%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM528+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 : 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 01:49:26 PM UTC 2026
% Result : Theorem 0.32s 0.75s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 91 ( 29 unt; 0 def)
% Number of atoms : 310 ( 122 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 341 ( 122 ~; 119 |; 75 &)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 51 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2987,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2987) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X2,X1) = sdtasdt0(X3,X1)
| sdtasdt0(X1,X2) = sdtasdt0(X1,X3) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(m__3059,hypothesis,
( xq = sdtsldt0(xn,xp)
& xn = sdtasdt0(xp,xq)
& aNaturalNumber0(xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3059) ).
fof(m__3082,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3082) ).
fof(m__3046,hypothesis,
( doDivides0(xp,xn)
& ? [X1] :
( xn = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [X1] :
( sdtasdt0(xn,xn) = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3046) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X2 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3014) ).
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(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
fof(m__,conjecture,
( ( sdtlseqdt0(xm,xn)
| ? [X1] :
( sdtpldt0(xm,X1) = xn
& aNaturalNumber0(X1) ) )
& xm != xn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__3152,hypothesis,
( ( sdtlseqdt0(xn,xm)
| ? [X1] :
( sdtpldt0(xn,X1) = xm
& aNaturalNumber0(X1) ) )
=> ( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
& ? [X1] :
( sdtpldt0(sdtasdt0(xn,xn),X1) = sdtasdt0(xm,xm)
& aNaturalNumber0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3152) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__3025,hypothesis,
( isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( xp = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xp
| X1 = sz10 ) )
& xp != sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3025) ).
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(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_18,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_simplification,[status(thm)],[m__2987]) ).
fof(c_0_19,plain,
! [X62,X63,X64] :
( sdtasdt0(sdtasdt0(X62,X63),X64) = sdtasdt0(X62,sdtasdt0(X63,X64))
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ aNaturalNumber0(X62) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
fof(c_0_20,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_nnf,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
! [X58,X59] :
( aNaturalNumber0(sdtasdt0(X58,X59))
| ~ aNaturalNumber0(X59)
| ~ aNaturalNumber0(X58) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
fof(c_0_22,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X2,X1) = sdtasdt0(X3,X1)
| sdtasdt0(X1,X2) = sdtasdt0(X1,X3) )
=> X2 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[mMulCanc]) ).
cnf(c_0_23,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,hypothesis,
xn = sdtasdt0(xp,xq),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xq),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_26,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(split_conjunct,[status(thm)],[m__3082]) ).
fof(c_0_29,plain,
! [X20,X21,X22] :
( ( ~ aNaturalNumber0(X20)
| X20 = sz00
| ~ aNaturalNumber0(X22)
| ~ aNaturalNumber0(X21)
| X21 = X22
| sdtasdt0(X21,X20) != sdtasdt0(X22,X20) )
& ( ~ aNaturalNumber0(X20)
| X20 = sz00
| ~ aNaturalNumber0(X22)
| ~ aNaturalNumber0(X21)
| X21 = X22
| sdtasdt0(X20,X21) != sdtasdt0(X20,X22) ) ),
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_22])])])])]) ).
fof(c_0_30,hypothesis,
( doDivides0(xp,xn)
& xn = sdtasdt0(xp,esk4_0)
& aNaturalNumber0(esk4_0)
& doDivides0(xp,sdtasdt0(xn,xn))
& sdtasdt0(xn,xn) = sdtasdt0(xp,esk3_0)
& aNaturalNumber0(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__3046])]) ).
cnf(c_0_31,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xp,sdtasdt0(xq,X1)) = sdtasdt0(xn,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_32,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xq,xq))
| aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_26])]) ).
fof(c_0_33,plain,
! [X25,X26] :
( X26 = sz00
| X25 = sz00
| sdtasdt0(X25,X26) != sz00
| ~ aNaturalNumber0(X26)
| ~ aNaturalNumber0(X25) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])])]) ).
cnf(c_0_34,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| X1 = sz00
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,hypothesis,
sdtasdt0(xn,xn) = sdtasdt0(xp,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,hypothesis,
aNaturalNumber0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_38,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_39,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xn,xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_31]),c_0_25])]) ).
cnf(c_0_40,hypothesis,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_27]),c_0_25])]) ).
fof(c_0_41,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mLETotal]) ).
fof(c_0_42,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
inference(fof_simplification,[status(thm)],[mMonMul2]) ).
cnf(c_0_43,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_44,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_45,hypothesis,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_46,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xp,X1) != sdtasdt0(xn,xn)
| X1 = esk3_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_26])]),c_0_37]) ).
cnf(c_0_47,hypothesis,
sdtasdt0(xp,sdtasdt0(xn,xq)) = sdtasdt0(xn,xn),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,hypothesis,
aNaturalNumber0(sdtasdt0(xn,xq)),
inference(rw,[status(thm)],[c_0_40,c_0_39]) ).
fof(c_0_49,negated_conjecture,
~ ( ( sdtlseqdt0(xm,xn)
| ? [X1] :
( sdtpldt0(xm,X1) = xn
& aNaturalNumber0(X1) ) )
& xm != xn ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_50,plain,
! [X88,X89] :
( ( ~ aNaturalNumber0(X89)
| ~ aNaturalNumber0(X88)
| sdtlseqdt0(X88,X89)
| sdtlseqdt0(X89,X88) )
& ( ~ aNaturalNumber0(X89)
| ~ aNaturalNumber0(X88)
| sdtlseqdt0(X88,X89)
| X89 != X88 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])]) ).
fof(c_0_51,hypothesis,
! [X15] :
( ( ~ sdtlseqdt0(xn,xm)
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) )
& ( ~ sdtlseqdt0(xn,xm)
| sdtpldt0(sdtasdt0(xn,xn),esk5_0) = sdtasdt0(xm,xm) )
& ( ~ sdtlseqdt0(xn,xm)
| aNaturalNumber0(esk5_0) )
& ( sdtpldt0(xn,X15) != xm
| ~ aNaturalNumber0(X15)
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) )
& ( sdtpldt0(xn,X15) != xm
| ~ aNaturalNumber0(X15)
| sdtpldt0(sdtasdt0(xn,xn),esk5_0) = sdtasdt0(xm,xm) )
& ( sdtpldt0(xn,X15) != xm
| ~ aNaturalNumber0(X15)
| aNaturalNumber0(esk5_0) ) ),
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)],[m__3152])])])])])]) ).
fof(c_0_52,plain,
! [X30,X31] :
( sdtlseqdt0(X31,sdtasdt0(X31,X30))
| X30 = sz00
| ~ aNaturalNumber0(X31)
| ~ aNaturalNumber0(X30) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])]) ).
fof(c_0_53,plain,
! [X60,X61] :
( sdtasdt0(X60,X61) = sdtasdt0(X61,X60)
| ~ aNaturalNumber0(X61)
| ~ aNaturalNumber0(X60) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_54,hypothesis,
sdtasdt0(xn,xq) != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_39]),c_0_44])]),c_0_45]) ).
cnf(c_0_55,hypothesis,
sdtasdt0(xn,xq) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48])]) ).
fof(c_0_56,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
fof(c_0_57,hypothesis,
( isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( xp = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xp
| X1 = sz10 ) )
& xp != sz10 ),
inference(fof_simplification,[status(thm)],[m__3025]) ).
fof(c_0_58,negated_conjecture,
~ ( ( sdtlseqdt0(xm,xn)
| ? [X1] :
( sdtpldt0(xm,X1) = xn
& aNaturalNumber0(X1) ) )
& xm != xn ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
cnf(c_0_59,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_60,hypothesis,
( ~ sdtlseqdt0(xn,xm)
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_61,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_62,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_63,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| X2 = sz00
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_64,hypothesis,
esk3_0 != sz00,
inference(rw,[status(thm)],[c_0_54,c_0_55]) ).
fof(c_0_65,plain,
! [X43] :
( ( ~ aNaturalNumber0(X43)
| X43 = sdtasdt0(sz10,X43) )
& ( ~ aNaturalNumber0(X43)
| sdtasdt0(X43,sz10) = X43 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
fof(c_0_66,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_56]) ).
fof(c_0_67,hypothesis,
! [X11,X12] :
( isPrime0(xp)
& ( X11 = xp
| X11 = sz10
| ~ aNaturalNumber0(X11)
| ~ doDivides0(X11,xp) )
& ( X11 = xp
| X11 = sz10
| ~ aNaturalNumber0(X11)
| xp != sdtasdt0(X11,X12)
| ~ aNaturalNumber0(X12) )
& xp != sz10 ),
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_57])])])])]) ).
fof(c_0_68,negated_conjecture,
! [X17] :
( ( xm = xn
| ~ sdtlseqdt0(xm,xn) )
& ( xm = xn
| sdtpldt0(xm,X17) != xn
| ~ aNaturalNumber0(X17) ) ),
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_58])])])])]) ).
cnf(c_0_69,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,xm)
| sdtlseqdt0(xm,X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_44]) ).
cnf(c_0_70,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_71,plain,
! [X83,X84] :
( X83 = X84
| ~ sdtlseqdt0(X84,X83)
| ~ sdtlseqdt0(X83,X84)
| ~ aNaturalNumber0(X84)
| ~ aNaturalNumber0(X83) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])])]) ).
cnf(c_0_72,hypothesis,
( ~ sdtlseqdt0(xn,xm)
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xn,xq)) ),
inference(rw,[status(thm)],[c_0_60,c_0_39]) ).
cnf(c_0_73,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| X1 = sz00 ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_74,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,esk3_0) != sdtasdt0(xn,xn)
| X1 = xp ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_35]),c_0_26]),c_0_36])]),c_0_64]) ).
cnf(c_0_75,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_76,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_77,hypothesis,
xp != sz10,
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_78,negated_conjecture,
( ~ sdtlseqdt0(xm,xn)
| xm = xn ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_79,hypothesis,
( sdtlseqdt0(xm,xn)
| sdtlseqdt0(xn,xm) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_80,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_81,hypothesis,
( ~ sdtlseqdt0(xn,xm)
| sdtlseqdt0(sdtasdt0(xn,xn),esk3_0) ),
inference(rw,[status(thm)],[c_0_72,c_0_55]) ).
cnf(c_0_82,hypothesis,
sdtlseqdt0(esk3_0,sdtasdt0(xn,xn)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_35]),c_0_36]),c_0_26])]),c_0_37]) ).
cnf(c_0_83,hypothesis,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_35]),c_0_36]),c_0_26])]) ).
cnf(c_0_84,hypothesis,
sdtasdt0(xn,xn) != esk3_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_36])]),c_0_77]) ).
cnf(c_0_85,negated_conjecture,
( sdtlseqdt0(xn,xm)
| xm = xn ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_86,hypothesis,
~ sdtlseqdt0(xn,xm),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_83]),c_0_36])]),c_0_84]) ).
cnf(c_0_87,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,xn)
| sdtlseqdt0(xn,X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_70]) ).
cnf(c_0_88,negated_conjecture,
xm = xn,
inference(sr,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_89,hypothesis,
sdtlseqdt0(xn,xn),
inference(spm,[status(thm)],[c_0_87,c_0_70]) ).
cnf(c_0_90,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_88]),c_0_89])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM528+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.46 % Computer : n003.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Mon Sep 21 02:39:30 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.54 Running first-order theorem proving
% 0.24/0.54 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
% 0.32/0.75 % Version: 3.5.1
% 0.32/0.75 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.32/0.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.75 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.32/0.75 % Starting new_bool_3 with 300s (1) cores
% 0.32/0.75 % Starting new_bool_1 with 300s (1) cores
% 0.32/0.75 % Starting sh5l with 300s (1) cores
% 0.32/0.75 % new_bool_3 with pid 3225529 completed with status 0
% 0.32/0.75 % Result found by new_bool_3
% 0.32/0.75 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.32/0.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.75 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.32/0.75 % Starting new_bool_3 with 300s (1) cores
% 0.32/0.75 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.32/0.75 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.32/0.75 % Search class: FGHSF-FSMM32-SFFFFFNN
% 0.32/0.75 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.32/0.75 % Starting SubtermCWHack with 31s (1) cores
% 0.32/0.75 % SubtermCWHack with pid 3225537 completed with status 0
% 0.32/0.75 % Result found by SubtermCWHack
% 0.32/0.75 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.32/0.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.75 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.32/0.75 % Starting new_bool_3 with 300s (1) cores
% 0.32/0.75 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.32/0.75 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.32/0.75 % Search class: FGHSF-FSMM32-SFFFFFNN
% 0.32/0.75 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.32/0.75 % Starting SubtermCWHack with 31s (1) cores
% 0.32/0.75 % Preprocessing time : 0.003 s
% 0.32/0.75
% 0.32/0.75 % Proof found!
% 0.32/0.75 % SZS status Theorem
% 0.32/0.75 % SZS output start CNFRefutation
% See solution above
% 0.32/0.75 % Parsed axioms : 48
% 0.32/0.75 % Removed by relevancy pruning/SinE : 1
% 0.32/0.75 % Initial clauses : 104
% 0.32/0.75 % Removed in clause preprocessing : 3
% 0.32/0.75 % Initial clauses in saturation : 101
% 0.32/0.75 % Processed clauses : 1742
% 0.32/0.75 % ...of these trivial : 48
% 0.32/0.75 % ...subsumed : 893
% 0.32/0.75 % ...remaining for further processing : 801
% 0.32/0.75 % Other redundant clauses eliminated : 45
% 0.32/0.75 % Clauses deleted for lack of memory : 0
% 0.32/0.75 % Backward-subsumed : 104
% 0.32/0.75 % Backward-rewritten : 280
% 0.32/0.75 % Generated clauses : 6227
% 0.32/0.75 % ...of the previous two non-redundant : 5271
% 0.32/0.75 % ...aggressively subsumed : 0
% 0.32/0.75 % Contextual simplify-reflections : 8
% 0.32/0.75 % Paramodulations : 6158
% 0.32/0.75 % Factorizations : 1
% 0.32/0.75 % NegExts : 0
% 0.32/0.75 % Equation resolutions : 56
% 0.32/0.75 % Disequality decompositions : 0
% 0.32/0.75 % Total rewrite steps : 7572
% 0.32/0.75 % ...of those cached : 7487
% 0.32/0.75 % Propositional unsat checks : 0
% 0.32/0.75 % Propositional check models : 0
% 0.32/0.75 % Propositional check unsatisfiable : 0
% 0.32/0.75 % Propositional clauses : 0
% 0.32/0.75 % Propositional clauses after purity: 0
% 0.32/0.75 % Propositional unsat core size : 0
% 0.32/0.75 % Propositional preprocessing time : 0.000
% 0.32/0.75 % Propositional encoding time : 0.000
% 0.32/0.75 % Propositional solver time : 0.000
% 0.32/0.75 % Success case prop preproc time : 0.000
% 0.32/0.75 % Success case prop encoding time : 0.000
% 0.32/0.75 % Success case prop solver time : 0.000
% 0.32/0.75 % Current number of processed clauses : 397
% 0.32/0.75 % Positive orientable unit clauses : 74
% 0.32/0.75 % Positive unorientable unit clauses: 0
% 0.32/0.75 % Negative unit clauses : 19
% 0.32/0.75 % Non-unit-clauses : 304
% 0.32/0.75 % Current number of unprocessed clauses: 3449
% 0.32/0.75 % ...number of literals in the above : 16527
% 0.32/0.75 % Current number of archived formulas : 0
% 0.32/0.75 % Current number of archived clauses : 396
% 0.32/0.75 % Clause-clause subsumption calls (NU) : 22877
% 0.32/0.75 % Rec. Clause-clause subsumption calls : 13027
% 0.32/0.75 % Non-unit clause-clause subsumptions : 882
% 0.32/0.75 % Unit Clause-clause subsumption calls : 2229
% 0.32/0.75 % Rewrite failures with RHS unbound : 0
% 0.32/0.75 % BW rewrite match attempts : 36
% 0.32/0.75 % BW rewrite match successes : 36
% 0.32/0.75 % Condensation attempts : 0
% 0.32/0.75 % Condensation successes : 0
% 0.32/0.75 % Termbank termtop insertions : 105586
% 0.32/0.75 % Search garbage collected termcells : 1662
% 0.32/0.75
% 0.32/0.75 % -------------------------------------------------
% 0.32/0.75 % User time : 0.136 s
% 0.32/0.75 % System time : 0.007 s
% 0.32/0.75 % Total time : 0.143 s
% 0.32/0.75 % Maximum resident set size: 3696 pages
% 0.32/0.75
% 0.32/0.75 % -------------------------------------------------
% 0.32/0.75 % User time : 0.138 s
% 0.32/0.75 % System time : 0.015 s
% 0.32/0.75 % Total time : 0.153 s
% 0.32/0.75 % Maximum resident set size: 4608 pages
% 0.32/0.75 % E exiting
%------------------------------------------------------------------------------