldt0(X50,X51)
| ~ aNaturalNumber0(X51)
| X49 = X50
| ~ sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) )
& ( sdtlseqdt0(sdtpldt0(X49,X51),sdtpldt0(X50,X51))
| ~ aNaturalNumber0(X51)
| X49 = X50
| ~ sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonAdd])])])]) ).
fof(c_0_25,hypothesis,
( xm != sz00
& xl != xn
& aNaturalNumber0(esk2_0)
& sdtpldt0(xl,esk2_0) = xn
& sdtlseqdt0(xl,xn) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__897_03])]) ).
cnf(c_0_26,plain,
( sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X1,X3))
| X2 = X3
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_27,hypothesis,
sdtlseqdt0(xl,xn),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__897]) ).
cnf(c_0_29,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__897]) ).
cnf(c_0_30,hypothesis,
xl != xn,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_31,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_32,plain,
! [X44,X45,X46] :
( ~ aNaturalNumber0(X44)
| ~ aNaturalNumber0(X45)
| ~ aNaturalNumber0(X46)
| ~ sdtlseqdt0(X44,X45)
| ~ sdtlseqdt0(X45,X46)
| sdtlseqdt0(X44,X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
cnf(c_0_33,hypothesis,
( sdtlseqdt0(sdtpldt0(X1,xl),sdtpldt0(X1,xn))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_34,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_36,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])])])])]) ).
fof(c_0_37,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_38,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,hypothesis,
sdtlseqdt0(sdtpldt0(sz00,xl),xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_28])]) ).
cnf(c_0_40,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,hypothesis,
( sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,sdtpldt0(sz00,xl))
| ~ aNaturalNumber0(sdtpldt0(sz00,xl))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_28])]) ).
cnf(c_0_43,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_40]),c_0_41]) ).
cnf(c_0_44,hypothesis,
( sdtlseqdt0(sz00,xn)
| ~ aNaturalNumber0(sdtpldt0(sz00,xl)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_35]),c_0_29])]) ).
cnf(c_0_45,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,hypothesis,
sdtlseqdt0(sz00,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_34]),c_0_29])]) ).
cnf(c_0_47,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_48,hypothesis,
sdtpldt0(sz00,esk1_2(sz00,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_28]),c_0_35])]) ).
cnf(c_0_49,hypothesis,
aNaturalNumber0(esk1_2(sz00,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_46]),c_0_28]),c_0_35])]) ).
fof(c_0_50,plain,
! [X8,X9] :
( ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X9)
| sdtpldt0(X8,X9) = sdtpldt0(X9,X8) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_51,hypothesis,
esk1_2(sz00,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_48]),c_0_49])]) ).
fof(c_0_52,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_53,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_54,hypothesis,
sdtpldt0(sz00,xn) = xn,
inference(rw,[status(thm)],[c_0_48,c_0_51]) ).
cnf(c_0_55,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_56,hypothesis,
sdtpldt0(xn,sz00) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_28]),c_0_35])]) ).
cnf(c_0_57,hypothesis,
( sdtpldt0(xn,sdtpldt0(sz00,X1)) = sdtpldt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_35]),c_0_28])]) ).
cnf(c_0_58,hypothesis,
( sdtlseqdt0(xn,sdtpldt0(xn,X1))
| ~ aNaturalNumber0(sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_57]),c_0_28])]) ).
cnf(c_0_59,hypothesis,
( aNaturalNumber0(sdtpldt0(xn,X1))
| ~ aNaturalNumber0(sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_57]),c_0_28])]) ).
fof(c_0_60,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])]) ).
fof(c_0_61,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_62,hypothesis,
sdtlseqdt0(xn,sdtpldt0(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_54]),c_0_28])]) ).
cnf(c_0_63,hypothesis,
aNaturalNumber0(sdtpldt0(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_54]),c_0_28])]) ).
cnf(c_0_64,plain,
( sdtlseqdt0(X1,sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_53]) ).
cnf(c_0_65,hypothesis,
sdtpldt0(xl,esk2_0) = xn,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_66,hypothesis,
aNaturalNumber0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_67,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_68,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_69,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
fof(c_0_70,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])])]) ).
cnf(c_0_71,hypothesis,
( sdtlseqdt0(X1,sdtpldt0(xn,xn))
| ~ sdtlseqdt0(X1,xn)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_62]),c_0_63]),c_0_28])]) ).
cnf(c_0_72,hypothesis,
sdtlseqdt0(esk2_0,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]),c_0_29])]) ).
fof(c_0_73,plain,
! [X24,X25,X26] :
( ( sdtpldt0(X24,X25) != sdtpldt0(X24,X26)
| X25 = X26
| ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X25)
| ~ aNaturalNumber0(X26) )
& ( sdtpldt0(X25,X24) != sdtpldt0(X26,X24)
| X25 = X26
| ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X25)
| ~ aNaturalNumber0(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).
cnf(c_0_74,plain,
( sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69])]) ).
cnf(c_0_75,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_76,hypothesis,
sdtlseqdt0(esk2_0,sdtpldt0(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_66])]) ).
cnf(c_0_77,plain,
( X2 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
fof(c_0_78,negated_conjecture,
~ ( sdtasdt0(xm,xl) != sdtasdt0(xm,xn)
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtasdt0(xm,xl),X1) = sdtasdt0(xm,xn) )
| sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn)) )
& sdtasdt0(xl,xm) != sdtasdt0(xn,xm)
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtasdt0(xl,xm),X1) = sdtasdt0(xn,xm) )
| sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_79,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_80,plain,
( sdtasdt0(sz10,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_35])]) ).
cnf(c_0_81,hypothesis,
aNaturalNumber0(esk1_2(esk2_0,sdtpldt0(xn,xn))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_76]),c_0_63]),c_0_66])]) ).
cnf(c_0_82,hypothesis,
( sz00 = X1
| sdtpldt0(xn,X1) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_56]),c_0_35]),c_0_28])]) ).
fof(c_0_83,negated_conjecture,
! [X53,X54] :
( ( ~ aNaturalNumber0(X54)
| sdtpldt0(sdtasdt0(xl,xm),X54) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X53)
| sdtpldt0(sdtasdt0(xm,xl),X53) != sdtasdt0(xm,xn)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm) )
& ( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X53)
| sdtpldt0(sdtasdt0(xm,xl),X53) != sdtasdt0(xm,xn)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm) )
& ( ~ aNaturalNumber0(X54)
| sdtpldt0(sdtasdt0(xl,xm),X54) != sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm) )
& ( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])])])]) ).
fof(c_0_84,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_85,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_86,hypothesis,
sdtasdt0(sz10,sz00) = sz00,
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_87,hypothesis,
( sdtpldt0(sz00,X1) = sz00
| sdtpldt0(xn,X1) != xn
| ~ aNaturalNumber0(sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_57]) ).
cnf(c_0_88,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_89,negated_conjecture,
( sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtasdt0(xm,xl),X1) != sdtasdt0(xm,xn) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_90,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__897]) ).
fof(c_0_91,plain,
! [X47,X48] :
( ( X48 != X47
| sdtlseqdt0(X47,X48)
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X48) )
& ( sdtlseqdt0(X48,X47)
| sdtlseqdt0(X47,X48)
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X48) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
fof(c_0_92,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_93,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_94,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_84]) ).
cnf(c_0_95,hypothesis,
( sdtpldt0(sz00,sdtpldt0(xn,X1)) = sdtpldt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_54]),c_0_28]),c_0_35])]) ).
cnf(c_0_96,hypothesis,
sdtpldt0(xn,esk1_2(xn,sdtpldt0(xn,xn))) = sdtpldt0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_62]),c_0_63]),c_0_28])]) ).
cnf(c_0_97,hypothesis,
aNaturalNumber0(esk1_2(xn,sdtpldt0(xn,xn))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_62]),c_0_63]),c_0_28])]) ).
cnf(c_0_98,plain,
( sdtasdt0(sz00,sdtasdt0(X1,X2)) = sdtasdt0(sz00,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_75]),c_0_35])]) ).
cnf(c_0_99,hypothesis,
sdtasdt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_35]),c_0_69])]) ).
cnf(c_0_100,hypothesis,
( sdtpldt0(sz00,sz00) = sz00
| ~ aNaturalNumber0(sdtpldt0(sz00,sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_35]),c_0_28])]) ).
cnf(c_0_101,negated_conjecture,
( sdtasdt0(xl,xm) = sdtasdt0(xm,xn)
| sdtasdt0(xm,xn) = sdtasdt0(xm,xl)
| sdtpldt0(sdtasdt0(xm,xl),X1) != sdtasdt0(xm,xn)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xm,xn))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_85]),c_0_28]),c_0_90])]) ).
cnf(c_0_102,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_103,plain,
( X1 = sz00
| sdtpldt0(X1,X2) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_104,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_105,plain,
( sdtpldt0(sdtasdt0(sz00,X1),sz00) = sdtasdt0(sz00,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_75]),c_0_35])]) ).
cnf(c_0_106,hypothesis,
sdtpldt0(sz00,sdtpldt0(xn,xn)) = sdtpldt0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97])]) ).
cnf(c_0_107,hypothesis,
sdtasdt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_99]),c_0_69]),c_0_35])]) ).
cnf(c_0_108,hypothesis,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_41]),c_0_35])]) ).
cnf(c_0_109,negated_conjecture,
( sdtasdt0(xm,xn) = sdtasdt0(xm,xl)
| sdtasdt0(xl,xm) = sdtasdt0(xm,xn)
| sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xl,xm))
| sdtpldt0(sdtasdt0(xm,xl),X1) != sdtasdt0(xm,xn)
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_110,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_102]) ).
cnf(c_0_111,plain,
( sdtlseqdt0(X1,X2)
| aNaturalNumber0(esk1_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_102]) ).
cnf(c_0_112,plain,
( sdtasdt0(X1,X2) = sz00
| sdtasdt0(X1,sdtpldt0(X2,X3)) != sz00
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_94]),c_0_104]),c_0_104]) ).
cnf(c_0_113,hypothesis,
sdtasdt0(sz00,sdtpldt0(xn,xn)) = sz00,
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_105,c_0_106]),c_0_107]),c_0_108]),c_0_63]),c_0_35])]) ).
cnf(c_0_114,negated_conjecture,
( sdtasdt0(xl,xm) = sdtasdt0(xm,xn)
| sdtasdt0(xm,xn) = sdtasdt0(xm,xl)
| sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xm,xl))
| sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xl,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xl)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110])]),c_0_111]) ).
cnf(c_0_115,plain,
( X1 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_116,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_117,hypothesis,
sdtasdt0(sz00,xn) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_28]),c_0_35])]) ).
cnf(c_0_118,negated_conjecture,
( sdtasdt0(xm,xn) = sdtasdt0(xm,xl)
| sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xm,xl))
| ~ aNaturalNumber0(sdtasdt0(xm,xl))
| ~ aNaturalNumber0(sdtasdt0(xm,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_85]),c_0_90]),c_0_29])]) ).
cnf(c_0_119,hypothesis,
( X1 = xl
| sdtpldt0(X1,esk2_0) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_65]),c_0_29]),c_0_66])]) ).
cnf(c_0_120,plain,
( sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_116]),c_0_69])]) ).
cnf(c_0_121,hypothesis,
sdtasdt0(xn,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_117]),c_0_28]),c_0_35])]) ).
fof(c_0_122,plain,
! [X42,X43] :
( ~ aNaturalNumber0(X42)
| ~ aNaturalNumber0(X43)
| ~ sdtlseqdt0(X42,X43)
| ~ sdtlseqdt0(X43,X42)
| X42 = X43 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_123,negated_conjecture,
( sdtasdt0(xm,xn) = sdtasdt0(xm,xl)
| sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xm,xl))
| ~ aNaturalNumber0(sdtasdt0(xm,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_104]),c_0_29]),c_0_90])]) ).
cnf(c_0_124,hypothesis,
( X1 = xl
| sdtpldt0(esk2_0,X1) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_53]),c_0_66])]) ).
cnf(c_0_125,hypothesis,
sdtpldt0(esk2_0,esk1_2(esk2_0,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_72]),c_0_28]),c_0_66])]) ).
cnf(c_0_126,hypothesis,
aNaturalNumber0(esk1_2(esk2_0,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_72]),c_0_28]),c_0_66])]) ).
fof(c_0_127,plain,
! [X38,X39,X40] :
( ( aNaturalNumber0(X40)
| X40 != sdtmndt0(X39,X38)
| ~ sdtlseqdt0(X38,X39)
| ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X39) )
& ( sdtpldt0(X38,X40) = X39
| X40 != sdtmndt0(X39,X38)
| ~ sdtlseqdt0(X38,X39)
| ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X39) )
& ( ~ aNaturalNumber0(X40)
| sdtpldt0(X38,X40) != X39
| X40 = sdtmndt0(X39,X38)
| ~ sdtlseqdt0(X38,X39)
| ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X39) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).
cnf(c_0_128,hypothesis,
sdtasdt0(xn,sdtpldt0(sz00,sz10)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_54]),c_0_35]),c_0_28])]) ).
cnf(c_0_129,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_130,negated_conjecture,
( sdtasdt0(xm,xn) = sdtasdt0(xm,xl)
| sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xm,xl)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_104]),c_0_28]),c_0_90])]) ).
cnf(c_0_131,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_94]),c_0_104]),c_0_104]) ).
cnf(c_0_132,hypothesis,
esk1_2(esk2_0,xn) = xl,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_126])]) ).
cnf(c_0_133,plain,
( X1 = sdtmndt0(X3,X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_134,hypothesis,
sdtasdt0(xn,sz10) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_34]),c_0_69])]) ).
cnf(c_0_135,negated_conjecture,
( sdtasdt0(xm,xn) = sdtasdt0(xm,xl)
| ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xl)) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_136,hypothesis,
( sdtlseqdt0(sdtasdt0(X1,xl),sdtasdt0(X1,xn))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_65]),c_0_66]),c_0_29])]) ).
cnf(c_0_137,hypothesis,
( sdtpldt0(xl,sdtpldt0(esk2_0,X1)) = sdtpldt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_65]),c_0_66]),c_0_29])]) ).
cnf(c_0_138,hypothesis,
sdtpldt0(esk2_0,xl) = xn,
inference(rw,[status(thm)],[c_0_125,c_0_132]) ).
cnf(c_0_139,plain,
( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_133]),c_0_41]),c_0_43]) ).
cnf(c_0_140,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_134]),c_0_69]),c_0_28])]) ).
cnf(c_0_141,negated_conjecture,
( sdtasdt0(xm,xn) = sdtasdt0(xm,xl)
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xl)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_90])]) ).
cnf(c_0_142,hypothesis,
sdtpldt0(xn,xl) = sdtpldt0(xl,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_29])]) ).
cnf(c_0_143,hypothesis,
( aNaturalNumber0(sdtpldt0(xn,X1))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_34]) ).
cnf(c_0_144,plain,
( aNaturalNumber0(sdtpldt0(X1,sdtpldt0(X2,X3)))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_55]),c_0_41]) ).
cnf(c_0_145,plain,
( sdtmndt0(sdtasdt0(X1,sdtpldt0(X2,X3)),sdtasdt0(X1,X2)) = sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_94]),c_0_104]),c_0_104]) ).
cnf(c_0_146,hypothesis,
sdtasdt0(sz10,sdtpldt0(xn,sz10)) = sdtpldt0(xn,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_140]),c_0_28]),c_0_69])]) ).
cnf(c_0_147,negated_conjecture,
( sdtasdt0(xm,xn) = sdtasdt0(xm,xl)
| ~ aNaturalNumber0(sdtasdt0(xm,xl)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_104]),c_0_28]),c_0_90])]) ).
cnf(c_0_148,hypothesis,
sdtpldt0(sz00,sdtpldt0(xl,xn)) = sdtpldt0(xl,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_142]),c_0_29])]) ).
cnf(c_0_149,hypothesis,
aNaturalNumber0(sdtpldt0(xl,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_142]),c_0_29])]) ).
cnf(c_0_150,hypothesis,
( aNaturalNumber0(sdtpldt0(X1,sz00))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_108]),c_0_35])]) ).
cnf(c_0_151,hypothesis,
sdtmndt0(sdtpldt0(xn,sz10),xn) = sdtasdt0(sz10,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_140]),c_0_69]),c_0_28])]) ).
cnf(c_0_152,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(X3,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_67]),c_0_104]) ).
cnf(c_0_153,negated_conjecture,
sdtasdt0(xm,xn) = sdtasdt0(xm,xl),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_104]),c_0_29]),c_0_90])]) ).
cnf(c_0_154,hypothesis,
sdtasdt0(sz00,sdtpldt0(xl,xn)) = sz00,
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_105,c_0_148]),c_0_107]),c_0_108]),c_0_149]),c_0_35])]) ).
cnf(c_0_155,hypothesis,
( aNaturalNumber0(sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_53]),c_0_35])]) ).
cnf(c_0_156,hypothesis,
sdtasdt0(sz10,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_151]),c_0_28]),c_0_69])]) ).
cnf(c_0_157,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(X2,sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_152,c_0_85]) ).
cnf(c_0_158,negated_conjecture,
sdtasdt0(sz00,sdtasdt0(xm,xl)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_153]),c_0_117]),c_0_28]),c_0_90])]) ).
cnf(c_0_159,hypothesis,
sdtasdt0(sz00,xl) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_154]),c_0_28]),c_0_29]),c_0_35])]) ).
cnf(c_0_160,hypothesis,
( sdtmndt0(sdtpldt0(xn,X1),xn) = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_57]),c_0_28])]),c_0_155]) ).
cnf(c_0_161,hypothesis,
sdtmndt0(sdtpldt0(xn,sz10),xn) = sz10,
inference(rw,[status(thm)],[c_0_151,c_0_156]) ).
cnf(c_0_162,negated_conjecture,
sdtasdt0(xm,sz00) = sz00,
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_157,c_0_158]),c_0_159]),c_0_90]),c_0_29]),c_0_35])]) ).
cnf(c_0_163,hypothesis,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_69])]) ).
fof(c_0_164,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_165,negated_conjecture,
sdtpldt0(sz00,xm) = sdtasdt0(xm,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_162]),c_0_163]),c_0_35]),c_0_90])]) ).
cnf(c_0_166,plain,
( X2 = X3
| X1 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_164]) ).
cnf(c_0_167,negated_conjecture,
sdtasdt0(xm,sz10) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_165]),c_0_90])]) ).
cnf(c_0_168,plain,
( X1 = sz00
| X2 = X3
| sdtasdt0(X1,X2) != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_166,c_0_85]) ).
cnf(c_0_169,hypothesis,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_170,negated_conjecture,
sdtasdt0(sz10,sdtasdt0(xm,xl)) = sdtasdt0(xm,xl),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_153]),c_0_28]),c_0_90])]) ).
cnf(c_0_171,negated_conjecture,
sdtasdt0(sz10,xm) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_167]),c_0_69]),c_0_90])]) ).
cnf(c_0_172,negated_conjecture,
( xn = X1
| sdtasdt0(xm,xl) != sdtasdt0(X1,xm)
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_153]),c_0_28]),c_0_90])]),c_0_169]) ).
cnf(c_0_173,negated_conjecture,
sdtasdt0(xl,xm) = sdtasdt0(xm,xl),
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_152,c_0_170]),c_0_171]),c_0_29]),c_0_90]),c_0_69])]) ).
cnf(c_0_174,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_172,c_0_30,c_0_173,c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM462+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 16:37:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 77.42/77.47 % Version : CSE_E---1.5
% 77.42/77.47 % Problem : theBenchmark.p
% 77.42/77.47 % Proof found
% 77.42/77.47 % SZS status Theorem for theBenchmark.p
% 77.42/77.47 % SZS output start Proof
% See solution above
% 77.42/77.48 % Total time : 76.880000 s
% 77.42/77.48 % SZS output end Proof
% 77.42/77.48 % Total time : 76.887000 s
%------------------------------------------------------------------------------