%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM461+1 : 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 : n018.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 38.71s 23.74s
% Output : CNFRefutation 38.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 94 ( 21 unt; 0 def)
% Number of atoms : 321 ( 104 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 394 ( 167 ~; 169 |; 38 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 125 ( 0 sgn 55 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X1 = sz00
& X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
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(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
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(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__840,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__840) ).
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(m__,conjecture,
( sdtpldt0(xm,xl) != sdtpldt0(xm,xn)
& sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
& sdtpldt0(xl,xm) != sdtpldt0(xn,xm)
& sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( X3 = sdtmndt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
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(mLERefl,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERefl) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
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(m__873,hypothesis,
aNaturalNumber0(xm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__873) ).
fof(m__840_03,hypothesis,
( xl != xn
& sdtlseqdt0(xl,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__840_03) ).
fof(c_0_19,plain,
! [X75,X76] :
( ( X75 = sz00
| sdtpldt0(X75,X76) != sz00
| ~ aNaturalNumber0(X75)
| ~ aNaturalNumber0(X76) )
& ( X76 = sz00
| sdtpldt0(X75,X76) != sz00
| ~ aNaturalNumber0(X75)
| ~ aNaturalNumber0(X76) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])]) ).
fof(c_0_20,plain,
! [X79,X80,X82] :
( ( aNaturalNumber0(esk1_2(X79,X80))
| ~ sdtlseqdt0(X79,X80)
| ~ aNaturalNumber0(X79)
| ~ aNaturalNumber0(X80) )
& ( sdtpldt0(X79,esk1_2(X79,X80)) = X80
| ~ sdtlseqdt0(X79,X80)
| ~ aNaturalNumber0(X79)
| ~ aNaturalNumber0(X80) )
& ( ~ aNaturalNumber0(X82)
| sdtpldt0(X79,X82) != X80
| sdtlseqdt0(X79,X80)
| ~ aNaturalNumber0(X79)
| ~ aNaturalNumber0(X80) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])]) ).
fof(c_0_21,plain,
! [X49,X50] :
( ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50)
| aNaturalNumber0(sdtpldt0(X49,X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(c_0_22,plain,
! [X72,X73,X74] :
( ( sdtasdt0(X72,X73) != sdtasdt0(X72,X74)
| X73 = X74
| ~ aNaturalNumber0(X73)
| ~ aNaturalNumber0(X74)
| X72 = sz00
| ~ aNaturalNumber0(X72) )
& ( sdtasdt0(X73,X72) != sdtasdt0(X74,X72)
| X73 = X74
| ~ aNaturalNumber0(X73)
| ~ aNaturalNumber0(X74)
| X72 = sz00
| ~ aNaturalNumber0(X72) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
cnf(c_0_23,plain,
( X1 = sz00
| sdtpldt0(X2,X1) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_26,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_28,plain,
! [X58] :
( ( sdtpldt0(X58,sz00) = X58
| ~ aNaturalNumber0(X58) )
& ( X58 = sdtpldt0(sz00,X58)
| ~ aNaturalNumber0(X58) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
cnf(c_0_29,plain,
( X2 = X3
| X1 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_30,plain,
! [X64] :
( ( sdtasdt0(X64,sz10) = X64
| ~ aNaturalNumber0(X64) )
& ( X64 = sdtasdt0(sz10,X64)
| ~ aNaturalNumber0(X64) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
cnf(c_0_31,plain,
( esk1_2(X1,sz00) = sz00
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(esk1_2(X1,sz00))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24])]),c_0_25])]) ).
cnf(c_0_32,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_33,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_26]),c_0_27]) ).
cnf(c_0_34,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__840]) ).
fof(c_0_36,plain,
! [X66,X67,X68] :
( ( sdtasdt0(X66,sdtpldt0(X67,X68)) = sdtpldt0(sdtasdt0(X66,X67),sdtasdt0(X66,X68))
| ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X67)
| ~ aNaturalNumber0(X68) )
& ( sdtasdt0(sdtpldt0(X67,X68),X66) = sdtpldt0(sdtasdt0(X67,X66),sdtasdt0(X68,X66))
| ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X67)
| ~ aNaturalNumber0(X68) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
cnf(c_0_37,plain,
( X1 = sz00
| X2 = sz00
| sdtasdt0(X2,X1) != sdtasdt0(X2,sz00)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
cnf(c_0_38,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_40,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
fof(c_0_41,plain,
! [X51,X52] :
( ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X52)
| aNaturalNumber0(sdtasdt0(X51,X52)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_42,plain,
( esk1_2(X1,sz00) = sz00
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_25])]) ).
cnf(c_0_43,plain,
( sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_25])]) ).
fof(c_0_44,negated_conjecture,
~ ( sdtpldt0(xm,xl) != sdtpldt0(xm,xn)
& sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
& sdtpldt0(xl,xm) != sdtpldt0(xn,xm)
& sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_45,plain,
! [X83,X84,X85] :
( ( aNaturalNumber0(X85)
| X85 != sdtmndt0(X84,X83)
| ~ sdtlseqdt0(X83,X84)
| ~ aNaturalNumber0(X83)
| ~ aNaturalNumber0(X84) )
& ( sdtpldt0(X83,X85) = X84
| X85 != sdtmndt0(X84,X83)
| ~ sdtlseqdt0(X83,X84)
| ~ aNaturalNumber0(X83)
| ~ aNaturalNumber0(X84) )
& ( ~ aNaturalNumber0(X85)
| sdtpldt0(X83,X85) != X84
| X85 = sdtmndt0(X84,X83)
| ~ sdtlseqdt0(X83,X84)
| ~ aNaturalNumber0(X83)
| ~ aNaturalNumber0(X84) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).
cnf(c_0_46,hypothesis,
( X1 = xn
| X2 = sz00
| sdtasdt0(X2,X1) != sdtasdt0(X2,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_35]) ).
cnf(c_0_47,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_36]) ).
cnf(c_0_48,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_37,c_0_38]),c_0_39])]),c_0_40])]) ).
cnf(c_0_49,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_50,plain,
! [X55,X56,X57] :
( ~ aNaturalNumber0(X55)
| ~ aNaturalNumber0(X56)
| ~ aNaturalNumber0(X57)
| sdtpldt0(sdtpldt0(X55,X56),X57) = sdtpldt0(X55,sdtpldt0(X56,X57)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_51,plain,
esk1_2(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_25])]) ).
fof(c_0_52,plain,
! [X86] :
( ~ aNaturalNumber0(X86)
| sdtlseqdt0(X86,X86) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERefl])]) ).
fof(c_0_53,negated_conjecture,
( sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) ),
inference(fof_nnf,[status(thm)],[c_0_44]) ).
fof(c_0_54,plain,
! [X53,X54] :
( ~ aNaturalNumber0(X53)
| ~ aNaturalNumber0(X54)
| sdtpldt0(X53,X54) = sdtpldt0(X54,X53) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_55,plain,
( X1 = sdtmndt0(X3,X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_56,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_46,c_0_38]),c_0_39])]),c_0_40])]) ).
cnf(c_0_57,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_47,c_0_38]),c_0_39])]) ).
cnf(c_0_58,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_25]),c_0_39])]) ).
fof(c_0_59,plain,
! [X92,X93] :
( ( X93 != X92
| sdtlseqdt0(X92,X93)
| ~ aNaturalNumber0(X92)
| ~ aNaturalNumber0(X93) )
& ( sdtlseqdt0(X93,X92)
| sdtlseqdt0(X92,X93)
| ~ aNaturalNumber0(X92)
| ~ aNaturalNumber0(X93) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
cnf(c_0_60,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_61,plain,
( sdtpldt0(sz00,sz00) = sz00
| ~ sdtlseqdt0(sz00,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_51]),c_0_25])]) ).
cnf(c_0_62,plain,
( sdtlseqdt0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_63,negated_conjecture,
( sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
| ~ sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_64,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_65,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__873]) ).
cnf(c_0_66,plain,
( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_55]),c_0_27]),c_0_33]) ).
cnf(c_0_67,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_49]),c_0_35]),c_0_39])]) ).
cnf(c_0_68,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_57,c_0_34]),c_0_58]),c_0_25])]) ).
cnf(c_0_69,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_70,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_71,plain,
( aNaturalNumber0(sdtpldt0(X1,sdtpldt0(X2,X3)))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_60]),c_0_27]) ).
cnf(c_0_72,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_25])]) ).
cnf(c_0_73,negated_conjecture,
( sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
| sdtpldt0(xl,xm) = sdtpldt0(xm,xn)
| ~ sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xm,xn))
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_35]),c_0_65])]) ).
cnf(c_0_74,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__840]) ).
cnf(c_0_75,plain,
( sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X1,sdtpldt0(X2,X3)))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_60]),c_0_27]) ).
cnf(c_0_76,plain,
( sdtpldt0(X1,X2) = X3
| X2 != sdtmndt0(X3,X1)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_77,plain,
( sdtmndt0(sdtpldt0(X1,X2),X2) = X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_64]) ).
cnf(c_0_78,hypothesis,
sdtpldt0(sz00,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_35])]) ).
cnf(c_0_79,hypothesis,
( sdtlseqdt0(X1,xn)
| sdtlseqdt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_35]) ).
cnf(c_0_80,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_70,c_0_60]),c_0_25])]),c_0_27]) ).
cnf(c_0_81,plain,
( aNaturalNumber0(sdtpldt0(X1,sz00))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_25])]) ).
cnf(c_0_82,negated_conjecture,
( sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_64]),c_0_65]),c_0_74])]) ).
cnf(c_0_83,plain,
( sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X1,X3))
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_24]),c_0_32]) ).
cnf(c_0_84,hypothesis,
sdtlseqdt0(xl,xn),
inference(split_conjunct,[status(thm)],[m__840_03]) ).
cnf(c_0_85,plain,
( sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[c_0_76]) ).
cnf(c_0_86,hypothesis,
sdtmndt0(xn,xn) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_35]),c_0_25])]) ).
cnf(c_0_87,hypothesis,
sdtlseqdt0(xn,xn),
inference(spm,[status(thm)],[c_0_79,c_0_35]) ).
cnf(c_0_88,plain,
( sdtmndt0(sdtpldt0(X1,X2),X1) = sdtpldt0(X2,sz00)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_80]),c_0_81]) ).
cnf(c_0_89,negated_conjecture,
sdtpldt0(xm,xn) = sdtpldt0(xm,xl),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]),c_0_74]),c_0_65]),c_0_35])]) ).
cnf(c_0_90,hypothesis,
sdtpldt0(xn,sz00) = xn,
inference(cn,[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_35])]) ).
cnf(c_0_91,negated_conjecture,
sdtmndt0(sdtpldt0(xm,xl),xm) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]),c_0_65]),c_0_35])]) ).
cnf(c_0_92,hypothesis,
xl != xn,
inference(split_conjunct,[status(thm)],[m__840_03]) ).
cnf(c_0_93,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_91]),c_0_65]),c_0_74])]),c_0_92]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM461+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % 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
% 0.12/0.30 % Computer : n018.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue May 5 00:36:02 EDT 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.31 % start to proof: theBenchmark
% 38.71/23.74 % Version : CSE_E---1.7
% 38.71/23.74 % Problem : theBenchmark.p
% 38.71/23.74 % SZS status Theorem for theBenchmark.p
% 38.71/23.74 % SZS output start CNFRefutation
% See solution above
% 38.91/23.92 % Total time : 16.391s
%------------------------------------------------------------------------------