%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM463+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.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 : Tue May 5 04:57:25 PM UTC 2026
% Result : Theorem 2.36s 2.00s
% Output : CNFRefutation 2.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 94 ( 20 unt; 0 def)
% Number of atoms : 326 ( 130 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 392 ( 160 ~; 171 |; 41 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn 59 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( xm != sz00
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = sdtasdt0(xn,xm) )
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
| sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(m__987,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__987) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mLENTr,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sz00
| X1 = sz10
| ( sz10 != X1
& sdtlseqdt0(sz10,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLENTr) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(mMonMul,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( X1 != sz00
& X2 != X3
& sdtlseqdt0(X2,X3) )
=> ( sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
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/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(c_0_18,negated_conjecture,
~ ( xm != sz00
=> ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = sdtasdt0(xn,xm) )
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_19,plain,
! [X80,X81,X82] :
( ( sdtasdt0(X80,X81) != sdtasdt0(X80,X82)
| X81 = X82
| ~ aNaturalNumber0(X81)
| ~ aNaturalNumber0(X82)
| X80 = sz00
| ~ aNaturalNumber0(X80) )
& ( sdtasdt0(X81,X80) != sdtasdt0(X82,X80)
| X81 = X82
| ~ aNaturalNumber0(X81)
| ~ aNaturalNumber0(X82)
| X80 = sz00
| ~ aNaturalNumber0(X80) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
fof(c_0_20,negated_conjecture,
! [X109] :
( xm != sz00
& ( ~ aNaturalNumber0(X109)
| sdtpldt0(xn,X109) != sdtasdt0(xn,xm) )
& ~ sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_21,plain,
! [X61,X62] :
( ~ aNaturalNumber0(X61)
| ~ aNaturalNumber0(X62)
| sdtpldt0(X61,X62) = sdtpldt0(X62,X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_22,plain,
( X2 = X3
| X1 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_24,plain,
! [X72] :
( ( sdtasdt0(X72,sz10) = X72
| ~ aNaturalNumber0(X72) )
& ( X72 = sdtasdt0(sz10,X72)
| ~ aNaturalNumber0(X72) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
cnf(c_0_25,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(xn,X1) != sdtasdt0(xn,xm) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__987]) ).
fof(c_0_28,plain,
! [X63,X64,X65] :
( ~ aNaturalNumber0(X63)
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X65)
| sdtpldt0(sdtpldt0(X63,X64),X65) = sdtpldt0(X63,sdtpldt0(X64,X65)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(c_0_29,plain,
! [X57,X58] :
( ~ aNaturalNumber0(X57)
| ~ aNaturalNumber0(X58)
| aNaturalNumber0(sdtpldt0(X57,X58)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(c_0_30,plain,
! [X74,X75,X76] :
( ( sdtasdt0(X74,sdtpldt0(X75,X76)) = sdtpldt0(sdtasdt0(X74,X75),sdtasdt0(X74,X76))
| ~ aNaturalNumber0(X74)
| ~ aNaturalNumber0(X75)
| ~ aNaturalNumber0(X76) )
& ( sdtasdt0(sdtpldt0(X75,X76),X74) = sdtpldt0(sdtasdt0(X75,X74),sdtasdt0(X76,X74))
| ~ aNaturalNumber0(X74)
| ~ aNaturalNumber0(X75)
| ~ aNaturalNumber0(X76) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
cnf(c_0_31,plain,
( X1 = sz00
| X2 = sz00
| sdtasdt0(X2,X1) != sdtasdt0(X2,sz00)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_32,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_34,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
fof(c_0_35,plain,
! [X59,X60] :
( ~ aNaturalNumber0(X59)
| ~ aNaturalNumber0(X60)
| aNaturalNumber0(sdtasdt0(X59,X60)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_36,plain,
! [X108] :
( ( sz10 != X108
| X108 = sz00
| X108 = sz10
| ~ aNaturalNumber0(X108) )
& ( sdtlseqdt0(sz10,X108)
| X108 = sz00
| X108 = sz10
| ~ aNaturalNumber0(X108) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLENTr])])]) ).
cnf(c_0_37,plain,
( X1 = X3
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_38,negated_conjecture,
( sdtpldt0(X1,xn) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_39,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_40,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_41,hypothesis,
( X1 = xn
| X2 = sz00
| sdtasdt0(X2,X1) != sdtasdt0(X2,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_42,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_30]) ).
fof(c_0_43,plain,
! [X66] :
( ( sdtpldt0(X66,sz00) = X66
| ~ aNaturalNumber0(X66) )
& ( X66 = sdtpldt0(sz00,X66)
| ~ aNaturalNumber0(X66) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
cnf(c_0_44,plain,
( sdtasdt0(sz10,sz00) = sz00
| ~ aNaturalNumber0(sdtasdt0(sz10,sz00)) ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]),c_0_34])]) ).
cnf(c_0_45,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_46,plain,
! [X105,X106,X107] :
( ( sdtasdt0(X105,X106) != sdtasdt0(X105,X107)
| X105 = sz00
| X106 = X107
| ~ sdtlseqdt0(X106,X107)
| ~ aNaturalNumber0(X105)
| ~ aNaturalNumber0(X106)
| ~ aNaturalNumber0(X107) )
& ( sdtlseqdt0(sdtasdt0(X105,X106),sdtasdt0(X105,X107))
| X105 = sz00
| X106 = X107
| ~ sdtlseqdt0(X106,X107)
| ~ aNaturalNumber0(X105)
| ~ aNaturalNumber0(X106)
| ~ aNaturalNumber0(X107) )
& ( sdtasdt0(X106,X105) != sdtasdt0(X107,X105)
| X105 = sz00
| X106 = X107
| ~ sdtlseqdt0(X106,X107)
| ~ aNaturalNumber0(X105)
| ~ aNaturalNumber0(X106)
| ~ aNaturalNumber0(X107) )
& ( sdtlseqdt0(sdtasdt0(X106,X105),sdtasdt0(X107,X105))
| X105 = sz00
| X106 = X107
| ~ sdtlseqdt0(X106,X107)
| ~ aNaturalNumber0(X105)
| ~ aNaturalNumber0(X106)
| ~ aNaturalNumber0(X107) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).
cnf(c_0_47,plain,
( sdtlseqdt0(sz10,X1)
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_48,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__987]) ).
cnf(c_0_49,negated_conjecture,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_50,hypothesis,
( X1 = xn
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(xn,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_27]) ).
cnf(c_0_51,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_52,plain,
! [X100,X101] :
( ( X101 != X100
| sdtlseqdt0(X100,X101)
| ~ aNaturalNumber0(X100)
| ~ aNaturalNumber0(X101) )
& ( sdtlseqdt0(X101,X100)
| sdtlseqdt0(X100,X101)
| ~ aNaturalNumber0(X100)
| ~ aNaturalNumber0(X101) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
cnf(c_0_53,negated_conjecture,
( sdtpldt0(X1,sdtpldt0(X2,xn)) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_27])]),c_0_40]) ).
cnf(c_0_54,hypothesis,
( sdtasdt0(sz10,xn) = xn
| ~ aNaturalNumber0(sdtasdt0(sz10,xn)) ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_32]),c_0_33])]),c_0_34])]) ).
cnf(c_0_55,plain,
( sdtasdt0(sz10,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(sz10,X1),X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_32]),c_0_33])]) ).
cnf(c_0_56,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_57,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_23]),c_0_33])]) ).
cnf(c_0_58,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| X1 = sz00
| X2 = X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_59,hypothesis,
( xm = sz10
| sdtlseqdt0(sz10,xm) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_60,hypothesis,
( sdtasdt0(xn,sz10) = xn
| ~ aNaturalNumber0(sdtasdt0(xn,sz10)) ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_33])]),c_0_34])]) ).
cnf(c_0_61,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_62,plain,
! [X69,X70,X71] :
( ~ aNaturalNumber0(X69)
| ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X71)
| sdtasdt0(sdtasdt0(X69,X70),X71) = sdtasdt0(X69,sdtasdt0(X70,X71)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(c_0_63,plain,
! [X73] :
( ( sdtasdt0(X73,sz00) = sz00
| ~ aNaturalNumber0(X73) )
& ( sz00 = sdtasdt0(sz00,X73)
| ~ aNaturalNumber0(X73) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_64,hypothesis,
( X1 = xm
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(xm,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_48]) ).
fof(c_0_65,plain,
! [X67,X68] :
( ~ aNaturalNumber0(X67)
| ~ aNaturalNumber0(X68)
| sdtasdt0(X67,X68) = sdtasdt0(X68,X67) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_66,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_67,negated_conjecture,
( sdtpldt0(X1,sdtpldt0(xn,X2)) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_26]),c_0_27])]) ).
cnf(c_0_68,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_39]),c_0_40]) ).
cnf(c_0_69,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_45]),c_0_27]),c_0_33])]) ).
cnf(c_0_70,plain,
( sdtasdt0(sz10,X1) = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_23])]) ).
cnf(c_0_71,hypothesis,
( xm = sz10
| X1 = sz00
| sdtlseqdt0(sdtasdt0(X1,sz10),sdtasdt0(X1,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_48]),c_0_33])]) ).
cnf(c_0_72,hypothesis,
sdtasdt0(xn,sz10) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_45]),c_0_33]),c_0_27])]) ).
cnf(c_0_73,negated_conjecture,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_74,hypothesis,
( sdtlseqdt0(X1,xn)
| sdtlseqdt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_27]) ).
cnf(c_0_75,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_76,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_77,hypothesis,
( sdtasdt0(xm,sz10) = xm
| ~ aNaturalNumber0(sdtasdt0(xm,sz10)) ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_51]),c_0_33])]),c_0_34])]) ).
cnf(c_0_78,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_79,plain,
( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_39]),c_0_23])]),c_0_40]) ).
cnf(c_0_80,plain,
( sdtpldt0(sz00,sdtpldt0(X1,X2)) = sdtpldt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_56]),c_0_23])]) ).
cnf(c_0_81,negated_conjecture,
( sdtpldt0(xn,sdtpldt0(X1,X2)) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_27])]) ).
cnf(c_0_82,hypothesis,
sdtpldt0(sz00,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_27])]) ).
cnf(c_0_83,hypothesis,
( xn = sz00
| xm = sz10 ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_27]),c_0_72]),c_0_73]) ).
cnf(c_0_84,hypothesis,
sdtlseqdt0(xn,xn),
inference(spm,[status(thm)],[c_0_74,c_0_27]) ).
cnf(c_0_85,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_75,c_0_76]),c_0_23])]) ).
cnf(c_0_86,hypothesis,
sdtasdt0(xm,sz10) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_45]),c_0_33]),c_0_48])]) ).
cnf(c_0_87,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_57]),c_0_23]),c_0_33])]) ).
cnf(c_0_88,plain,
( sdtpldt0(X1,sz00) = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_23])]) ).
cnf(c_0_89,negated_conjecture,
sdtasdt0(xn,xm) != sdtpldt0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_23]),c_0_27])]) ).
cnf(c_0_90,negated_conjecture,
xn = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_83]),c_0_72]),c_0_84])]) ).
cnf(c_0_91,hypothesis,
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_85,c_0_86]),c_0_87]),c_0_33]),c_0_48])]) ).
cnf(c_0_92,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_88]),c_0_23])]) ).
cnf(c_0_93,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90]),c_0_91]),c_0_90]),c_0_90]),c_0_92])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM463+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n022.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 00:36:06 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 2.36/2.00 % Version : CSE_E---1.7
% 2.36/2.00 % Problem : theBenchmark.p
% 2.36/2.00 % SZS status Theorem for theBenchmark.p
% 2.36/2.00 % SZS output start CNFRefutation
% See solution above
% 2.36/2.01 % Total time : 1.371s
%------------------------------------------------------------------------------