%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM459+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 01:49:09 PM UTC 2026
% Result : Theorem 7.49s 1.54s
% Output : CNFRefutation 7.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 20
% Syntax : Number of formulae : 162 ( 53 unt; 0 def)
% Number of atoms : 468 ( 179 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 542 ( 236 ~; 233 |; 43 &)
% ( 2 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 199 ( 5 sgn 72 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(m__,conjecture,
( ( sdtlseqdt0(xn,xm)
& sdtlseqdt0(xm,xn) )
=> xm = xn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X2,X1) = sdtasdt0(X3,X1)
| sdtasdt0(X1,X2) = sdtasdt0(X1,X3) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
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/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
fof(m__745,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__745) ).
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/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X2 = sz00
& X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(mLERefl,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).
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/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(c_0_20,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])])])])]) ).
fof(c_0_21,negated_conjecture,
~ ( ( sdtlseqdt0(xn,xm)
& sdtlseqdt0(xm,xn) )
=> xm = xn ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_22,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_23,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])])]) ).
cnf(c_0_24,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X3)
| X2 != sdtmndt0(X3,X1)
| sdtpldt0(X1,X2) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_25,negated_conjecture,
( xm != xn
& sdtlseqdt0(xn,xm)
& sdtlseqdt0(xm,xn) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])]) ).
cnf(c_0_26,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X3,X2)
| X1 != sdtmndt0(X2,X3)
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_29,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])])]) ).
fof(c_0_30,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X2,X1) = sdtasdt0(X3,X1)
| sdtasdt0(X1,X2) = sdtasdt0(X1,X3) )
=> X2 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[mMulCanc]) ).
fof(c_0_31,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])])])]) ).
cnf(c_0_32,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,sdtmndt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_33,negated_conjecture,
sdtlseqdt0(xn,xm),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__745]) ).
cnf(c_0_35,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__745]) ).
cnf(c_0_36,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| aNaturalNumber0(sdtmndt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_37,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_27]),c_0_28]) ).
cnf(c_0_38,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_39,plain,
! [X28,X29,X30] :
( ( ~ aNaturalNumber0(X28)
| X28 = sz00
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X29)
| X29 = X30
| sdtasdt0(X29,X28) != sdtasdt0(X30,X28) )
& ( ~ aNaturalNumber0(X28)
| X28 = sz00
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X29)
| X29 = X30
| sdtasdt0(X28,X29) != sdtasdt0(X28,X30) ) ),
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_30])])])])]) ).
fof(c_0_40,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_41,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_42,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
cnf(c_0_43,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_44,negated_conjecture,
sdtpldt0(xn,sdtmndt0(xm,xn)) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35])]) ).
cnf(c_0_45,negated_conjecture,
aNaturalNumber0(sdtmndt0(xm,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_35]),c_0_34])]) ).
cnf(c_0_46,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtpldt0(X2,X1)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_47,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| X2 = sz00
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_50,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_51,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_42]) ).
cnf(c_0_52,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sdtmndt0(xm,xn)) != xm
| X1 = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_35]),c_0_45])]) ).
cnf(c_0_53,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,esk1_2(X1,X2)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_54,negated_conjecture,
sdtlseqdt0(sdtmndt0(xm,xn),xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_44]),c_0_45]),c_0_35])]) ).
cnf(c_0_55,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| aNaturalNumber0(esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_56,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X1,sdtasdt0(X2,X4)) != sdtasdt0(X3,X4)
| X4 = sz00
| sdtasdt0(X1,X2) = X3 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_57,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_58,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_59,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_60,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])])])]) ).
fof(c_0_61,plain,
! [X11,X12,X13] :
( sdtpldt0(sdtpldt0(X11,X12),X13) = sdtpldt0(X11,sdtpldt0(X12,X13))
| ~ aNaturalNumber0(X13)
| ~ aNaturalNumber0(X12)
| ~ aNaturalNumber0(X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
cnf(c_0_62,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(sdtmndt0(xm,xn),X1) != xm
| X1 = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_38]),c_0_45])]) ).
cnf(c_0_63,negated_conjecture,
sdtpldt0(sdtmndt0(xm,xn),esk1_2(sdtmndt0(xm,xn),xm)) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_34]),c_0_45])]) ).
cnf(c_0_64,negated_conjecture,
aNaturalNumber0(esk1_2(sdtmndt0(xm,xn),xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_54]),c_0_34]),c_0_45])]) ).
cnf(c_0_65,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X1,X2) != sdtasdt0(X3,sz10)
| sdtasdt0(X1,X2) = X3 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58])]),c_0_59]) ).
cnf(c_0_66,plain,
( ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_67,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_68,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])])]) ).
fof(c_0_69,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_70,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_71,negated_conjecture,
esk1_2(sdtmndt0(xm,xn),xm) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64])]) ).
cnf(c_0_72,negated_conjecture,
sdtlseqdt0(xm,xn),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_73,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz10) != sz00
| sz00 = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67])]) ).
cnf(c_0_74,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_75,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_76,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(xn,sdtpldt0(sdtmndt0(xm,xn),X1)) = sdtpldt0(xm,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_44]),c_0_45]),c_0_35])]) ).
cnf(c_0_77,negated_conjecture,
sdtpldt0(sdtmndt0(xm,xn),xn) = xm,
inference(rw,[status(thm)],[c_0_63,c_0_71]) ).
cnf(c_0_78,negated_conjecture,
sdtpldt0(xm,sdtmndt0(xn,xm)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_72]),c_0_35]),c_0_34])]) ).
cnf(c_0_79,negated_conjecture,
aNaturalNumber0(sdtmndt0(xn,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_72]),c_0_34]),c_0_35])]) ).
cnf(c_0_80,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sz10,X1) != sz00
| sz00 = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_58])]) ).
cnf(c_0_81,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_57,c_0_48]),c_0_58])]),c_0_49]) ).
cnf(c_0_82,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(sz00,sdtpldt0(X1,X2)) = sdtpldt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_75]),c_0_67])]) ).
cnf(c_0_83,negated_conjecture,
sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_35])]) ).
cnf(c_0_84,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sdtmndt0(xn,xm)) != xn
| X1 = xm ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_78]),c_0_34]),c_0_79])]) ).
cnf(c_0_85,negated_conjecture,
sdtlseqdt0(sdtmndt0(xn,xm),xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_78]),c_0_79]),c_0_34])]) ).
cnf(c_0_86,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_87,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X1,sz10))
| sdtasdt0(sz10,X1) != sz00
| sdtasdt0(X1,sz10) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_58])]) ).
cnf(c_0_88,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_89,negated_conjecture,
sdtpldt0(sz00,sdtpldt0(xm,xn)) = sdtpldt0(xm,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_34]),c_0_35])]) ).
cnf(c_0_90,negated_conjecture,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_83]),c_0_34]),c_0_35])]) ).
fof(c_0_91,plain,
! [X31,X32] :
( ( ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X31)
| sdtpldt0(X31,X32) != sz00
| X32 = sz00 )
& ( ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X31)
| sdtpldt0(X31,X32) != sz00
| X31 = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])])]) ).
cnf(c_0_92,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_75]),c_0_67])]) ).
fof(c_0_93,plain,
! [X42] :
( sdtlseqdt0(X42,X42)
| ~ aNaturalNumber0(X42) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERefl])])]) ).
cnf(c_0_94,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(sdtmndt0(xn,xm),X1) != xn
| X1 = xm ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_38]),c_0_79])]) ).
cnf(c_0_95,negated_conjecture,
sdtpldt0(sdtmndt0(xn,xm),esk1_2(sdtmndt0(xn,xm),xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_85]),c_0_35]),c_0_79])]) ).
cnf(c_0_96,negated_conjecture,
aNaturalNumber0(esk1_2(sdtmndt0(xn,xm),xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_85]),c_0_35]),c_0_79])]) ).
cnf(c_0_97,negated_conjecture,
sdtpldt0(xm,sz00) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_86]),c_0_44]),c_0_67]),c_0_45])]) ).
cnf(c_0_98,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtasdt0(sz00,sz10))
| sdtasdt0(sz00,sz10) = 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_67]),c_0_58])]) ).
cnf(c_0_99,negated_conjecture,
sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(xm,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_89]),c_0_90]),c_0_67])]) ).
cnf(c_0_100,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_101,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(sz00,esk1_2(sz00,X1)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_92]),c_0_67])]) ).
cnf(c_0_102,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_103,negated_conjecture,
esk1_2(sdtmndt0(xn,xm),xn) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96])]) ).
fof(c_0_104,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])])])]) ).
cnf(c_0_105,negated_conjecture,
sdtpldt0(sz00,xm) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_97]),c_0_67]),c_0_34])]) ).
cnf(c_0_106,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(sz00,sz10) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_49]),c_0_58]),c_0_67])]) ).
cnf(c_0_107,negated_conjecture,
aNaturalNumber0(esk1_2(sdtpldt0(xm,xn),sdtpldt0(xm,xn))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_99]),c_0_90])]) ).
cnf(c_0_108,plain,
( ~ aNaturalNumber0(esk1_2(sz00,sz00))
| esk1_2(sz00,sz00) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_67])])]),c_0_67])]) ).
cnf(c_0_109,plain,
( ~ aNaturalNumber0(X1)
| aNaturalNumber0(esk1_2(X1,X1)) ),
inference(spm,[status(thm)],[c_0_55,c_0_102]) ).
cnf(c_0_110,negated_conjecture,
sdtpldt0(sdtmndt0(xn,xm),xm) = xn,
inference(rw,[status(thm)],[c_0_95,c_0_103]) ).
cnf(c_0_111,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_104]) ).
cnf(c_0_112,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(sz00,sdtpldt0(xm,X1)) = sdtpldt0(xm,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_105]),c_0_34]),c_0_67])]) ).
cnf(c_0_113,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_48,c_0_66]),c_0_67])]) ).
cnf(c_0_114,negated_conjecture,
sdtasdt0(sz00,sz10) = sz00,
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_115,plain,
esk1_2(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_67])]) ).
cnf(c_0_116,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_117,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_20]) ).
cnf(c_0_118,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(sdtmndt0(xn,xm),sdtpldt0(xm,X1)) = sdtpldt0(xn,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_110]),c_0_34]),c_0_79])]) ).
cnf(c_0_119,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(sz00,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(sz00,X1),sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_66]),c_0_67])]) ).
cnf(c_0_120,negated_conjecture,
sdtpldt0(sz00,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_78]),c_0_79])]) ).
cnf(c_0_121,negated_conjecture,
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_113,c_0_114]),c_0_114]),c_0_58]),c_0_67])]) ).
cnf(c_0_122,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_115]),c_0_67])]) ).
cnf(c_0_123,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_48,c_0_116]),c_0_58])]) ).
cnf(c_0_124,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_117]),c_0_28]),c_0_37]) ).
cnf(c_0_125,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(sz00,sdtpldt0(X1,X2)) = sdtpldt0(sz00,sdtasdt0(sz00,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_66]),c_0_67])]) ).
cnf(c_0_126,negated_conjecture,
sdtpldt0(sdtmndt0(xn,xm),xn) = sdtpldt0(xn,sdtmndt0(xn,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_78]),c_0_79])]) ).
cnf(c_0_127,negated_conjecture,
sdtasdt0(sz00,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_119,c_0_120]),c_0_121]),c_0_122]),c_0_35]),c_0_67])]) ).
cnf(c_0_128,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(sz10,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(sz10,X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_116]),c_0_58])]) ).
cnf(c_0_129,negated_conjecture,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_114]),c_0_58]),c_0_67])]) ).
cnf(c_0_130,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_104]) ).
cnf(c_0_131,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtmndt0(sdtasdt0(X1,sdtpldt0(X2,X3)),sdtasdt0(X1,X2)) = sdtasdt0(X1,X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_111]),c_0_49]),c_0_49]) ).
cnf(c_0_132,negated_conjecture,
sdtasdt0(sz00,sdtpldt0(xn,sdtmndt0(xn,xm))) = 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_125,c_0_126]),c_0_127]),c_0_122]),c_0_35]),c_0_79])]) ).
cnf(c_0_133,plain,
sdtmndt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_122]),c_0_67])]) ).
cnf(c_0_134,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(sz10,X1) = sdtpldt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_75]),c_0_129]),c_0_67])]) ).
cnf(c_0_135,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(sdtasdt0(X1,X2),X2) = sdtasdt0(sdtpldt0(X1,sz10),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_116]),c_0_58])]) ).
cnf(c_0_136,negated_conjecture,
sdtasdt0(sz00,sdtmndt0(xn,xm)) = sz00,
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(spm,[status(thm)],[c_0_131,c_0_132]),c_0_127]),c_0_133]),c_0_79]),c_0_35]),c_0_67])]) ).
cnf(c_0_137,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_134]),c_0_58])]) ).
cnf(c_0_138,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_139,negated_conjecture,
sdtlseqdt0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_120]),c_0_35]),c_0_67])]) ).
cnf(c_0_140,negated_conjecture,
sdtasdt0(sz10,sdtmndt0(xn,xm)) = sdtpldt0(sz00,sdtmndt0(xn,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_137]),c_0_79]),c_0_67])]) ).
cnf(c_0_141,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,esk1_2(X1,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_53,c_0_102]) ).
cnf(c_0_142,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_138,c_0_86]),c_0_67])]) ).
cnf(c_0_143,negated_conjecture,
sdtpldt0(xn,esk1_2(xn,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_139]),c_0_35])]) ).
cnf(c_0_144,negated_conjecture,
aNaturalNumber0(esk1_2(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_139]),c_0_35])]) ).
cnf(c_0_145,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(xm,sdtpldt0(sz00,X1)) = sdtpldt0(xm,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_97]),c_0_67]),c_0_34])]) ).
cnf(c_0_146,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| aNaturalNumber0(sdtpldt0(X1,sdtpldt0(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_70]),c_0_28]) ).
cnf(c_0_147,negated_conjecture,
sdtpldt0(sz00,sdtmndt0(xn,xm)) = sdtmndt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_140]),c_0_79])]) ).
cnf(c_0_148,plain,
( ~ aNaturalNumber0(X1)
| esk1_2(X1,X1) = sdtmndt0(X1,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_141]),c_0_109]) ).
cnf(c_0_149,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_142,c_0_143]),c_0_144]),c_0_35])]) ).
cnf(c_0_150,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(xm,sdtpldt0(X1,sz00)) = sdtpldt0(xm,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_38]),c_0_67])]) ).
cnf(c_0_151,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_70]),c_0_28]) ).
cnf(c_0_152,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),X1))
| sdtmndt0(sdtpldt0(xm,X1),xn) = sdtpldt0(sdtmndt0(xm,xn),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_76]),c_0_35])]) ).
cnf(c_0_153,negated_conjecture,
( ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,sdtmndt0(xn,xm))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_79]),c_0_67])]) ).
cnf(c_0_154,negated_conjecture,
sdtmndt0(xn,xn) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_35])]) ).
cnf(c_0_155,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,xm) = sdtpldt0(xm,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_105]),c_0_34]),c_0_67])]) ).
cnf(c_0_156,negated_conjecture,
xm != xn,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_157,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) != sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_158,negated_conjecture,
sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) = 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_152,c_0_153]),c_0_78]),c_0_154]),c_0_79]),c_0_45])]) ).
cnf(c_0_159,negated_conjecture,
sdtpldt0(xm,sdtmndt0(xm,xn)) != xm,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_155]),c_0_34]),c_0_45])]),c_0_156]) ).
cnf(c_0_160,negated_conjecture,
sdtmndt0(xm,xn) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_79]),c_0_45])]) ).
cnf(c_0_161,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_160]),c_0_97])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM459+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 02:29:50 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 7.49/1.54 % Version: 3.5.1
% 7.49/1.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.49/1.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.49/1.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.49/1.54 % Starting new_bool_3 with 300s (1) cores
% 7.49/1.54 % Starting new_bool_1 with 300s (1) cores
% 7.49/1.54 % Starting sh5l with 300s (1) cores
% 7.49/1.54 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 4171137 completed with status 0
% 7.49/1.54 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 7.49/1.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.49/1.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.49/1.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.49/1.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.49/1.54 % No SInE strategy applied
% 7.49/1.54 % Search class: FGUSF-FFMM22-SFFFFFNN
% 7.49/1.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.49/1.54 % Starting SubtermCWHack with 136s (1) cores
% 7.49/1.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 7.49/1.54 % Starting G-E--_107_B42_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 7.49/1.54 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 7.49/1.54 % Starting new_bool_3 with 136s (1) cores
% 7.49/1.54 % new_bool_3 with pid 4171148 completed with status 0
% 7.49/1.54 % Result found by new_bool_3
% 7.49/1.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.49/1.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.49/1.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.49/1.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.49/1.54 % No SInE strategy applied
% 7.49/1.54 % Search class: FGUSF-FFMM22-SFFFFFNN
% 7.49/1.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.49/1.54 % Starting SubtermCWHack with 136s (1) cores
% 7.49/1.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 7.49/1.54 % Starting G-E--_107_B42_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 7.49/1.54 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 7.49/1.54 % Starting new_bool_3 with 136s (1) cores
% 7.49/1.54 % Preprocessing time : 0.002 s
% 7.49/1.54 % Presaturation interreduction done
% 7.49/1.54
% 7.49/1.54 % Proof found!
% 7.49/1.54 % SZS status Theorem
% 7.49/1.54 % SZS output start CNFRefutation
% See solution above
% 7.49/1.55 % Parsed axioms : 22
% 7.49/1.55 % Removed by relevancy pruning/SinE : 0
% 7.49/1.55 % Initial clauses : 37
% 7.49/1.55 % Removed in clause preprocessing : 1
% 7.49/1.55 % Initial clauses in saturation : 36
% 7.49/1.55 % Processed clauses : 6563
% 7.49/1.55 % ...of these trivial : 213
% 7.49/1.55 % ...subsumed : 4960
% 7.49/1.55 % ...remaining for further processing : 1390
% 7.49/1.55 % Other redundant clauses eliminated : 205
% 7.49/1.55 % Clauses deleted for lack of memory : 0
% 7.49/1.55 % Backward-subsumed : 28
% 7.49/1.55 % Backward-rewritten : 202
% 7.49/1.55 % Generated clauses : 55691
% 7.49/1.55 % ...of the previous two non-redundant : 50511
% 7.49/1.55 % ...aggressively subsumed : 0
% 7.49/1.55 % Contextual simplify-reflections : 313
% 7.49/1.55 % Paramodulations : 55451
% 7.49/1.55 % Factorizations : 0
% 7.49/1.55 % NegExts : 0
% 7.49/1.55 % Equation resolutions : 240
% 7.49/1.55 % Disequality decompositions : 0
% 7.49/1.55 % Total rewrite steps : 65626
% 7.49/1.55 % ...of those cached : 65392
% 7.49/1.55 % Propositional unsat checks : 0
% 7.49/1.55 % Propositional check models : 0
% 7.49/1.55 % Propositional check unsatisfiable : 0
% 7.49/1.55 % Propositional clauses : 0
% 7.49/1.55 % Propositional clauses after purity: 0
% 7.49/1.55 % Propositional unsat core size : 0
% 7.49/1.55 % Propositional preprocessing time : 0.000
% 7.49/1.55 % Propositional encoding time : 0.000
% 7.49/1.55 % Propositional solver time : 0.000
% 7.49/1.55 % Success case prop preproc time : 0.000
% 7.49/1.55 % Success case prop encoding time : 0.000
% 7.49/1.55 % Success case prop solver time : 0.000
% 7.49/1.55 % Current number of processed clauses : 1120
% 7.49/1.55 % Positive orientable unit clauses : 172
% 7.49/1.55 % Positive unorientable unit clauses: 0
% 7.49/1.55 % Negative unit clauses : 227
% 7.49/1.55 % Non-unit-clauses : 721
% 7.49/1.55 % Current number of unprocessed clauses: 43774
% 7.49/1.55 % ...number of literals in the above : 211965
% 7.49/1.55 % Current number of archived formulas : 0
% 7.49/1.55 % Current number of archived clauses : 266
% 7.49/1.55 % Clause-clause subsumption calls (NU) : 144520
% 7.49/1.55 % Rec. Clause-clause subsumption calls : 74624
% 7.49/1.55 % Non-unit clause-clause subsumptions : 3491
% 7.49/1.55 % Unit Clause-clause subsumption calls : 20828
% 7.49/1.55 % Rewrite failures with RHS unbound : 0
% 7.49/1.55 % BW rewrite match attempts : 98
% 7.49/1.55 % BW rewrite match successes : 55
% 7.49/1.55 % Condensation attempts : 0
% 7.49/1.55 % Condensation successes : 0
% 7.49/1.55 % Termbank termtop insertions : 1009312
% 7.49/1.55 % Search garbage collected termcells : 496
% 7.49/1.55
% 7.49/1.55 % -------------------------------------------------
% 7.49/1.55 % User time : 1.011 s
% 7.49/1.55 % System time : 0.042 s
% 7.49/1.55 % Total time : 1.053 s
% 7.49/1.55 % Maximum resident set size: 3652 pages
% 7.49/1.55
% 7.49/1.55 % -------------------------------------------------
% 7.49/1.55 % User time : 5.056 s
% 7.49/1.55 % System time : 0.224 s
% 7.49/1.55 % Total time : 5.281 s
% 7.49/1.55 % Maximum resident set size: 4864 pages
% 7.49/1.55 % E exiting
%------------------------------------------------------------------------------