%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM481+3 : 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 : n020.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 01:49:15 PM UTC 2026
% Result : Theorem 0.15s 0.54s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 14 unt; 0 def)
% Number of atoms : 460 ( 190 equ)
% Maximal formula atoms : 128 ( 6 avg)
% Number of connectives : 612 ( 220 ~; 248 |; 111 &)
% ( 1 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 121 ( 0 sgn 52 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
! [X1] :
( ( X1 != sz10
& X1 != sz00
& aNaturalNumber0(X1) )
=> ( ! [X2] :
( ( X2 != sz10
& X2 != sz00
& aNaturalNumber0(X2) )
=> ( iLess0(X2,X1)
=> ? [X3] :
( isPrime0(X3)
& ! [X4] :
( ( ( doDivides0(X4,X3)
| ? [X5] :
( X3 = sdtasdt0(X4,X5)
& aNaturalNumber0(X5) ) )
& aNaturalNumber0(X4) )
=> ( X4 = X3
| X4 = sz10 ) )
& X3 != sz10
& X3 != sz00
& doDivides0(X3,X2)
& ? [X4] :
( X2 = sdtasdt0(X3,X4)
& aNaturalNumber0(X4) )
& aNaturalNumber0(X3) ) ) )
=> ? [X2] :
( ( isPrime0(X2)
| ( ! [X3] :
( ( doDivides0(X3,X2)
& ? [X4] :
( X2 = sdtasdt0(X3,X4)
& aNaturalNumber0(X4) )
& aNaturalNumber0(X3) )
=> ( X3 = X2
| X3 = sz10 ) )
& X2 != sz10
& X2 != sz00 ) )
& ( doDivides0(X2,X1)
| ? [X3] :
( X1 = sdtasdt0(X2,X3)
& aNaturalNumber0(X3) ) )
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
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/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( X2 != sz00
& doDivides0(X1,X2) )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivLE) ).
fof(mIH_03,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2 )
=> iLess0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ( X1 != sz10
& X1 != sz00
& aNaturalNumber0(X1) )
=> ( ! [X2] :
( ( X2 != sz10
& X2 != sz00
& aNaturalNumber0(X2) )
=> ( iLess0(X2,X1)
=> ? [X3] :
( isPrime0(X3)
& ! [X4] :
( ( ( doDivides0(X4,X3)
| ? [X5] :
( X3 = sdtasdt0(X4,X5)
& aNaturalNumber0(X5) ) )
& aNaturalNumber0(X4) )
=> ( X4 = X3
| X4 = sz10 ) )
& X3 != sz10
& X3 != sz00
& doDivides0(X3,X2)
& ? [X4] :
( X2 = sdtasdt0(X3,X4)
& aNaturalNumber0(X4) )
& aNaturalNumber0(X3) ) ) )
=> ? [X2] :
( ( isPrime0(X2)
| ( ! [X3] :
( ( doDivides0(X3,X2)
& ? [X4] :
( X2 = sdtasdt0(X3,X4)
& aNaturalNumber0(X4) )
& aNaturalNumber0(X3) )
=> ( X3 = X2
| X3 = sz10 ) )
& X2 != sz10
& X2 != sz00 ) )
& ( doDivides0(X2,X1)
| ? [X3] :
( X1 = sdtasdt0(X2,X3)
& aNaturalNumber0(X3) ) )
& aNaturalNumber0(X2) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( ( X1 != sz10
& X1 != sz00
& aNaturalNumber0(X1) )
=> ( ! [X2] :
( ( X2 != sz10
& X2 != sz00
& aNaturalNumber0(X2) )
=> ( iLess0(X2,X1)
=> ? [X3] :
( isPrime0(X3)
& ! [X4] :
( ( ( doDivides0(X4,X3)
| ? [X5] :
( X3 = sdtasdt0(X4,X5)
& aNaturalNumber0(X5) ) )
& aNaturalNumber0(X4) )
=> ( X4 = X3
| X4 = sz10 ) )
& X3 != sz10
& X3 != sz00
& doDivides0(X3,X2)
& ? [X4] :
( X2 = sdtasdt0(X3,X4)
& aNaturalNumber0(X4) )
& aNaturalNumber0(X3) ) ) )
=> ? [X2] :
( ( isPrime0(X2)
| ( ! [X3] :
( ( doDivides0(X3,X2)
& ? [X4] :
( X2 = sdtasdt0(X3,X4)
& aNaturalNumber0(X4) )
& aNaturalNumber0(X3) )
=> ( X3 = X2
| X3 = sz10 ) )
& X2 != sz10
& X2 != sz00 ) )
& ( doDivides0(X2,X1)
| ? [X3] :
( X1 = sdtasdt0(X2,X3)
& aNaturalNumber0(X3) ) )
& aNaturalNumber0(X2) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_12,negated_conjecture,
! [X90,X93,X94,X95,X96] :
( ( ~ aNaturalNumber0(X95)
| ~ doDivides0(X95,esk4_0)
| ~ isPrime0(X95) )
& ( ~ aNaturalNumber0(X95)
| ~ doDivides0(X95,esk4_0)
| X95 = sz10
| X95 = sz00
| esk7_1(X95) != X95 )
& ( ~ aNaturalNumber0(X95)
| ~ doDivides0(X95,esk4_0)
| X95 = sz10
| X95 = sz00
| esk7_1(X95) != sz10 )
& ( ~ aNaturalNumber0(X95)
| ~ doDivides0(X95,esk4_0)
| X95 = sz10
| X95 = sz00
| doDivides0(esk7_1(X95),X95) )
& ( ~ aNaturalNumber0(X95)
| ~ doDivides0(X95,esk4_0)
| X95 = sz10
| X95 = sz00
| X95 = sdtasdt0(esk7_1(X95),esk8_1(X95)) )
& ( ~ aNaturalNumber0(X95)
| ~ doDivides0(X95,esk4_0)
| X95 = sz10
| X95 = sz00
| aNaturalNumber0(esk8_1(X95)) )
& ( ~ aNaturalNumber0(X95)
| ~ doDivides0(X95,esk4_0)
| X95 = sz10
| X95 = sz00
| aNaturalNumber0(esk7_1(X95)) )
& ( ~ aNaturalNumber0(X95)
| esk4_0 != sdtasdt0(X95,X96)
| ~ aNaturalNumber0(X96)
| ~ isPrime0(X95) )
& ( ~ aNaturalNumber0(X95)
| esk4_0 != sdtasdt0(X95,X96)
| ~ aNaturalNumber0(X96)
| X95 = sz10
| X95 = sz00
| esk7_1(X95) != X95 )
& ( ~ aNaturalNumber0(X95)
| esk4_0 != sdtasdt0(X95,X96)
| ~ aNaturalNumber0(X96)
| X95 = sz10
| X95 = sz00
| esk7_1(X95) != sz10 )
& ( ~ aNaturalNumber0(X95)
| esk4_0 != sdtasdt0(X95,X96)
| ~ aNaturalNumber0(X96)
| X95 = sz10
| X95 = sz00
| doDivides0(esk7_1(X95),X95) )
& ( ~ aNaturalNumber0(X95)
| esk4_0 != sdtasdt0(X95,X96)
| ~ aNaturalNumber0(X96)
| X95 = sz10
| X95 = sz00
| X95 = sdtasdt0(esk7_1(X95),esk8_1(X95)) )
& ( ~ aNaturalNumber0(X95)
| esk4_0 != sdtasdt0(X95,X96)
| ~ aNaturalNumber0(X96)
| X95 = sz10
| X95 = sz00
| aNaturalNumber0(esk8_1(X95)) )
& ( ~ aNaturalNumber0(X95)
| esk4_0 != sdtasdt0(X95,X96)
| ~ aNaturalNumber0(X96)
| X95 = sz10
| X95 = sz00
| aNaturalNumber0(esk7_1(X95)) )
& ( X90 = sz10
| X90 = sz00
| ~ aNaturalNumber0(X90)
| ~ iLess0(X90,esk4_0)
| isPrime0(esk5_1(X90)) )
& ( X90 = sz10
| X90 = sz00
| ~ aNaturalNumber0(X90)
| ~ iLess0(X90,esk4_0)
| X93 = esk5_1(X90)
| X93 = sz10
| ~ aNaturalNumber0(X93)
| ~ doDivides0(X93,esk5_1(X90)) )
& ( X90 = sz10
| X90 = sz00
| ~ aNaturalNumber0(X90)
| ~ iLess0(X90,esk4_0)
| X93 = esk5_1(X90)
| X93 = sz10
| ~ aNaturalNumber0(X93)
| esk5_1(X90) != sdtasdt0(X93,X94)
| ~ aNaturalNumber0(X94) )
& ( X90 = sz10
| X90 = sz00
| ~ aNaturalNumber0(X90)
| ~ iLess0(X90,esk4_0)
| esk5_1(X90) != sz10 )
& ( X90 = sz10
| X90 = sz00
| ~ aNaturalNumber0(X90)
| ~ iLess0(X90,esk4_0)
| esk5_1(X90) != sz00 )
& ( X90 = sz10
| X90 = sz00
| ~ aNaturalNumber0(X90)
| ~ iLess0(X90,esk4_0)
| doDivides0(esk5_1(X90),X90) )
& ( X90 = sz10
| X90 = sz00
| ~ aNaturalNumber0(X90)
| ~ iLess0(X90,esk4_0)
| X90 = sdtasdt0(esk5_1(X90),esk6_1(X90)) )
& ( X90 = sz10
| X90 = sz00
| ~ aNaturalNumber0(X90)
| ~ iLess0(X90,esk4_0)
| aNaturalNumber0(esk6_1(X90)) )
& ( X90 = sz10
| X90 = sz00
| ~ aNaturalNumber0(X90)
| ~ iLess0(X90,esk4_0)
| aNaturalNumber0(esk5_1(X90)) )
& esk4_0 != sz10
& esk4_0 != sz00
& aNaturalNumber0(esk4_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)],[c_0_11])])])])])]) ).
fof(c_0_13,plain,
! [X17,X18] :
( sdtasdt0(X17,X18) = sdtasdt0(X18,X17)
| ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_14,negated_conjecture,
( ~ aNaturalNumber0(X1)
| esk4_0 != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ isPrime0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X19,X20,X21] :
( sdtasdt0(sdtasdt0(X19,X20),X21) = sdtasdt0(X19,sdtasdt0(X20,X21))
| ~ aNaturalNumber0(X21)
| ~ aNaturalNumber0(X20)
| ~ aNaturalNumber0(X19) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
fof(c_0_17,plain,
! [X9,X10] :
( aNaturalNumber0(sdtasdt0(X9,X10))
| ~ aNaturalNumber0(X10)
| ~ aNaturalNumber0(X9) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
cnf(c_0_18,negated_conjecture,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ isPrime0(X2)
| sdtasdt0(X1,X2) != esk4_0 ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ isPrime0(X3)
| sdtasdt0(X1,sdtasdt0(X2,X3)) != esk4_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
fof(c_0_22,plain,
! [X65,X66,X68] :
( ( ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X65)
| doDivides0(X65,X66)
| X66 != sdtasdt0(X65,X68)
| ~ aNaturalNumber0(X68) )
& ( ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X65)
| ~ doDivides0(X65,X66)
| X66 = sdtasdt0(X65,esk2_2(X65,X66)) )
& ( ~ aNaturalNumber0(X66)
| ~ aNaturalNumber0(X65)
| ~ doDivides0(X65,X66)
| aNaturalNumber0(esk2_2(X65,X66)) ) ),
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)],[mDefDiv])])])])])]) ).
fof(c_0_23,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
cnf(c_0_24,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ isPrime0(X2)
| sdtasdt0(X1,sdtasdt0(X2,X3)) != esk4_0 ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_25,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X1 = sdtasdt0(X2,esk2_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_27,plain,
! [X22] :
( ( ~ aNaturalNumber0(X22)
| X22 = sdtasdt0(sz10,X22) )
& ( ~ aNaturalNumber0(X22)
| sdtasdt0(X22,sz10) = X22 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
fof(c_0_28,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| ~ isPrime0(X3)
| sdtasdt0(X1,X2) != esk4_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( ~ aNaturalNumber0(X1)
| esk4_0 != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| X1 = sz10
| X1 = sz00
| X1 = sdtasdt0(esk7_1(X1),esk8_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_31,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,negated_conjecture,
aNaturalNumber0(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_34,negated_conjecture,
esk4_0 != sz00,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_35,negated_conjecture,
esk4_0 != sz10,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_36,negated_conjecture,
( ~ aNaturalNumber0(X1)
| esk4_0 != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk8_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_37,negated_conjecture,
( ~ aNaturalNumber0(X1)
| esk4_0 != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_38,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X1)
| ~ isPrime0(X3)
| sdtasdt0(X1,X2) != esk4_0 ),
inference(spm,[status(thm)],[c_0_29,c_0_15]) ).
cnf(c_0_39,negated_conjecture,
sdtasdt0(esk7_1(esk4_0),esk8_1(esk4_0)) = esk4_0,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])])]),c_0_33])]),c_0_34]),c_0_35]) ).
cnf(c_0_40,negated_conjecture,
aNaturalNumber0(esk8_1(esk4_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_31]),c_0_32])])]),c_0_33])]),c_0_34]),c_0_35]) ).
cnf(c_0_41,negated_conjecture,
aNaturalNumber0(esk7_1(esk4_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_31]),c_0_32])])]),c_0_33])]),c_0_34]),c_0_35]) ).
cnf(c_0_42,negated_conjecture,
( ~ aNaturalNumber0(X1)
| esk4_0 != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| esk7_1(X1) != sz10
| X1 = sz10
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_43,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( X2 != sz00
& doDivides0(X1,X2) )
=> sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mDivLE]) ).
cnf(c_0_44,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,esk7_1(esk4_0))
| ~ isPrime0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41])]) ).
cnf(c_0_45,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ iLess0(X1,esk4_0)
| X1 = sz10
| X1 = sz00
| doDivides0(esk5_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_46,negated_conjecture,
esk7_1(esk4_0) != sz10,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_31]),c_0_32])])]),c_0_33])]),c_0_34]),c_0_35]) ).
fof(c_0_47,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2 )
=> iLess0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mIH_03]) ).
fof(c_0_48,plain,
! [X81,X82] :
( sdtlseqdt0(X81,X82)
| X82 = sz00
| ~ doDivides0(X81,X82)
| ~ aNaturalNumber0(X82)
| ~ aNaturalNumber0(X81) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])]) ).
cnf(c_0_49,negated_conjecture,
( ~ aNaturalNumber0(X1)
| esk4_0 != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| X1 = sz10
| X1 = sz00
| doDivides0(esk7_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_50,negated_conjecture,
( ~ aNaturalNumber0(esk5_1(esk7_1(esk4_0)))
| ~ iLess0(esk7_1(esk4_0),esk4_0)
| ~ isPrime0(esk5_1(esk7_1(esk4_0)))
| esk7_1(esk4_0) = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_41])]),c_0_46]) ).
cnf(c_0_51,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ iLess0(X1,esk4_0)
| X1 = sz10
| X1 = sz00
| isPrime0(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_52,plain,
! [X63,X64] :
( iLess0(X63,X64)
| ~ sdtlseqdt0(X63,X64)
| X63 = X64
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])]) ).
cnf(c_0_53,plain,
( ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X2)
| X2 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,negated_conjecture,
doDivides0(esk7_1(esk4_0),esk4_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_31]),c_0_32])])]),c_0_33])]),c_0_34]),c_0_35]) ).
cnf(c_0_55,negated_conjecture,
( ~ aNaturalNumber0(X1)
| esk4_0 != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| esk7_1(X1) != X1
| X1 = sz10
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_56,negated_conjecture,
( ~ aNaturalNumber0(esk5_1(esk7_1(esk4_0)))
| ~ iLess0(esk7_1(esk4_0),esk4_0)
| esk7_1(esk4_0) = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_41])]),c_0_46]) ).
cnf(c_0_57,plain,
( ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| iLess0(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_58,negated_conjecture,
sdtlseqdt0(esk7_1(esk4_0),esk4_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_33]),c_0_41])]),c_0_34]) ).
cnf(c_0_59,negated_conjecture,
esk7_1(esk4_0) != esk4_0,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_31]),c_0_32])])]),c_0_33])]),c_0_34]),c_0_35]) ).
cnf(c_0_60,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ iLess0(X1,esk4_0)
| X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_61,negated_conjecture,
( ~ aNaturalNumber0(esk5_1(esk7_1(esk4_0)))
| esk7_1(esk4_0) = sz00 ),
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_56,c_0_57]),c_0_58]),c_0_33]),c_0_41])]),c_0_59]) ).
cnf(c_0_62,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,esk4_0)
| aNaturalNumber0(esk5_1(X1))
| X1 = sz00
| X1 = sz10
| X1 = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_57]),c_0_33])]) ).
fof(c_0_63,plain,
! [X23] :
( ( ~ aNaturalNumber0(X23)
| sz00 = sdtasdt0(sz00,X23) )
& ( ~ aNaturalNumber0(X23)
| sdtasdt0(X23,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_64,negated_conjecture,
esk7_1(esk4_0) = sz00,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_58]),c_0_41])]),c_0_59]),c_0_46]) ).
cnf(c_0_65,plain,
( ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_66,negated_conjecture,
sdtasdt0(sz00,esk8_1(esk4_0)) = esk4_0,
inference(rw,[status(thm)],[c_0_39,c_0_64]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_40])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM481+3 : 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 : n020.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
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 02:34:33 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.45 Running first-order theorem proving
% 0.15/0.45 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
% 0.15/0.54 % Version: 3.5.1
% 0.15/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.54 % Starting sh5l with 300s (1) cores
% 0.15/0.54 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1806115 completed with status 0
% 0.15/0.54 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.15/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.54 % No SInE strategy applied
% 0.15/0.54 % Search class: FGHSF-FSMS21-SFFFFFNN
% 0.15/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.15/0.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.15/0.54 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.54 % Starting new_bool_1 with 136s (1) cores
% 0.15/0.54 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 1806123 completed with status 0
% 0.15/0.54 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.15/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.54 % No SInE strategy applied
% 0.15/0.54 % Search class: FGHSF-FSMS21-SFFFFFNN
% 0.15/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.15/0.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.15/0.54 % Preprocessing time : 0.002 s
% 0.15/0.54 % Presaturation interreduction done
% 0.15/0.54
% 0.15/0.54 % Proof found!
% 0.15/0.54 % SZS status Theorem
% 0.15/0.54 % SZS output start CNFRefutation
% See solution above
% 0.15/0.55 % Parsed axioms : 38
% 0.15/0.55 % Removed by relevancy pruning/SinE : 0
% 0.15/0.55 % Initial clauses : 93
% 0.15/0.55 % Removed in clause preprocessing : 3
% 0.15/0.55 % Initial clauses in saturation : 90
% 0.15/0.55 % Processed clauses : 521
% 0.15/0.55 % ...of these trivial : 4
% 0.15/0.55 % ...subsumed : 181
% 0.15/0.55 % ...remaining for further processing : 336
% 0.15/0.55 % Other redundant clauses eliminated : 92
% 0.15/0.55 % Clauses deleted for lack of memory : 0
% 0.15/0.55 % Backward-subsumed : 23
% 0.15/0.55 % Backward-rewritten : 52
% 0.15/0.55 % Generated clauses : 1218
% 0.15/0.55 % ...of the previous two non-redundant : 1056
% 0.15/0.55 % ...aggressively subsumed : 0
% 0.15/0.55 % Contextual simplify-reflections : 19
% 0.15/0.55 % Paramodulations : 1120
% 0.15/0.55 % Factorizations : 0
% 0.15/0.55 % NegExts : 0
% 0.15/0.55 % Equation resolutions : 96
% 0.15/0.55 % Disequality decompositions : 0
% 0.15/0.55 % Total rewrite steps : 907
% 0.15/0.55 % ...of those cached : 891
% 0.15/0.55 % Propositional unsat checks : 0
% 0.15/0.55 % Propositional check models : 0
% 0.15/0.55 % Propositional check unsatisfiable : 0
% 0.15/0.55 % Propositional clauses : 0
% 0.15/0.55 % Propositional clauses after purity: 0
% 0.15/0.55 % Propositional unsat core size : 0
% 0.15/0.55 % Propositional preprocessing time : 0.000
% 0.15/0.55 % Propositional encoding time : 0.000
% 0.15/0.55 % Propositional solver time : 0.000
% 0.15/0.55 % Success case prop preproc time : 0.000
% 0.15/0.55 % Success case prop encoding time : 0.000
% 0.15/0.55 % Success case prop solver time : 0.000
% 0.15/0.55 % Current number of processed clauses : 163
% 0.15/0.55 % Positive orientable unit clauses : 16
% 0.15/0.55 % Positive unorientable unit clauses: 0
% 0.15/0.55 % Negative unit clauses : 11
% 0.15/0.55 % Non-unit-clauses : 136
% 0.15/0.55 % Current number of unprocessed clauses: 676
% 0.15/0.55 % ...number of literals in the above : 4041
% 0.15/0.55 % Current number of archived formulas : 0
% 0.15/0.55 % Current number of archived clauses : 162
% 0.15/0.55 % Clause-clause subsumption calls (NU) : 4207
% 0.15/0.55 % Rec. Clause-clause subsumption calls : 1231
% 0.15/0.55 % Non-unit clause-clause subsumptions : 149
% 0.15/0.55 % Unit Clause-clause subsumption calls : 352
% 0.15/0.55 % Rewrite failures with RHS unbound : 0
% 0.15/0.55 % BW rewrite match attempts : 7
% 0.15/0.55 % BW rewrite match successes : 7
% 0.15/0.55 % Condensation attempts : 0
% 0.15/0.55 % Condensation successes : 0
% 0.15/0.55 % Termbank termtop insertions : 29114
% 0.15/0.55 % Search garbage collected termcells : 1776
% 0.15/0.55
% 0.15/0.55 % -------------------------------------------------
% 0.15/0.55 % User time : 0.048 s
% 0.15/0.55 % System time : 0.009 s
% 0.15/0.55 % Total time : 0.058 s
% 0.15/0.55 % Maximum resident set size: 3936 pages
% 0.15/0.55
% 0.15/0.55 % -------------------------------------------------
% 0.15/0.55 % User time : 0.176 s
% 0.15/0.55 % System time : 0.029 s
% 0.15/0.55 % Total time : 0.204 s
% 0.15/0.55 % Maximum resident set size: 4864 pages
% 0.15/0.55 % E exiting
%------------------------------------------------------------------------------