%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM507+3 : 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 : n013.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 01:49:21 PM UTC 2026
% Result : Theorem 4.44s 1.12s
% Output : CNFRefutation 4.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 87 ( 34 unt; 0 def)
% Number of atoms : 287 ( 92 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 322 ( 122 ~; 115 |; 71 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn 40 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ? [X1] :
( sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X1) = sdtpldt0(sdtpldt0(xn,xm),xp)
& aNaturalNumber0(X1) ) )
& sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__2377,hypothesis,
( sdtlseqdt0(xk,xp)
& ? [X1] :
( sdtpldt0(xk,X1) = xp
& aNaturalNumber0(X1) )
& xk != xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2377) ).
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(m__2342,hypothesis,
( isPrime0(xr)
& ! [X1] :
( ( ( doDivides0(X1,xr)
| ? [X2] :
( xr = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xr
| X1 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X1] :
( xk = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) )
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(m__2362,hypothesis,
( doDivides0(xr,sdtasdt0(xn,xm))
& ? [X1] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) )
& ? [X1] :
( sdtpldt0(xr,X1) = xk
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2362) ).
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(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(m__2306,hypothesis,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
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(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& sdtlseqdt0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(c_0_13,negated_conjecture,
~ ( ( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ? [X1] :
( sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X1) = sdtpldt0(sdtpldt0(xn,xm),xp)
& aNaturalNumber0(X1) ) )
& sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_14,hypothesis,
( sdtlseqdt0(xk,xp)
& ? [X1] :
( sdtpldt0(xk,X1) = xp
& aNaturalNumber0(X1) )
& xk != xp ),
inference(fof_simplification,[status(thm)],[m__2377]) ).
fof(c_0_15,plain,
! [X37,X38,X40] :
( ( ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X37)
| sdtlseqdt0(X37,X38)
| sdtpldt0(X37,X40) != X38
| ~ aNaturalNumber0(X40) )
& ( ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X37)
| ~ sdtlseqdt0(X37,X38)
| sdtpldt0(X37,esk1_2(X37,X38)) = X38 )
& ( ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X37)
| ~ sdtlseqdt0(X37,X38)
| aNaturalNumber0(esk1_2(X37,X38)) ) ),
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_16,plain,
! [X7,X8] :
( aNaturalNumber0(sdtpldt0(X7,X8))
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
fof(c_0_17,hypothesis,
( isPrime0(xr)
& ! [X1] :
( ( ( doDivides0(X1,xr)
| ? [X2] :
( xr = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xr
| X1 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X1] :
( xk = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) )
& aNaturalNumber0(xr) ),
inference(fof_simplification,[status(thm)],[m__2342]) ).
fof(c_0_18,negated_conjecture,
~ ( ( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ? [X1] :
( sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X1) = sdtpldt0(sdtpldt0(xn,xm),xp)
& aNaturalNumber0(X1) ) )
& sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_19,plain,
! [X47,X48,X49] :
( sdtlseqdt0(X47,X49)
| ~ sdtlseqdt0(X48,X49)
| ~ sdtlseqdt0(X47,X48)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X48)
| ~ aNaturalNumber0(X47) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])])]) ).
fof(c_0_20,hypothesis,
( sdtlseqdt0(xk,xp)
& sdtpldt0(xk,esk15_0) = xp
& aNaturalNumber0(esk15_0)
& xk != xp ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_14])])]) ).
cnf(c_0_21,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_23,hypothesis,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xr,esk14_0)
& aNaturalNumber0(esk14_0)
& sdtpldt0(xr,esk13_0) = xk
& aNaturalNumber0(esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2362])]) ).
fof(c_0_24,hypothesis,
! [X107,X108] :
( isPrime0(xr)
& ( X107 = xr
| X107 = sz10
| ~ aNaturalNumber0(X107)
| ~ doDivides0(X107,xr) )
& ( X107 = xr
| X107 = sz10
| ~ aNaturalNumber0(X107)
| xr != sdtasdt0(X107,X108)
| ~ aNaturalNumber0(X108) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,esk12_0)
& aNaturalNumber0(esk12_0)
& aNaturalNumber0(xr) ),
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)],[c_0_17])])])])])]) ).
fof(c_0_25,negated_conjecture,
! [X112] :
( ( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) )
& ( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X112) != sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(X112) ) ),
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_18])])])])]) ).
fof(c_0_26,plain,
! [X13,X14,X15] :
( sdtpldt0(sdtpldt0(X13,X14),X15) = sdtpldt0(X13,sdtpldt0(X14,X15))
| ~ aNaturalNumber0(X15)
| ~ aNaturalNumber0(X14)
| ~ aNaturalNumber0(X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
cnf(c_0_27,plain,
( ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,hypothesis,
sdtlseqdt0(xk,xp),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_30,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_31,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_21]),c_0_22]) ).
cnf(c_0_32,hypothesis,
sdtpldt0(xr,esk13_0) = xk,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,hypothesis,
aNaturalNumber0(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_35,negated_conjecture,
( sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X1) != sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,xk)
| sdtlseqdt0(X1,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])]) ).
cnf(c_0_38,hypothesis,
sdtlseqdt0(xr,xk),
inference(cn,[status(thm)],[inference(rw,[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_39,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sdtpldt0(sdtpldt0(xn,xm),sdtpldt0(xr,X1)) != sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_33])]) ).
cnf(c_0_40,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_41,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_42,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| sdtpldt0(X1,esk1_2(X1,X2)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_43,hypothesis,
sdtlseqdt0(xr,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_33])]) ).
cnf(c_0_44,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X2)
| aNaturalNumber0(esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_45,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(xn,xm),sdtpldt0(xr,X1)) != sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_22]),c_0_40]),c_0_41])]) ).
cnf(c_0_46,hypothesis,
sdtpldt0(xr,esk1_2(xr,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_29]),c_0_33])]) ).
cnf(c_0_47,hypothesis,
aNaturalNumber0(esk1_2(xr,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_43]),c_0_29]),c_0_33])]) ).
cnf(c_0_48,negated_conjecture,
sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
cnf(c_0_49,negated_conjecture,
sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xr)),
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_48]),c_0_33]),c_0_40]),c_0_41])]) ).
fof(c_0_50,plain,
! [X11,X12] :
( sdtpldt0(X11,X12) = sdtpldt0(X12,X11)
| ~ aNaturalNumber0(X12)
| ~ aNaturalNumber0(X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_51,negated_conjecture,
sdtpldt0(xn,sdtpldt0(xm,xr)) = sdtpldt0(xn,sdtpldt0(xm,xp)),
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_49]),c_0_29]),c_0_40]),c_0_41])]) ).
cnf(c_0_52,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_53,negated_conjecture,
sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp)),
inference(rw,[status(thm)],[c_0_49,c_0_51]) ).
cnf(c_0_54,negated_conjecture,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_48]),c_0_33])]) ).
fof(c_0_55,plain,
! [X41,X42,X43] :
( ( ~ aNaturalNumber0(X42)
| ~ aNaturalNumber0(X41)
| ~ sdtlseqdt0(X41,X42)
| X43 = sdtmndt0(X42,X41)
| sdtpldt0(X41,X43) != X42
| ~ aNaturalNumber0(X43) )
& ( ~ aNaturalNumber0(X42)
| ~ aNaturalNumber0(X41)
| ~ sdtlseqdt0(X41,X42)
| X43 != sdtmndt0(X42,X41)
| sdtpldt0(X41,X43) = X42 )
& ( ~ aNaturalNumber0(X42)
| ~ aNaturalNumber0(X41)
| ~ sdtlseqdt0(X41,X42)
| X43 != sdtmndt0(X42,X41)
| aNaturalNumber0(X43) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])])]) ).
cnf(c_0_56,negated_conjecture,
( ~ aNaturalNumber0(sdtpldt0(xm,xr))
| sdtlseqdt0(xn,sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_51]),c_0_41])]) ).
cnf(c_0_57,negated_conjecture,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_29])]) ).
cnf(c_0_58,negated_conjecture,
aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_22]),c_0_40]),c_0_41])]) ).
cnf(c_0_59,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_55]) ).
cnf(c_0_60,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X3,X2)
| X1 != sdtmndt0(X2,X3)
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_61,negated_conjecture,
sdtlseqdt0(xn,sdtpldt0(xn,sdtpldt0(xm,xp))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_22]),c_0_33]),c_0_40])]) ).
cnf(c_0_62,negated_conjecture,
sdtpldt0(xn,sdtpldt0(xm,xp)) = sdtpldt0(xp,sdtpldt0(xn,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_22]),c_0_40]),c_0_41])]) ).
cnf(c_0_63,negated_conjecture,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_52]),c_0_29])]) ).
cnf(c_0_64,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_59]),c_0_22]),c_0_31]) ).
cnf(c_0_65,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| aNaturalNumber0(sdtmndt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_60]) ).
cnf(c_0_66,negated_conjecture,
sdtlseqdt0(xn,sdtpldt0(xp,sdtpldt0(xn,xm))),
inference(rw,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_67,negated_conjecture,
aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_22]),c_0_40]),c_0_41])]) ).
cnf(c_0_68,negated_conjecture,
( ~ aNaturalNumber0(sdtpldt0(xm,xp))
| sdtmndt0(sdtpldt0(xp,sdtpldt0(xn,xm)),xn) = sdtpldt0(xm,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_62]),c_0_41])]) ).
cnf(c_0_69,negated_conjecture,
aNaturalNumber0(sdtmndt0(sdtpldt0(xp,sdtpldt0(xn,xm)),xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_41]),c_0_67])]) ).
cnf(c_0_70,negated_conjecture,
sdtmndt0(sdtpldt0(xp,sdtpldt0(xn,xm)),xn) = sdtpldt0(xm,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_22]),c_0_29]),c_0_40])]) ).
cnf(c_0_71,negated_conjecture,
sdtpldt0(xn,sdtpldt0(xp,xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_52]),c_0_29]),c_0_40])]) ).
cnf(c_0_72,negated_conjecture,
aNaturalNumber0(sdtpldt0(xm,xp)),
inference(rw,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_73,negated_conjecture,
sdtpldt0(xn,sdtpldt0(xm,xr)) = sdtpldt0(xp,sdtpldt0(xn,xm)),
inference(rw,[status(thm)],[c_0_51,c_0_62]) ).
cnf(c_0_74,negated_conjecture,
( ~ aNaturalNumber0(sdtpldt0(xp,xm))
| sdtmndt0(sdtpldt0(xp,sdtpldt0(xn,xm)),xn) = sdtpldt0(xp,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_71]),c_0_41])]) ).
cnf(c_0_75,negated_conjecture,
aNaturalNumber0(sdtpldt0(xp,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_52]),c_0_29]),c_0_40])]) ).
cnf(c_0_76,negated_conjecture,
( ~ aNaturalNumber0(sdtpldt0(xm,xr))
| sdtmndt0(sdtpldt0(xp,sdtpldt0(xn,xm)),xn) = sdtpldt0(xm,xr) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_73]),c_0_41])]) ).
cnf(c_0_77,negated_conjecture,
sdtpldt0(xm,xp) = sdtpldt0(xp,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_70]),c_0_75])]) ).
cnf(c_0_78,negated_conjecture,
( ~ aNaturalNumber0(sdtpldt0(xm,xr))
| sdtpldt0(xm,xr) = sdtpldt0(xp,xm) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_70]),c_0_77]) ).
fof(c_0_79,plain,
! [X45,X46] :
( X45 = X46
| ~ sdtlseqdt0(X46,X45)
| ~ sdtlseqdt0(X45,X46)
| ~ aNaturalNumber0(X46)
| ~ aNaturalNumber0(X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])])]) ).
cnf(c_0_80,negated_conjecture,
sdtpldt0(xm,xr) = sdtpldt0(xp,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_22]),c_0_33]),c_0_40])]) ).
cnf(c_0_81,negated_conjecture,
sdtmndt0(sdtpldt0(xp,xm),xm) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_77]),c_0_40]),c_0_29])]) ).
cnf(c_0_82,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_83,hypothesis,
xk != xp,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_84,negated_conjecture,
xr = xp,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_80]),c_0_40]),c_0_33])]),c_0_81]) ).
cnf(c_0_85,hypothesis,
~ sdtlseqdt0(xp,xk),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_28]),c_0_30]),c_0_29])]),c_0_83]) ).
cnf(c_0_86,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_84]),c_0_85]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM507+3 : 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 : n013.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 02:35:05 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 4.44/1.12 % Version: 3.5.1
% 4.44/1.12 % Preprocessing class: FSLSSMSSSSSNFFN.
% 4.44/1.12 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.44/1.12 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.44/1.12 % Starting new_bool_3 with 300s (1) cores
% 4.44/1.12 % Starting new_bool_1 with 300s (1) cores
% 4.44/1.12 % Starting sh5l with 300s (1) cores
% 4.44/1.12 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3960121 completed with status 0
% 4.44/1.12 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 4.44/1.12 % Preprocessing class: FSLSSMSSSSSNFFN.
% 4.44/1.12 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.44/1.12 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.44/1.12 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.44/1.12 % No SInE strategy applied
% 4.44/1.12 % Search class: FGHSF-FSLM32-MFFFFFNN
% 4.44/1.12 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.44/1.12 % Starting SubtermCWHack with 136s (1) cores
% 4.44/1.12 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 4.44/1.12 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 4.44/1.12 % Starting G-E--_302_C18_F1_URBAN_S0Y with 136s (1) cores
% 4.44/1.12 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0U with 136s (1) cores
% 4.44/1.12 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3960128 completed with status 0
% 4.44/1.12 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 4.44/1.12 % Preprocessing class: FSLSSMSSSSSNFFN.
% 4.44/1.12 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.44/1.12 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 4.44/1.12 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.44/1.12 % No SInE strategy applied
% 4.44/1.12 % Search class: FGHSF-FSLM32-MFFFFFNN
% 4.44/1.12 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.44/1.12 % Starting SubtermCWHack with 136s (1) cores
% 4.44/1.12 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 4.44/1.12 % Preprocessing time : 0.005 s
% 4.44/1.12 % Presaturation interreduction done
% 4.44/1.12
% 4.44/1.12 % Proof found!
% 4.44/1.12 % SZS status Theorem
% 4.44/1.12 % SZS output start CNFRefutation
% See solution above
% 4.44/1.12 % Parsed axioms : 51
% 4.44/1.12 % Removed by relevancy pruning/SinE : 0
% 4.44/1.12 % Initial clauses : 246
% 4.44/1.12 % Removed in clause preprocessing : 3
% 4.44/1.12 % Initial clauses in saturation : 243
% 4.44/1.12 % Processed clauses : 2731
% 4.44/1.12 % ...of these trivial : 108
% 4.44/1.12 % ...subsumed : 1093
% 4.44/1.12 % ...remaining for further processing : 1530
% 4.44/1.12 % Other redundant clauses eliminated : 240
% 4.44/1.12 % Clauses deleted for lack of memory : 0
% 4.44/1.12 % Backward-subsumed : 80
% 4.44/1.12 % Backward-rewritten : 633
% 4.44/1.12 % Generated clauses : 11070
% 4.44/1.12 % ...of the previous two non-redundant : 9975
% 4.44/1.12 % ...aggressively subsumed : 0
% 4.44/1.12 % Contextual simplify-reflections : 31
% 4.44/1.12 % Paramodulations : 10748
% 4.44/1.12 % Factorizations : 6
% 4.44/1.12 % NegExts : 0
% 4.44/1.12 % Equation resolutions : 315
% 4.44/1.12 % Disequality decompositions : 0
% 4.44/1.12 % Total rewrite steps : 17898
% 4.44/1.12 % ...of those cached : 17607
% 4.44/1.12 % Propositional unsat checks : 0
% 4.44/1.12 % Propositional check models : 0
% 4.44/1.12 % Propositional check unsatisfiable : 0
% 4.44/1.12 % Propositional clauses : 0
% 4.44/1.12 % Propositional clauses after purity: 0
% 4.44/1.12 % Propositional unsat core size : 0
% 4.44/1.12 % Propositional preprocessing time : 0.000
% 4.44/1.12 % Propositional encoding time : 0.000
% 4.44/1.12 % Propositional solver time : 0.000
% 4.44/1.12 % Success case prop preproc time : 0.000
% 4.44/1.12 % Success case prop encoding time : 0.000
% 4.44/1.12 % Success case prop solver time : 0.000
% 4.44/1.12 % Current number of processed clauses : 569
% 4.44/1.12 % Positive orientable unit clauses : 192
% 4.44/1.12 % Positive unorientable unit clauses: 0
% 4.44/1.12 % Negative unit clauses : 41
% 4.44/1.12 % Non-unit-clauses : 336
% 4.44/1.12 % Current number of unprocessed clauses: 7297
% 4.44/1.12 % ...number of literals in the above : 48208
% 4.44/1.12 % Current number of archived formulas : 0
% 4.44/1.12 % Current number of archived clauses : 950
% 4.44/1.12 % Clause-clause subsumption calls (NU) : 150606
% 4.44/1.12 % Rec. Clause-clause subsumption calls : 17154
% 4.44/1.12 % Non-unit clause-clause subsumptions : 842
% 4.44/1.12 % Unit Clause-clause subsumption calls : 31459
% 4.44/1.12 % Rewrite failures with RHS unbound : 0
% 4.44/1.12 % BW rewrite match attempts : 215
% 4.44/1.12 % BW rewrite match successes : 120
% 4.44/1.12 % Condensation attempts : 0
% 4.44/1.12 % Condensation successes : 0
% 4.44/1.12 % Termbank termtop insertions : 339765
% 4.44/1.12 % Search garbage collected termcells : 2442
% 4.44/1.12
% 4.44/1.12 % -------------------------------------------------
% 4.44/1.12 % User time : 0.627 s
% 4.44/1.12 % System time : 0.030 s
% 4.44/1.12 % Total time : 0.657 s
% 4.44/1.12 % Maximum resident set size: 4164 pages
% 4.44/1.12
% 4.44/1.12 % -------------------------------------------------
% 4.44/1.12 % User time : 3.048 s
% 4.44/1.12 % System time : 0.125 s
% 4.44/1.12 % Total time : 3.173 s
% 4.44/1.12 % Maximum resident set size: 4864 pages
% 4.44/1.12 % E exiting
%------------------------------------------------------------------------------