%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM494+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 : n026.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 01:55:14 PM UTC 2026
% Result : Theorem 0.15s 0.48s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 96 ( 31 unt; 0 def)
% Number of atoms : 310 ( 92 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 379 ( 165 ~; 154 |; 41 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn 48 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(m__1870,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(m__1883,hypothesis,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
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/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(mMonAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2 )
=> ! [X3] :
( aNaturalNumber0(X3)
=> ( sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3))
& sdtpldt0(X1,X3) != sdtpldt0(X2,X3)
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtpldt0(X3,X1) != sdtpldt0(X3,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).
fof(m__1894,hypothesis,
( sdtlseqdt0(xr,xn)
& xr != xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1894) ).
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(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
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(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(c_0_15,negated_conjecture,
~ ( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_16,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_17,negated_conjecture,
~ ( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X3,X2)
| X1 != sdtmndt0(X2,X3)
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])]) ).
fof(c_0_20,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_21,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| aNaturalNumber0(sdtmndt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_22,hypothesis,
sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[m__1870]) ).
cnf(c_0_23,hypothesis,
xr = sdtmndt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__1883]) ).
cnf(c_0_24,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_26,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_29,hypothesis,
aNaturalNumber0(xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24]),c_0_25])]) ).
fof(c_0_30,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_31,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X3)
| X2 != sdtmndt0(X3,X1)
| sdtpldt0(X1,X2) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_32,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2 )
=> ! [X3] :
( aNaturalNumber0(X3)
=> ( sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3))
& sdtpldt0(X1,X3) != sdtpldt0(X2,X3)
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtpldt0(X3,X1) != sdtpldt0(X3,X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[mMonAdd]) ).
fof(c_0_33,hypothesis,
( sdtlseqdt0(xr,xn)
& xr != xn ),
inference(fof_simplification,[status(thm)],[m__1894]) ).
cnf(c_0_34,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xr),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xm,xr),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]),c_0_29])]) ).
cnf(c_0_35,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,sdtmndt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_31]) ).
fof(c_0_37,plain,
! [X50,X51,X52] :
( ( ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X50)
| ~ sdtlseqdt0(X50,X51)
| X50 = X51
| ~ aNaturalNumber0(X52)
| sdtlseqdt0(sdtpldt0(X50,X52),sdtpldt0(X51,X52)) )
& ( ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X50)
| ~ sdtlseqdt0(X50,X51)
| X50 = X51
| ~ aNaturalNumber0(X52)
| sdtpldt0(X50,X52) != sdtpldt0(X51,X52) )
& ( ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X50)
| ~ sdtlseqdt0(X50,X51)
| X50 = X51
| ~ aNaturalNumber0(X52)
| sdtlseqdt0(sdtpldt0(X52,X50),sdtpldt0(X52,X51)) )
& ( ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X50)
| ~ sdtlseqdt0(X50,X51)
| X50 = X51
| ~ aNaturalNumber0(X52)
| sdtpldt0(X52,X50) != sdtpldt0(X52,X51) ) ),
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_32])])])])]) ).
fof(c_0_38,hypothesis,
( sdtlseqdt0(xr,xn)
& xr != xn ),
inference(fof_nnf,[status(thm)],[c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xm,sdtpldt0(xr,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_24]),c_0_29]),c_0_28])]) ).
cnf(c_0_40,hypothesis,
sdtpldt0(xp,xr) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_22]),c_0_23]),c_0_25]),c_0_24])]) ).
fof(c_0_41,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_42,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_43,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| X2 = X3
| sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,hypothesis,
sdtlseqdt0(xr,xn),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,hypothesis,
xr != xn,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_46,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_47,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xm,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_39,c_0_27]),c_0_40]),c_0_40]),c_0_24]),c_0_29])]) ).
cnf(c_0_48,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sdtpldt0(X1,xr),sdtpldt0(X1,xn)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_25]),c_0_29])]),c_0_45]) ).
cnf(c_0_51,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_53,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_27]),c_0_25]),c_0_28])]) ).
cnf(c_0_54,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_48]),c_0_49]) ).
cnf(c_0_55,hypothesis,
sdtlseqdt0(sdtpldt0(sz00,xr),xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_25])]) ).
cnf(c_0_56,negated_conjecture,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_24])]) ).
fof(c_0_57,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_58,hypothesis,
( ~ aNaturalNumber0(sdtpldt0(sz00,xr))
| aNaturalNumber0(sdtmndt0(xn,sdtpldt0(sz00,xr))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_55]),c_0_25])]) ).
cnf(c_0_59,negated_conjecture,
sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_49]),c_0_28]),c_0_25])]) ).
cnf(c_0_60,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_61,hypothesis,
sdtpldt0(xr,sdtmndt0(xn,xr)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_44]),c_0_25]),c_0_29])]) ).
cnf(c_0_62,hypothesis,
aNaturalNumber0(sdtmndt0(xn,xr)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_51]),c_0_29])]) ).
cnf(c_0_63,negated_conjecture,
sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_59]),c_0_24]),c_0_28]),c_0_25])]) ).
cnf(c_0_64,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtpldt0(xr,X1) != xn
| sdtmndt0(xn,xr) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_29])]) ).
cnf(c_0_65,negated_conjecture,
( ~ aNaturalNumber0(sdtpldt0(xm,xp))
| aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_63]),c_0_25])]) ).
cnf(c_0_66,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,xr) != xn
| sdtmndt0(xn,xr) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_27]),c_0_29])]) ).
cnf(c_0_67,negated_conjecture,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xr),xp),sdtpldt0(xp,sdtpldt0(xn,xm)))
| sdtpldt0(sdtpldt0(xm,xr),xp) = sdtpldt0(xp,sdtpldt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_27]),c_0_24])]) ).
cnf(c_0_68,negated_conjecture,
aNaturalNumber0(sdtpldt0(xn,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_49]),c_0_24]),c_0_28])]) ).
cnf(c_0_69,hypothesis,
sdtmndt0(xn,xr) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_40]),c_0_24])]) ).
fof(c_0_70,plain,
! [X45,X46,X47] :
( sdtlseqdt0(X45,X47)
| ~ sdtlseqdt0(X46,X47)
| ~ sdtlseqdt0(X45,X46)
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X46)
| ~ aNaturalNumber0(X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])])]) ).
cnf(c_0_71,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xr),xp),sdtpldt0(xp,sdtpldt0(xn,xm)))
| sdtpldt0(sdtpldt0(xm,xr),xp) = sdtpldt0(xp,sdtpldt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
cnf(c_0_72,hypothesis,
sdtpldt0(xr,xp) = xn,
inference(rw,[status(thm)],[c_0_61,c_0_69]) ).
cnf(c_0_73,plain,
( ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_74,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(xp,sdtpldt0(xn,xm)))
| sdtpldt0(xp,sdtpldt0(xn,xm)) = sdtpldt0(xm,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(spm,[status(thm)],[c_0_71,c_0_35]),c_0_72]),c_0_72]),c_0_24]),c_0_29]),c_0_28])]) ).
cnf(c_0_75,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtpldt0(sz00,xr))
| ~ sdtlseqdt0(X1,sdtpldt0(sz00,xr))
| sdtlseqdt0(X1,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_55]),c_0_25])]) ).
cnf(c_0_76,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(xp,sdtpldt0(xn,xm)))
| sdtpldt0(xp,sdtpldt0(xn,xm)) = sdtpldt0(xn,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_27]),c_0_25]),c_0_28])]) ).
cnf(c_0_77,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtpldt0(X2,X1)) ),
inference(spm,[status(thm)],[c_0_54,c_0_27]) ).
cnf(c_0_78,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,xr)
| sdtlseqdt0(X1,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_51]),c_0_29])]) ).
cnf(c_0_79,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_51]),c_0_52])]) ).
cnf(c_0_80,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_16]) ).
cnf(c_0_81,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,esk1_2(X1,X2)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_82,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| aNaturalNumber0(esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_83,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_84,negated_conjecture,
sdtpldt0(xp,sdtpldt0(xn,xm)) = sdtpldt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_68]),c_0_24])]) ).
cnf(c_0_85,hypothesis,
sdtlseqdt0(sz00,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_52]),c_0_29])]) ).
cnf(c_0_86,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_80]),c_0_49]),c_0_54]) ).
cnf(c_0_87,hypothesis,
sdtpldt0(xp,esk1_2(xp,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_22]),c_0_25]),c_0_24])]) ).
cnf(c_0_88,hypothesis,
aNaturalNumber0(esk1_2(xp,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_22]),c_0_25]),c_0_24])]) ).
cnf(c_0_89,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sdtpldt0(xn,xm)) != sdtpldt0(xn,xm)
| X1 = xp ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_24]),c_0_68])]) ).
cnf(c_0_90,hypothesis,
sdtpldt0(sz00,esk1_2(sz00,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_85]),c_0_25]),c_0_52])]) ).
cnf(c_0_91,hypothesis,
aNaturalNumber0(esk1_2(sz00,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_85]),c_0_25]),c_0_52])]) ).
cnf(c_0_92,hypothesis,
esk1_2(xp,xn) = xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_23]),c_0_24]),c_0_88])]) ).
cnf(c_0_93,negated_conjecture,
xp = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_51]),c_0_52]),c_0_68])]) ).
cnf(c_0_94,hypothesis,
esk1_2(sz00,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_90]),c_0_91])]) ).
cnf(c_0_95,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93]),c_0_94]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM494+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 02:37:52 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 0.15/0.48 % Version: 3.5.1
% 0.15/0.48 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.48 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.48 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.48 % Starting sh5l with 300s (1) cores
% 0.15/0.48 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1184287 completed with status 0
% 0.15/0.48 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.15/0.48 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.48 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.48 % No SInE strategy applied
% 0.15/0.48 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.15/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.48 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.15/0.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.15/0.48 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.15/0.48 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.15/0.48 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with pid 1184295 completed with status 0
% 0.15/0.48 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m
% 0.15/0.48 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.48 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.48 % No SInE strategy applied
% 0.15/0.48 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.15/0.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.48 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.15/0.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.15/0.48 % Preprocessing time : 0.001 s
% 0.15/0.48 % Presaturation interreduction done
% 0.15/0.48
% 0.15/0.48 % Proof found!
% 0.15/0.48 % SZS status Theorem
% 0.15/0.48 % SZS output start CNFRefutation
% See solution above
% 0.15/0.48 % Parsed axioms : 46
% 0.15/0.48 % Removed by relevancy pruning/SinE : 0
% 0.15/0.48 % Initial clauses : 82
% 0.15/0.48 % Removed in clause preprocessing : 3
% 0.15/0.48 % Initial clauses in saturation : 79
% 0.15/0.48 % Processed clauses : 471
% 0.15/0.48 % ...of these trivial : 7
% 0.15/0.48 % ...subsumed : 145
% 0.15/0.48 % ...remaining for further processing : 319
% 0.15/0.48 % Other redundant clauses eliminated : 19
% 0.15/0.48 % Clauses deleted for lack of memory : 0
% 0.15/0.48 % Backward-subsumed : 3
% 0.15/0.48 % Backward-rewritten : 100
% 0.15/0.48 % Generated clauses : 1121
% 0.15/0.48 % ...of the previous two non-redundant : 1038
% 0.15/0.48 % ...aggressively subsumed : 0
% 0.15/0.48 % Contextual simplify-reflections : 8
% 0.15/0.48 % Paramodulations : 1096
% 0.15/0.48 % Factorizations : 2
% 0.15/0.48 % NegExts : 0
% 0.15/0.48 % Equation resolutions : 23
% 0.15/0.48 % Disequality decompositions : 0
% 0.15/0.48 % Total rewrite steps : 1468
% 0.15/0.48 % ...of those cached : 1422
% 0.15/0.48 % Propositional unsat checks : 0
% 0.15/0.48 % Propositional check models : 0
% 0.15/0.48 % Propositional check unsatisfiable : 0
% 0.15/0.48 % Propositional clauses : 0
% 0.15/0.48 % Propositional clauses after purity: 0
% 0.15/0.48 % Propositional unsat core size : 0
% 0.15/0.48 % Propositional preprocessing time : 0.000
% 0.15/0.48 % Propositional encoding time : 0.000
% 0.15/0.48 % Propositional solver time : 0.000
% 0.15/0.48 % Success case prop preproc time : 0.000
% 0.15/0.48 % Success case prop encoding time : 0.000
% 0.15/0.48 % Success case prop solver time : 0.000
% 0.15/0.48 % Current number of processed clauses : 131
% 0.15/0.48 % Positive orientable unit clauses : 29
% 0.15/0.48 % Positive unorientable unit clauses: 0
% 0.15/0.48 % Negative unit clauses : 5
% 0.15/0.48 % Non-unit-clauses : 97
% 0.15/0.48 % Current number of unprocessed clauses: 679
% 0.15/0.48 % ...number of literals in the above : 2801
% 0.15/0.48 % Current number of archived formulas : 0
% 0.15/0.48 % Current number of archived clauses : 177
% 0.15/0.48 % Clause-clause subsumption calls (NU) : 3136
% 0.15/0.48 % Rec. Clause-clause subsumption calls : 1886
% 0.15/0.48 % Non-unit clause-clause subsumptions : 151
% 0.15/0.48 % Unit Clause-clause subsumption calls : 577
% 0.15/0.48 % Rewrite failures with RHS unbound : 0
% 0.15/0.48 % BW rewrite match attempts : 25
% 0.15/0.48 % BW rewrite match successes : 24
% 0.15/0.48 % Condensation attempts : 0
% 0.15/0.48 % Condensation successes : 0
% 0.15/0.48 % Termbank termtop insertions : 26512
% 0.15/0.48 % Search garbage collected termcells : 1347
% 0.15/0.48
% 0.15/0.48 % -------------------------------------------------
% 0.15/0.48 % User time : 0.026 s
% 0.15/0.48 % System time : 0.008 s
% 0.15/0.48 % Total time : 0.034 s
% 0.15/0.48 % Maximum resident set size: 3940 pages
% 0.15/0.48
% 0.15/0.48 % -------------------------------------------------
% 0.15/0.48 % User time : 0.119 s
% 0.15/0.48 % System time : 0.020 s
% 0.15/0.48 % Total time : 0.139 s
% 0.15/0.48 % Maximum resident set size: 4864 pages
% 0.15/0.48 % E exiting
%------------------------------------------------------------------------------