%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM466+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:49:11 PM UTC 2026
% Result : Theorem 16.87s 2.95s
% Output : CNFRefutation 16.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 20
% Syntax : Number of formulae : 161 ( 58 unt; 0 def)
% Number of atoms : 481 ( 172 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 548 ( 228 ~; 237 |; 51 &)
% ( 5 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 192 ( 0 sgn 75 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__,conjecture,
( ( doDivides0(xm,xn)
& doDivides0(xl,xm) )
=> doDivides0(xl,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(m__1218,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1218) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X2 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
fof(mAddCanc,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtpldt0(X2,X1) = sdtpldt0(X3,X1)
| sdtpldt0(X1,X2) = sdtpldt0(X1,X3) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( X3 = sdtmndt0(X2,X1)
<=> ( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(c_0_20,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
fof(c_0_21,negated_conjecture,
~ ( ( doDivides0(xm,xn)
& doDivides0(xl,xm) )
=> doDivides0(xl,xn) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_22,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefQuot]) ).
fof(c_0_23,plain,
! [X63,X64,X66] :
( ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| doDivides0(X63,X64)
| X64 != sdtasdt0(X63,X66)
| ~ aNaturalNumber0(X66) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| X64 = sdtasdt0(X63,esk2_2(X63,X64)) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| aNaturalNumber0(esk2_2(X63,X64)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])])]) ).
fof(c_0_24,plain,
! [X7,X8] :
( aNaturalNumber0(sdtasdt0(X7,X8))
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
fof(c_0_25,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
inference(fof_simplification,[status(thm)],[mMonMul2]) ).
fof(c_0_26,plain,
! [X17,X18,X19] :
( sdtasdt0(sdtasdt0(X17,X18),X19) = sdtasdt0(X17,sdtasdt0(X18,X19))
| ~ aNaturalNumber0(X19)
| ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
fof(c_0_27,plain,
! [X20] :
( ( ~ aNaturalNumber0(X20)
| X20 = sdtasdt0(sz10,X20) )
& ( ~ aNaturalNumber0(X20)
| sdtasdt0(X20,sz10) = X20 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
fof(c_0_28,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_20]) ).
fof(c_0_29,negated_conjecture,
( ~ doDivides0(xl,xn)
& doDivides0(xm,xn)
& doDivides0(xl,xm) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])]) ).
fof(c_0_30,plain,
! [X67,X68,X69] :
( ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 = sdtsldt0(X68,X67)
| X68 != sdtasdt0(X67,X69)
| ~ aNaturalNumber0(X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| X68 = sdtasdt0(X67,X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| aNaturalNumber0(X69) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])])]) ).
cnf(c_0_31,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_33,plain,
! [X57,X58] :
( sdtlseqdt0(X58,sdtasdt0(X58,X57))
| X57 = sz00
| ~ aNaturalNumber0(X58)
| ~ aNaturalNumber0(X57) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
fof(c_0_34,plain,
! [X15,X16] :
( sdtasdt0(X15,X16) = sdtasdt0(X16,X15)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_35,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X1 = sdtasdt0(X2,esk2_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_39,negated_conjecture,
doDivides0(xl,xm),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_40,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1218]) ).
cnf(c_0_41,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1218]) ).
cnf(c_0_42,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_43,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2)
| X2 = sz00
| X1 = sdtasdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_44,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_31]),c_0_32]) ).
cnf(c_0_45,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X1 != sdtsldt0(X2,X3)
| X3 = sz00
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_46,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_47,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_48,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_49,negated_conjecture,
sdtasdt0(xl,esk2_2(xl,xm)) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41])]) ).
cnf(c_0_50,negated_conjecture,
aNaturalNumber0(esk2_2(xl,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_39]),c_0_41]),c_0_40])]) ).
cnf(c_0_51,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| X3 = sz00
| X1 = sdtsldt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_52,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| X1 = sz00
| sdtasdt0(X1,sdtsldt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_43]) ).
cnf(c_0_53,plain,
( ~ aNaturalNumber0(X1)
| doDivides0(sz10,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_36]),c_0_37])]) ).
cnf(c_0_54,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_55,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(sdtsldt0(X2,X1))
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_45]) ).
fof(c_0_56,plain,
! [X35,X36,X38] :
( ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| sdtlseqdt0(X35,X36)
| sdtpldt0(X35,X38) != X36
| ~ aNaturalNumber0(X38) )
& ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| ~ sdtlseqdt0(X35,X36)
| sdtpldt0(X35,esk1_2(X35,X36)) = X36 )
& ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| ~ sdtlseqdt0(X35,X36)
| aNaturalNumber0(esk1_2(X35,X36)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_57,plain,
! [X5,X6] :
( aNaturalNumber0(sdtpldt0(X5,X6))
| ~ aNaturalNumber0(X6)
| ~ aNaturalNumber0(X5) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
fof(c_0_58,plain,
! [X33,X34] :
( X34 = sz00
| X33 = sz00
| sdtasdt0(X33,X34) != sz00
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X33) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])])]) ).
fof(c_0_59,plain,
! [X25,X26,X27] :
( ( ~ aNaturalNumber0(X27)
| ~ aNaturalNumber0(X26)
| ~ aNaturalNumber0(X25)
| X26 = X27
| sdtpldt0(X26,X25) != sdtpldt0(X27,X25) )
& ( ~ aNaturalNumber0(X27)
| ~ aNaturalNumber0(X26)
| ~ aNaturalNumber0(X25)
| X26 = X27
| sdtpldt0(X25,X26) != sdtpldt0(X25,X27) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])])]) ).
fof(c_0_60,plain,
! [X14] :
( ( ~ aNaturalNumber0(X14)
| X14 = sdtpldt0(sz00,X14) )
& ( ~ aNaturalNumber0(X14)
| sdtpldt0(X14,sz00) = X14 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])])]) ).
cnf(c_0_61,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| X1 = sz00 ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_62,negated_conjecture,
sdtasdt0(sz10,xm) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_40])]) ).
fof(c_0_63,plain,
! [X39,X40,X41] :
( ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ sdtlseqdt0(X39,X40)
| X41 = sdtmndt0(X40,X39)
| sdtpldt0(X39,X41) != X40
| ~ aNaturalNumber0(X41) )
& ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ sdtlseqdt0(X39,X40)
| X41 != sdtmndt0(X40,X39)
| sdtpldt0(X39,X41) = X40 )
& ( ~ aNaturalNumber0(X40)
| ~ aNaturalNumber0(X39)
| ~ sdtlseqdt0(X39,X40)
| X41 != sdtmndt0(X40,X39)
| aNaturalNumber0(X41) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])])]) ).
cnf(c_0_64,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = sz00
| sdtsldt0(sdtasdt0(X1,X2),X1) = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_51]),c_0_32]),c_0_44]) ).
cnf(c_0_65,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(sz10,sdtsldt0(X1,sz10)) = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_37])]),c_0_54]) ).
cnf(c_0_66,plain,
( ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtsldt0(X1,sz10)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_53]),c_0_37])]),c_0_54]) ).
cnf(c_0_67,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_68,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
fof(c_0_69,plain,
! [X21] :
( ( ~ aNaturalNumber0(X21)
| sz00 = sdtasdt0(sz00,X21) )
& ( ~ aNaturalNumber0(X21)
| sdtasdt0(X21,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])])]) ).
cnf(c_0_70,negated_conjecture,
doDivides0(xm,xn),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_71,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1218]) ).
cnf(c_0_72,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_73,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_74,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_75,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_76,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,esk1_2(X1,X2)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_77,negated_conjecture,
sdtlseqdt0(xm,xm),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_41]),c_0_37])]),c_0_54]) ).
cnf(c_0_78,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| aNaturalNumber0(esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_79,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X3)
| X2 != sdtmndt0(X3,X1)
| sdtpldt0(X1,X2) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_80,plain,
( ~ aNaturalNumber0(X1)
| sdtsldt0(X1,sz10) = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_36]),c_0_37])]),c_0_54]) ).
cnf(c_0_81,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sz10,X1)
| sdtsldt0(X1,sz10) = sz00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_65]),c_0_37])]),c_0_66]) ).
cnf(c_0_82,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X3)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X1)
| X1 = sdtmndt0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_83,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_67]),c_0_68]) ).
cnf(c_0_84,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_85,negated_conjecture,
sdtasdt0(xm,esk2_2(xm,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_70]),c_0_41]),c_0_71])]) ).
cnf(c_0_86,negated_conjecture,
aNaturalNumber0(esk2_2(xm,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_70]),c_0_71]),c_0_41])]) ).
cnf(c_0_87,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X2,X1)) ),
inference(spm,[status(thm)],[c_0_44,c_0_47]) ).
cnf(c_0_88,plain,
( ~ aNaturalNumber0(sdtsldt0(sz00,sz10))
| sdtsldt0(sz00,sz10) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_65]),c_0_37])]),c_0_54])]),c_0_73])]) ).
cnf(c_0_89,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X2
| X1 = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_73])]) ).
cnf(c_0_90,negated_conjecture,
sdtpldt0(xm,esk1_2(xm,xm)) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_41])]) ).
cnf(c_0_91,negated_conjecture,
aNaturalNumber0(esk1_2(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_77]),c_0_41])]) ).
cnf(c_0_92,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,sdtmndt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_79]) ).
cnf(c_0_93,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sz10,X1)
| sz00 = X1 ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_94,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtmndt0(sdtpldt0(X1,X2),X1) = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_82]),c_0_68]),c_0_83]) ).
cnf(c_0_95,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,sdtasdt0(X2,sz00)) = sz00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_35]),c_0_73])]),c_0_32]) ).
cnf(c_0_96,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xm,sdtasdt0(esk2_2(xm,xn),X1)) = sdtasdt0(xn,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_85]),c_0_86]),c_0_41])]) ).
cnf(c_0_97,negated_conjecture,
doDivides0(esk2_2(xm,xn),xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_85]),c_0_86]),c_0_41])]) ).
cnf(c_0_98,plain,
sdtsldt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_66]),c_0_73])]) ).
fof(c_0_99,plain,
! [X22,X23,X24] :
( ( ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X22)
| sdtasdt0(sdtpldt0(X23,X24),X22) = sdtpldt0(sdtasdt0(X23,X22),sdtasdt0(X24,X22)) )
& ( ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X22)
| sdtasdt0(X22,sdtpldt0(X23,X24)) = sdtpldt0(sdtasdt0(X22,X23),sdtasdt0(X22,X24)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])])]) ).
fof(c_0_100,plain,
! [X9,X10] :
( sdtpldt0(X9,X10) = sdtpldt0(X10,X9)
| ~ aNaturalNumber0(X10)
| ~ aNaturalNumber0(X9) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_101,negated_conjecture,
esk1_2(xm,xm) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]),c_0_41])]) ).
cnf(c_0_102,plain,
( ~ aNaturalNumber0(X1)
| sz00 = X1
| sdtpldt0(sz10,sdtmndt0(X1,sz10)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_37])]) ).
cnf(c_0_103,plain,
( ~ aNaturalNumber0(X1)
| sdtmndt0(X1,X1) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_75]),c_0_73])]) ).
cnf(c_0_104,negated_conjecture,
sdtasdt0(xn,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_86]),c_0_41]),c_0_73])]) ).
cnf(c_0_105,negated_conjecture,
sdtasdt0(esk2_2(xm,xn),esk2_2(esk2_2(xm,xn),xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_97]),c_0_86]),c_0_71])]) ).
cnf(c_0_106,negated_conjecture,
aNaturalNumber0(esk2_2(esk2_2(xm,xn),xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_97]),c_0_71]),c_0_86])]) ).
cnf(c_0_107,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_98]),c_0_73])]) ).
cnf(c_0_108,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_109,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_110,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_111,negated_conjecture,
sdtpldt0(xm,sz00) = xm,
inference(rw,[status(thm)],[c_0_90,c_0_101]) ).
cnf(c_0_112,plain,
sdtpldt0(sz10,sz00) = sz10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_37])]),c_0_54]) ).
cnf(c_0_113,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xl,sdtasdt0(esk2_2(xl,xm),X1)) = sdtasdt0(xm,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_49]),c_0_50]),c_0_40])]) ).
cnf(c_0_114,negated_conjecture,
sdtasdt0(xm,sz00) = sz00,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_84]),c_0_73]),c_0_86])]),c_0_104]) ).
cnf(c_0_115,negated_conjecture,
sdtasdt0(sz10,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_105]),c_0_106]),c_0_86])]) ).
cnf(c_0_116,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_107]),c_0_73]),c_0_37])]) ).
cnf(c_0_117,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz00
| sdtsldt0(X1,X1) = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_108]),c_0_37])]) ).
cnf(c_0_118,plain,
( ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_119,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_108]),c_0_37])]) ).
cnf(c_0_120,negated_conjecture,
sdtpldt0(sz00,xm) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_73]),c_0_41])]) ).
cnf(c_0_121,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_112]),c_0_73]),c_0_37])]) ).
cnf(c_0_122,negated_conjecture,
sdtasdt0(xl,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_84]),c_0_114]),c_0_73]),c_0_50])]) ).
cnf(c_0_123,negated_conjecture,
sdtlseqdt0(xn,xn),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_115]),c_0_71]),c_0_37])]),c_0_54]) ).
cnf(c_0_124,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(sz00,sdtasdt0(sz10,X1)) = sdtasdt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_116]),c_0_37]),c_0_73])]) ).
cnf(c_0_125,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| aNaturalNumber0(sdtasdt0(X1,sdtasdt0(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_35]),c_0_32]) ).
cnf(c_0_126,plain,
sdtasdt0(sz10,sz10) = sz10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_117]),c_0_37])]),c_0_54]) ).
cnf(c_0_127,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(sz00,sdtasdt0(X1,X2)) = sdtasdt0(sz00,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_118]),c_0_73])]) ).
cnf(c_0_128,negated_conjecture,
sdtasdt0(xm,sz10) = xm,
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_119,c_0_114]),c_0_120]),c_0_121]),c_0_73]),c_0_41])]) ).
cnf(c_0_129,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_130,negated_conjecture,
sdtpldt0(sz00,xl) = sdtasdt0(xl,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_122]),c_0_121]),c_0_73]),c_0_40])]) ).
cnf(c_0_131,negated_conjecture,
sdtpldt0(xn,esk1_2(xn,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_123]),c_0_71])]) ).
cnf(c_0_132,negated_conjecture,
aNaturalNumber0(esk1_2(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_123]),c_0_71])]) ).
cnf(c_0_133,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_134,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(sz00,sdtasdt0(X1,sz10)) = sdtasdt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_47]),c_0_37])]) ).
cnf(c_0_135,plain,
( ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_37])]) ).
cnf(c_0_136,negated_conjecture,
sdtasdt0(sz00,xm) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_116]),c_0_37]),c_0_41])]) ).
cnf(c_0_137,negated_conjecture,
sdtasdt0(xl,sz10) = xl,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_40])]) ).
cnf(c_0_138,negated_conjecture,
esk1_2(xn,xn) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_131]),c_0_132]),c_0_71])]) ).
cnf(c_0_139,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(sdtasdt0(sz00,X1),sdtasdt0(X2,sdtasdt0(X1,sz10))) = sdtasdt0(sdtpldt0(sz00,X2),sdtasdt0(X1,sz10)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_73])]),c_0_135]) ).
cnf(c_0_140,negated_conjecture,
sdtasdt0(sz00,esk2_2(xl,xm)) = sz00,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_49]),c_0_50]),c_0_40])]),c_0_136]) ).
cnf(c_0_141,negated_conjecture,
sdtpldt0(sz00,xl) = xl,
inference(rw,[status(thm)],[c_0_130,c_0_137]) ).
cnf(c_0_142,negated_conjecture,
sdtasdt0(sz00,esk2_2(xm,xn)) = sdtasdt0(sz00,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_85]),c_0_86]),c_0_41])]) ).
cnf(c_0_143,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_35]),c_0_37])]),c_0_32]) ).
cnf(c_0_144,negated_conjecture,
sdtpldt0(xn,sz00) = xn,
inference(rw,[status(thm)],[c_0_131,c_0_138]) ).
cnf(c_0_145,negated_conjecture,
sdtasdt0(xl,sdtasdt0(esk2_2(xl,xm),sz10)) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_113]),c_0_140]),c_0_128]),c_0_120]),c_0_141]),c_0_40]),c_0_50]),c_0_37])]) ).
cnf(c_0_146,negated_conjecture,
sdtasdt0(sz00,xn) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_142]),c_0_86])]) ).
cnf(c_0_147,negated_conjecture,
sdtasdt0(xn,sz10) = xn,
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_143,c_0_96]),c_0_85]),c_0_86]),c_0_41]),c_0_37])]) ).
cnf(c_0_148,negated_conjecture,
sdtpldt0(sz00,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_144]),c_0_73]),c_0_71])]) ).
cnf(c_0_149,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(X3,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_35]),c_0_32]) ).
cnf(c_0_150,negated_conjecture,
sdtasdt0(xl,sdtasdt0(sz10,esk2_2(xl,xm))) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_47]),c_0_37]),c_0_50])]) ).
cnf(c_0_151,negated_conjecture,
sdtasdt0(xm,sdtasdt0(esk2_2(xm,xn),sz10)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_96]),c_0_142]),c_0_146]),c_0_147]),c_0_148]),c_0_120]),c_0_41]),c_0_86]),c_0_37])]) ).
cnf(c_0_152,negated_conjecture,
sdtasdt0(sz10,sdtasdt0(esk2_2(xl,xm),xl)) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_40]),c_0_50]),c_0_37])]) ).
cnf(c_0_153,negated_conjecture,
sdtasdt0(xm,sdtasdt0(sz10,esk2_2(xm,xn))) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_47]),c_0_37]),c_0_86])]) ).
cnf(c_0_154,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X2,sdtasdt0(X3,X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_35]),c_0_32]) ).
cnf(c_0_155,negated_conjecture,
sdtasdt0(esk2_2(xl,xm),xl) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_152]),c_0_40]),c_0_50])]) ).
cnf(c_0_156,negated_conjecture,
sdtasdt0(sz10,sdtasdt0(esk2_2(xm,xn),xm)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_153]),c_0_41]),c_0_86]),c_0_37])]) ).
cnf(c_0_157,negated_conjecture,
( ~ aNaturalNumber0(X1)
| doDivides0(xl,sdtasdt0(X1,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_40]),c_0_50])]) ).
cnf(c_0_158,negated_conjecture,
sdtasdt0(esk2_2(xm,xn),xm) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_156]),c_0_41]),c_0_86])]) ).
cnf(c_0_159,negated_conjecture,
~ doDivides0(xl,xn),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_160,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_86])]),c_0_159]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM466+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 02:34:30 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.45 Running first-order theorem proving
% 0.16/0.45 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.87/2.95 % Version: 3.5.1
% 16.87/2.95 % Preprocessing class: FSLSSMSSSSSNFFN.
% 16.87/2.95 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 16.87/2.95 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 16.87/2.95 % Starting new_bool_3 with 300s (1) cores
% 16.87/2.95 % Starting new_bool_1 with 300s (1) cores
% 16.87/2.95 % Starting sh5l with 300s (1) cores
% 16.87/2.95 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 777896 completed with status 0
% 16.87/2.95 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 16.87/2.95 % Preprocessing class: FSLSSMSSSSSNFFN.
% 16.87/2.95 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 16.87/2.95 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 16.87/2.95 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 16.87/2.95 % No SInE strategy applied
% 16.87/2.95 % Search class: FGUSF-FFMM22-SFFFFFNN
% 16.87/2.95 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 16.87/2.95 % Starting SubtermCWHack with 136s (1) cores
% 16.87/2.95 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 16.87/2.95 % Starting G-E--_107_B42_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 16.87/2.95 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 16.87/2.95 % Starting new_bool_3 with 136s (1) cores
% 16.87/2.95 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 777903 completed with status 0
% 16.87/2.95 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 16.87/2.95 % Preprocessing class: FSLSSMSSSSSNFFN.
% 16.87/2.95 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 16.87/2.95 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 16.87/2.95 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 16.87/2.95 % No SInE strategy applied
% 16.87/2.95 % Search class: FGUSF-FFMM22-SFFFFFNN
% 16.87/2.95 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 16.87/2.95 % Starting SubtermCWHack with 136s (1) cores
% 16.87/2.95 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 16.87/2.95 % Preprocessing time : 0.003 s
% 16.87/2.95 % Presaturation interreduction done
% 16.87/2.95
% 16.87/2.95 % Proof found!
% 16.87/2.95 % SZS status Theorem
% 16.87/2.95 % SZS output start CNFRefutation
% See solution above
% 16.87/2.96 % Parsed axioms : 33
% 16.87/2.96 % Removed by relevancy pruning/SinE : 0
% 16.87/2.96 % Initial clauses : 61
% 16.87/2.96 % Removed in clause preprocessing : 3
% 16.87/2.96 % Initial clauses in saturation : 58
% 16.87/2.96 % Processed clauses : 8431
% 16.87/2.96 % ...of these trivial : 383
% 16.87/2.96 % ...subsumed : 5850
% 16.87/2.96 % ...remaining for further processing : 2198
% 16.87/2.96 % Other redundant clauses eliminated : 210
% 16.87/2.96 % Clauses deleted for lack of memory : 0
% 16.87/2.96 % Backward-subsumed : 90
% 16.87/2.96 % Backward-rewritten : 204
% 16.87/2.96 % Generated clauses : 77052
% 16.87/2.96 % ...of the previous two non-redundant : 70353
% 16.87/2.96 % ...aggressively subsumed : 0
% 16.87/2.96 % Contextual simplify-reflections : 510
% 16.87/2.96 % Paramodulations : 76816
% 16.87/2.96 % Factorizations : 4
% 16.87/2.96 % NegExts : 0
% 16.87/2.96 % Equation resolutions : 232
% 16.87/2.96 % Disequality decompositions : 0
% 16.87/2.96 % Total rewrite steps : 89451
% 16.87/2.96 % ...of those cached : 89096
% 16.87/2.96 % Propositional unsat checks : 0
% 16.87/2.96 % Propositional check models : 0
% 16.87/2.96 % Propositional check unsatisfiable : 0
% 16.87/2.96 % Propositional clauses : 0
% 16.87/2.96 % Propositional clauses after purity: 0
% 16.87/2.96 % Propositional unsat core size : 0
% 16.87/2.96 % Propositional preprocessing time : 0.000
% 16.87/2.96 % Propositional encoding time : 0.000
% 16.87/2.96 % Propositional solver time : 0.000
% 16.87/2.96 % Success case prop preproc time : 0.000
% 16.87/2.96 % Success case prop encoding time : 0.000
% 16.87/2.96 % Success case prop solver time : 0.000
% 16.87/2.96 % Current number of processed clauses : 1842
% 16.87/2.96 % Positive orientable unit clauses : 355
% 16.87/2.96 % Positive unorientable unit clauses: 0
% 16.87/2.96 % Negative unit clauses : 139
% 16.87/2.96 % Non-unit-clauses : 1348
% 16.87/2.96 % Current number of unprocessed clauses: 61577
% 16.87/2.96 % ...number of literals in the above : 279048
% 16.87/2.96 % Current number of archived formulas : 0
% 16.87/2.96 % Current number of archived clauses : 347
% 16.87/2.96 % Clause-clause subsumption calls (NU) : 199129
% 16.87/2.96 % Rec. Clause-clause subsumption calls : 97650
% 16.87/2.96 % Non-unit clause-clause subsumptions : 4315
% 16.87/2.96 % Unit Clause-clause subsumption calls : 16832
% 16.87/2.96 % Rewrite failures with RHS unbound : 0
% 16.87/2.96 % BW rewrite match attempts : 191
% 16.87/2.96 % BW rewrite match successes : 78
% 16.87/2.96 % Condensation attempts : 0
% 16.87/2.96 % Condensation successes : 0
% 16.87/2.96 % Termbank termtop insertions : 1546384
% 16.87/2.96 % Search garbage collected termcells : 973
% 16.87/2.96
% 16.87/2.96 % -------------------------------------------------
% 16.87/2.96 % User time : 2.357 s
% 16.87/2.96 % System time : 0.081 s
% 16.87/2.96 % Total time : 2.438 s
% 16.87/2.96 % Maximum resident set size: 3360 pages
% 16.87/2.96
% 16.87/2.96 % -------------------------------------------------
% 16.87/2.96 % User time : 11.505 s
% 16.87/2.96 % System time : 0.443 s
% 16.87/2.96 % Total time : 11.947 s
% 16.87/2.96 % Maximum resident set size: 4608 pages
% 16.87/2.96 % E exiting
%------------------------------------------------------------------------------