%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM463+2 : 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 : n003.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 01:55:07 PM UTC 2026
% Result : Theorem 1.80s 0.78s
% Output : CNFRefutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 73 ( 13 unt; 0 def)
% Number of atoms : 260 ( 95 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 307 ( 120 ~; 122 |; 46 &)
% ( 0 <=>; 19 =>; 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 : 86 ( 0 sgn 43 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
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_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(mLENTr,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( ( sdtlseqdt0(sz10,X1)
& sz10 != X1 )
| X1 = sz10
| X1 = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLENTr) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__,conjecture,
( xm != sz00
=> ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ? [X1] :
( sdtpldt0(xn,X1) = sdtasdt0(xn,xm)
& aNaturalNumber0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mMonMul,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& X2 != X3
& X1 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X1,X2) != sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
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(m__987,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__987) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(c_0_14,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mLETotal]) ).
fof(c_0_15,plain,
! [X45,X46,X47] :
( sdtpldt0(sdtpldt0(X45,X46),X47) = sdtpldt0(X45,sdtpldt0(X46,X47))
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X46)
| ~ aNaturalNumber0(X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
fof(c_0_16,plain,
! [X48] :
( ( ~ aNaturalNumber0(X48)
| X48 = sdtpldt0(sz00,X48) )
& ( ~ aNaturalNumber0(X48)
| sdtpldt0(X48,sz00) = X48 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])])]) ).
fof(c_0_17,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( ( sdtlseqdt0(sz10,X1)
& sz10 != X1 )
| X1 = sz10
| X1 = sz00 ) ),
inference(fof_simplification,[status(thm)],[mLENTr]) ).
fof(c_0_18,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
fof(c_0_19,plain,
! [X15,X16] :
( ( ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X15)
| sdtlseqdt0(X15,X16)
| sdtlseqdt0(X16,X15) )
& ( ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X15)
| sdtlseqdt0(X15,X16)
| X16 != X15 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
fof(c_0_20,negated_conjecture,
~ ( xm != sz00
=> ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ? [X1] :
( sdtpldt0(xn,X1) = sdtasdt0(xn,xm)
& aNaturalNumber0(X1) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_21,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_24,plain,
! [X43,X44] :
( sdtpldt0(X43,X44) = sdtpldt0(X44,X43)
| ~ aNaturalNumber0(X44)
| ~ aNaturalNumber0(X43) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
fof(c_0_25,plain,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& X2 != X3
& X1 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X1,X2) != sdtasdt0(X1,X3) ) ) ),
inference(fof_simplification,[status(thm)],[mMonMul]) ).
fof(c_0_26,plain,
! [X10,X11] :
( X10 = X11
| ~ sdtlseqdt0(X11,X10)
| ~ sdtlseqdt0(X10,X11)
| ~ aNaturalNumber0(X11)
| ~ aNaturalNumber0(X10) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])])]) ).
fof(c_0_27,plain,
! [X23] :
( ( ~ aNaturalNumber0(X23)
| X23 = sz10
| X23 = sz00
| sdtlseqdt0(sz10,X23) )
& ( ~ aNaturalNumber0(X23)
| X23 = sz10
| X23 = sz00
| sz10 != X23 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
fof(c_0_28,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__987]) ).
fof(c_0_31,negated_conjecture,
~ ( xm != sz00
=> ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ? [X1] :
( sdtpldt0(xn,X1) = sdtasdt0(xn,xm)
& aNaturalNumber0(X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
cnf(c_0_32,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_33,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,sdtpldt0(sz00,X2)) = sdtpldt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_34,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_35,plain,
! [X20,X21,X22] :
( ( ~ aNaturalNumber0(X22)
| ~ aNaturalNumber0(X21)
| ~ aNaturalNumber0(X20)
| ~ sdtlseqdt0(X21,X22)
| X21 = X22
| X20 = sz00
| sdtlseqdt0(sdtasdt0(X21,X20),sdtasdt0(X22,X20)) )
& ( ~ aNaturalNumber0(X22)
| ~ aNaturalNumber0(X21)
| ~ aNaturalNumber0(X20)
| ~ sdtlseqdt0(X21,X22)
| X21 = X22
| X20 = sz00
| sdtasdt0(X21,X20) != sdtasdt0(X22,X20) )
& ( ~ aNaturalNumber0(X22)
| ~ aNaturalNumber0(X21)
| ~ aNaturalNumber0(X20)
| ~ sdtlseqdt0(X21,X22)
| X21 = X22
| X20 = sz00
| sdtlseqdt0(sdtasdt0(X20,X21),sdtasdt0(X20,X22)) )
& ( ~ aNaturalNumber0(X22)
| ~ aNaturalNumber0(X21)
| ~ aNaturalNumber0(X20)
| ~ sdtlseqdt0(X21,X22)
| X21 = X22
| X20 = sz00
| sdtasdt0(X20,X21) != sdtasdt0(X20,X22) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])]) ).
fof(c_0_36,plain,
! [X31] :
( ( ~ aNaturalNumber0(X31)
| X31 = sdtasdt0(sz10,X31) )
& ( ~ aNaturalNumber0(X31)
| sdtasdt0(X31,sz10) = X31 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
cnf(c_0_37,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_38,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz10
| X1 = sz00
| sdtlseqdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_39,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_40,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,xm)
| sdtlseqdt0(xm,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_41,negated_conjecture,
! [X4] :
( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
& ( sdtpldt0(xn,X4) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X4) )
& xm != sz00 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
cnf(c_0_42,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(sz00,sdtpldt0(X1,X2)) = sdtpldt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_32]),c_0_23])]) ).
cnf(c_0_43,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_23])]) ).
fof(c_0_44,plain,
! [X41,X42] :
( aNaturalNumber0(sdtpldt0(X41,X42))
| ~ aNaturalNumber0(X42)
| ~ aNaturalNumber0(X41) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
cnf(c_0_45,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| X2 = X3
| X1 = sz00
| sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_46,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_47,plain,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,sz10)
| X1 = sz10
| X1 = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_48,hypothesis,
( sdtlseqdt0(xm,sz10)
| sdtlseqdt0(sz10,xm) ),
inference(spm,[status(thm)],[c_0_40,c_0_39]) ).
cnf(c_0_49,negated_conjecture,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,negated_conjecture,
( sdtpldt0(xn,X1) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_51,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__987]) ).
cnf(c_0_52,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(sz00,X1) = sdtpldt0(X1,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_23])]) ).
cnf(c_0_53,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_54,negated_conjecture,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_55,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(sz10,X1)
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| X2 = sz00
| sz10 = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_39])]) ).
cnf(c_0_56,hypothesis,
( sdtlseqdt0(sz10,xm)
| xm = sz10 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_30])]),c_0_49]) ).
cnf(c_0_57,negated_conjecture,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,xn) != sdtasdt0(xn,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_34]),c_0_51])]) ).
cnf(c_0_58,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(sz00,sdtpldt0(X1,sz00)) = sdtpldt0(X1,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_52]),c_0_23])]) ).
cnf(c_0_59,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_21]),c_0_53]) ).
cnf(c_0_60,negated_conjecture,
( xm = sz10
| xn = sz00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_30]),c_0_51])]),c_0_56]) ).
cnf(c_0_61,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,xn)
| sdtlseqdt0(xn,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_51]) ).
cnf(c_0_62,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,sdtpldt0(X2,xn)) != sdtasdt0(xn,xm) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_21]),c_0_51])]),c_0_53]) ).
cnf(c_0_63,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(sz00,sdtpldt0(sz00,X1)) = sdtpldt0(X1,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_23])]) ).
cnf(c_0_64,negated_conjecture,
( ~ sdtlseqdt0(xn,sdtasdt0(xn,sz10))
| xn = sz00 ),
inference(spm,[status(thm)],[c_0_54,c_0_60]) ).
cnf(c_0_65,hypothesis,
sdtlseqdt0(xn,xn),
inference(spm,[status(thm)],[c_0_61,c_0_51]) ).
cnf(c_0_66,negated_conjecture,
sdtpldt0(xn,sz00) != sdtasdt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_23]),c_0_51])]) ).
cnf(c_0_67,negated_conjecture,
xn = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_46]),c_0_65]),c_0_51])]) ).
cnf(c_0_68,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_52]),c_0_23])]) ).
fof(c_0_69,plain,
! [X32] :
( ( ~ aNaturalNumber0(X32)
| sz00 = sdtasdt0(sz00,X32) )
& ( ~ aNaturalNumber0(X32)
| sdtasdt0(X32,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])])]) ).
cnf(c_0_70,negated_conjecture,
sdtasdt0(sz00,xm) != sz00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_67]) ).
cnf(c_0_71,plain,
( ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_72,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM463+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 21 02:33:31 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.80/0.78 % Version: 3.5.1
% 1.80/0.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.80/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.80/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.80/0.78 % Starting new_bool_3 with 300s (1) cores
% 1.80/0.78 % Starting new_bool_1 with 300s (1) cores
% 1.80/0.78 % Starting sh5l with 300s (1) cores
% 1.80/0.78 % sh5l with pid 3214270 completed with status 0
% 1.80/0.78 % Result found by sh5l
% 1.80/0.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.80/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.80/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.80/0.78 % Starting new_bool_3 with 300s (1) cores
% 1.80/0.78 % Starting new_bool_1 with 300s (1) cores
% 1.80/0.78 % Starting sh5l with 300s (1) cores
% 1.80/0.78 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 1.80/0.78 % SinE strategy is gf500_gu_R04_F100_L20000
% 1.80/0.78 % Search class: FGHSF-FFMS22-SFFFFFNN
% 1.80/0.78 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.80/0.78 % Starting SubtermCWHack with 31s (1) cores
% 1.80/0.78 % SubtermCWHack with pid 3214280 completed with status 0
% 1.80/0.78 % Result found by SubtermCWHack
% 1.80/0.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.80/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.80/0.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.80/0.78 % Starting new_bool_3 with 300s (1) cores
% 1.80/0.78 % Starting new_bool_1 with 300s (1) cores
% 1.80/0.78 % Starting sh5l with 300s (1) cores
% 1.80/0.78 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 1.80/0.78 % SinE strategy is gf500_gu_R04_F100_L20000
% 1.80/0.78 % Search class: FGHSF-FFMS22-SFFFFFNN
% 1.80/0.78 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.80/0.78 % Starting SubtermCWHack with 31s (1) cores
% 1.80/0.78 % Preprocessing time : 0.002 s
% 1.80/0.78
% 1.80/0.78 % Proof found!
% 1.80/0.78 % SZS status Theorem
% 1.80/0.78 % SZS output start CNFRefutation
% See solution above
% 1.80/0.78 % Parsed axioms : 28
% 1.80/0.78 % Removed by relevancy pruning/SinE : 1
% 1.80/0.78 % Initial clauses : 48
% 1.80/0.78 % Removed in clause preprocessing : 2
% 1.80/0.78 % Initial clauses in saturation : 46
% 1.80/0.78 % Processed clauses : 1937
% 1.80/0.78 % ...of these trivial : 23
% 1.80/0.78 % ...subsumed : 1433
% 1.80/0.78 % ...remaining for further processing : 481
% 1.80/0.78 % Other redundant clauses eliminated : 47
% 1.80/0.78 % Clauses deleted for lack of memory : 0
% 1.80/0.78 % Backward-subsumed : 10
% 1.80/0.78 % Backward-rewritten : 136
% 1.80/0.78 % Generated clauses : 11307
% 1.80/0.78 % ...of the previous two non-redundant : 9425
% 1.80/0.78 % ...aggressively subsumed : 0
% 1.80/0.78 % Contextual simplify-reflections : 66
% 1.80/0.78 % Paramodulations : 11252
% 1.80/0.78 % Factorizations : 2
% 1.80/0.78 % NegExts : 0
% 1.80/0.78 % Equation resolutions : 53
% 1.80/0.78 % Disequality decompositions : 0
% 1.80/0.78 % Total rewrite steps : 11059
% 1.80/0.78 % ...of those cached : 11016
% 1.80/0.78 % Propositional unsat checks : 0
% 1.80/0.78 % Propositional check models : 0
% 1.80/0.78 % Propositional check unsatisfiable : 0
% 1.80/0.78 % Propositional clauses : 0
% 1.80/0.78 % Propositional clauses after purity: 0
% 1.80/0.78 % Propositional unsat core size : 0
% 1.80/0.78 % Propositional preprocessing time : 0.000
% 1.80/0.78 % Propositional encoding time : 0.000
% 1.80/0.78 % Propositional solver time : 0.000
% 1.80/0.78 % Success case prop preproc time : 0.000
% 1.80/0.78 % Success case prop encoding time : 0.000
% 1.80/0.78 % Success case prop solver time : 0.000
% 1.80/0.78 % Current number of processed clauses : 333
% 1.80/0.78 % Positive orientable unit clauses : 30
% 1.80/0.78 % Positive unorientable unit clauses: 0
% 1.80/0.78 % Negative unit clauses : 5
% 1.80/0.78 % Non-unit-clauses : 298
% 1.80/0.78 % Current number of unprocessed clauses: 7486
% 1.80/0.78 % ...number of literals in the above : 40008
% 1.80/0.78 % Current number of archived formulas : 0
% 1.80/0.78 % Current number of archived clauses : 146
% 1.80/0.78 % Clause-clause subsumption calls (NU) : 22925
% 1.80/0.78 % Rec. Clause-clause subsumption calls : 15089
% 1.80/0.78 % Non-unit clause-clause subsumptions : 1428
% 1.80/0.78 % Unit Clause-clause subsumption calls : 295
% 1.80/0.78 % Rewrite failures with RHS unbound : 0
% 1.80/0.78 % BW rewrite match attempts : 14
% 1.80/0.78 % BW rewrite match successes : 11
% 1.80/0.78 % Condensation attempts : 0
% 1.80/0.78 % Condensation successes : 0
% 1.80/0.78 % Termbank termtop insertions : 202367
% 1.80/0.78 % Search garbage collected termcells : 745
% 1.80/0.78
% 1.80/0.78 % -------------------------------------------------
% 1.80/0.78 % User time : 0.312 s
% 1.80/0.78 % System time : 0.011 s
% 1.80/0.78 % Total time : 0.323 s
% 1.80/0.78 % Maximum resident set size: 3660 pages
% 1.80/0.78
% 1.80/0.78 % -------------------------------------------------
% 1.80/0.78 % User time : 0.317 s
% 1.80/0.78 % System time : 0.014 s
% 1.80/0.78 % Total time : 0.331 s
% 1.80/0.78 % Maximum resident set size: 4608 pages
% 1.80/0.78 % E exiting
%------------------------------------------------------------------------------