%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM483+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 : n011.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 01:49:16 PM UTC 2026
% Result : Theorem 0.29s 0.78s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 13 unt; 0 def)
% Number of atoms : 417 ( 177 equ)
% Maximal formula atoms : 73 ( 5 avg)
% Number of connectives : 521 ( 175 ~; 229 |; 93 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 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 : 89 ( 0 sgn 43 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( ( isPrime0(X1)
| ( ! [X2] :
( ( doDivides0(X2,X1)
& ? [X3] :
( X1 = sdtasdt0(X2,X3)
& aNaturalNumber0(X3) )
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) )
& ( doDivides0(X1,xk)
| ? [X2] :
( xk = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
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(m__1716_04,hypothesis,
( xk != sz10
& xk != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716_04) ).
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__1716,hypothesis,
aNaturalNumber0(xk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716) ).
fof(m__1700,hypothesis,
! [X1] :
( ( X1 != sz10
& X1 != sz00
& aNaturalNumber0(X1) )
=> ( iLess0(X1,xk)
=> ? [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__1700) ).
fof(mDivTrans,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X2,X3)
& doDivides0(X1,X2) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
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_12,negated_conjecture,
~ ? [X1] :
( ( isPrime0(X1)
| ( ! [X2] :
( ( doDivides0(X2,X1)
& ? [X3] :
( X1 = sdtasdt0(X2,X3)
& aNaturalNumber0(X3) )
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) )
& ( doDivides0(X1,xk)
| ? [X2] :
( xk = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_13,plain,
! [X64,X65,X67] :
( ( ~ aNaturalNumber0(X65)
| ~ aNaturalNumber0(X64)
| doDivides0(X64,X65)
| X65 != sdtasdt0(X64,X67)
| ~ aNaturalNumber0(X67) )
& ( ~ aNaturalNumber0(X65)
| ~ aNaturalNumber0(X64)
| ~ doDivides0(X64,X65)
| X65 = sdtasdt0(X64,esk2_2(X64,X65)) )
& ( ~ aNaturalNumber0(X65)
| ~ aNaturalNumber0(X64)
| ~ doDivides0(X64,X65)
| aNaturalNumber0(esk2_2(X64,X65)) ) ),
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_14,plain,
! [X8,X9] :
( aNaturalNumber0(sdtasdt0(X8,X9))
| ~ aNaturalNumber0(X9)
| ~ aNaturalNumber0(X8) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
fof(c_0_15,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
fof(c_0_16,negated_conjecture,
~ ? [X1] :
( ( isPrime0(X1)
| ( ! [X2] :
( ( doDivides0(X2,X1)
& ? [X3] :
( X1 = sdtasdt0(X2,X3)
& aNaturalNumber0(X3) )
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) )
& ( doDivides0(X1,xk)
| ? [X2] :
( xk = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X21] :
( ( ~ aNaturalNumber0(X21)
| X21 = sdtasdt0(sz10,X21) )
& ( ~ aNaturalNumber0(X21)
| sdtasdt0(X21,sz10) = X21 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
fof(c_0_20,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_15]) ).
fof(c_0_21,hypothesis,
( xk != sz10
& xk != sz00 ),
inference(fof_simplification,[status(thm)],[m__1716_04]) ).
fof(c_0_22,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( X2 != sz00
& doDivides0(X1,X2) )
=> sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mDivLE]) ).
fof(c_0_23,negated_conjecture,
! [X95,X96] :
( ( ~ aNaturalNumber0(X95)
| ~ doDivides0(X95,xk)
| ~ isPrime0(X95) )
& ( ~ aNaturalNumber0(X95)
| ~ doDivides0(X95,xk)
| X95 = sz10
| X95 = sz00
| esk8_1(X95) != X95 )
& ( ~ aNaturalNumber0(X95)
| ~ doDivides0(X95,xk)
| X95 = sz10
| X95 = sz00
| esk8_1(X95) != sz10 )
& ( ~ aNaturalNumber0(X95)
| ~ doDivides0(X95,xk)
| X95 = sz10
| X95 = sz00
| doDivides0(esk8_1(X95),X95) )
& ( ~ aNaturalNumber0(X95)
| ~ doDivides0(X95,xk)
| X95 = sz10
| X95 = sz00
| X95 = sdtasdt0(esk8_1(X95),esk9_1(X95)) )
& ( ~ aNaturalNumber0(X95)
| ~ doDivides0(X95,xk)
| X95 = sz10
| X95 = sz00
| aNaturalNumber0(esk9_1(X95)) )
& ( ~ aNaturalNumber0(X95)
| ~ doDivides0(X95,xk)
| X95 = sz10
| X95 = sz00
| aNaturalNumber0(esk8_1(X95)) )
& ( ~ aNaturalNumber0(X95)
| xk != sdtasdt0(X95,X96)
| ~ aNaturalNumber0(X96)
| ~ isPrime0(X95) )
& ( ~ aNaturalNumber0(X95)
| xk != sdtasdt0(X95,X96)
| ~ aNaturalNumber0(X96)
| X95 = sz10
| X95 = sz00
| esk8_1(X95) != X95 )
& ( ~ aNaturalNumber0(X95)
| xk != sdtasdt0(X95,X96)
| ~ aNaturalNumber0(X96)
| X95 = sz10
| X95 = sz00
| esk8_1(X95) != sz10 )
& ( ~ aNaturalNumber0(X95)
| xk != sdtasdt0(X95,X96)
| ~ aNaturalNumber0(X96)
| X95 = sz10
| X95 = sz00
| doDivides0(esk8_1(X95),X95) )
& ( ~ aNaturalNumber0(X95)
| xk != sdtasdt0(X95,X96)
| ~ aNaturalNumber0(X96)
| X95 = sz10
| X95 = sz00
| X95 = sdtasdt0(esk8_1(X95),esk9_1(X95)) )
& ( ~ aNaturalNumber0(X95)
| xk != sdtasdt0(X95,X96)
| ~ aNaturalNumber0(X96)
| X95 = sz10
| X95 = sz00
| aNaturalNumber0(esk9_1(X95)) )
& ( ~ aNaturalNumber0(X95)
| xk != sdtasdt0(X95,X96)
| ~ aNaturalNumber0(X96)
| X95 = sz10
| X95 = sz00
| aNaturalNumber0(esk8_1(X95)) ) ),
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_16])])])])])]) ).
cnf(c_0_24,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_17]),c_0_18]) ).
cnf(c_0_25,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_27,hypothesis,
( xk != sz10
& xk != sz00 ),
inference(fof_nnf,[status(thm)],[c_0_21]) ).
fof(c_0_28,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_29,plain,
! [X80,X81] :
( sdtlseqdt0(X80,X81)
| X81 = sz00
| ~ doDivides0(X80,X81)
| ~ aNaturalNumber0(X81)
| ~ aNaturalNumber0(X80) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
cnf(c_0_30,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xk)
| X1 = sz10
| X1 = sz00
| doDivides0(esk8_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
( ~ aNaturalNumber0(X1)
| doDivides0(X1,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_32,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__1716]) ).
cnf(c_0_33,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,hypothesis,
xk != sz10,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( ~ aNaturalNumber0(X1)
| xk != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk8_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_36,hypothesis,
! [X1] :
( ( X1 != sz10
& X1 != sz00
& aNaturalNumber0(X1) )
=> ( iLess0(X1,xk)
=> ? [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)],[m__1700]) ).
fof(c_0_37,plain,
! [X62,X63] :
( iLess0(X62,X63)
| ~ sdtlseqdt0(X62,X63)
| X62 = X63
| ~ aNaturalNumber0(X63)
| ~ aNaturalNumber0(X62) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
cnf(c_0_38,plain,
( ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X2)
| X2 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,negated_conjecture,
doDivides0(esk8_1(xk),xk),
inference(sr,[status(thm)],[inference(sr,[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]) ).
cnf(c_0_40,negated_conjecture,
aNaturalNumber0(esk8_1(xk)),
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_35,c_0_25]),c_0_26])])]),c_0_32])]),c_0_33]),c_0_34]) ).
fof(c_0_41,plain,
! [X71,X72,X73] :
( doDivides0(X71,X73)
| ~ doDivides0(X72,X73)
| ~ doDivides0(X71,X72)
| ~ aNaturalNumber0(X73)
| ~ aNaturalNumber0(X72)
| ~ aNaturalNumber0(X71) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])])]) ).
fof(c_0_42,hypothesis,
! [X88,X91,X92] :
( ( X88 = sz10
| X88 = sz00
| ~ aNaturalNumber0(X88)
| ~ iLess0(X88,xk)
| isPrime0(esk4_1(X88)) )
& ( X88 = sz10
| X88 = sz00
| ~ aNaturalNumber0(X88)
| ~ iLess0(X88,xk)
| X91 = esk4_1(X88)
| X91 = sz10
| ~ aNaturalNumber0(X91)
| ~ doDivides0(X91,esk4_1(X88)) )
& ( X88 = sz10
| X88 = sz00
| ~ aNaturalNumber0(X88)
| ~ iLess0(X88,xk)
| X91 = esk4_1(X88)
| X91 = sz10
| ~ aNaturalNumber0(X91)
| esk4_1(X88) != sdtasdt0(X91,X92)
| ~ aNaturalNumber0(X92) )
& ( X88 = sz10
| X88 = sz00
| ~ aNaturalNumber0(X88)
| ~ iLess0(X88,xk)
| esk4_1(X88) != sz10 )
& ( X88 = sz10
| X88 = sz00
| ~ aNaturalNumber0(X88)
| ~ iLess0(X88,xk)
| esk4_1(X88) != sz00 )
& ( X88 = sz10
| X88 = sz00
| ~ aNaturalNumber0(X88)
| ~ iLess0(X88,xk)
| doDivides0(esk4_1(X88),X88) )
& ( X88 = sz10
| X88 = sz00
| ~ aNaturalNumber0(X88)
| ~ iLess0(X88,xk)
| X88 = sdtasdt0(esk4_1(X88),esk5_1(X88)) )
& ( X88 = sz10
| X88 = sz00
| ~ aNaturalNumber0(X88)
| ~ iLess0(X88,xk)
| aNaturalNumber0(esk5_1(X88)) )
& ( X88 = sz10
| X88 = sz00
| ~ aNaturalNumber0(X88)
| ~ iLess0(X88,xk)
| aNaturalNumber0(esk4_1(X88)) ) ),
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_36])])])])])]) ).
cnf(c_0_43,plain,
( ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| iLess0(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,negated_conjecture,
sdtlseqdt0(esk8_1(xk),xk),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_32]),c_0_40])]),c_0_33]) ).
cnf(c_0_45,plain,
( ~ doDivides0(X2,X3)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_46,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ iLess0(X1,xk)
| X1 = sz10
| X1 = sz00
| doDivides0(esk4_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_47,negated_conjecture,
( iLess0(esk8_1(xk),xk)
| esk8_1(xk) = xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_32]),c_0_40])]) ).
cnf(c_0_48,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ iLess0(X1,xk)
| X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk4_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,esk8_1(xk))
| doDivides0(X1,xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_39]),c_0_32]),c_0_40])]) ).
cnf(c_0_50,hypothesis,
( doDivides0(esk4_1(esk8_1(xk)),esk8_1(xk))
| esk8_1(xk) = sz00
| esk8_1(xk) = sz10
| esk8_1(xk) = xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_40])]) ).
cnf(c_0_51,hypothesis,
( aNaturalNumber0(esk4_1(esk8_1(xk)))
| esk8_1(xk) = sz00
| esk8_1(xk) = sz10
| esk8_1(xk) = xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_47]),c_0_40])]) ).
cnf(c_0_52,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ iLess0(X1,xk)
| X1 = sz10
| X1 = sz00
| isPrime0(esk4_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_53,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xk)
| ~ isPrime0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_54,negated_conjecture,
( doDivides0(esk4_1(esk8_1(xk)),xk)
| esk8_1(xk) = xk
| esk8_1(xk) = sz10
| esk8_1(xk) = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_55,hypothesis,
( isPrime0(esk4_1(esk8_1(xk)))
| esk8_1(xk) = sz00
| esk8_1(xk) = sz10
| esk8_1(xk) = xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_47]),c_0_40])]) ).
cnf(c_0_56,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xk)
| esk8_1(X1) != X1
| X1 = sz10
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_57,negated_conjecture,
( esk8_1(xk) = sz00
| esk8_1(xk) = sz10
| esk8_1(xk) = xk ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_51]),c_0_55]) ).
cnf(c_0_58,negated_conjecture,
( ~ doDivides0(xk,xk)
| esk8_1(xk) = sz10
| esk8_1(xk) = sz00 ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_32])]),c_0_33]),c_0_34]) ).
cnf(c_0_59,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xk)
| esk8_1(X1) != sz10
| X1 = sz10
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_60,negated_conjecture,
( esk8_1(xk) = sz00
| esk8_1(xk) = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_31]),c_0_32])]) ).
cnf(c_0_61,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xk)
| X1 = sz10
| X1 = sz00
| X1 = sdtasdt0(esk8_1(X1),esk9_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_62,negated_conjecture,
( ~ doDivides0(xk,xk)
| esk8_1(xk) = sz00 ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_32])]),c_0_33]),c_0_34]) ).
fof(c_0_63,plain,
! [X22] :
( ( ~ aNaturalNumber0(X22)
| sz00 = sdtasdt0(sz00,X22) )
& ( ~ aNaturalNumber0(X22)
| sdtasdt0(X22,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,
sdtasdt0(esk8_1(xk),esk9_1(xk)) = xk,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_31]),c_0_32])]),c_0_33]),c_0_34]) ).
cnf(c_0_65,negated_conjecture,
esk8_1(xk) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_31]),c_0_32])]) ).
cnf(c_0_66,negated_conjecture,
( ~ aNaturalNumber0(X1)
| xk != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk9_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_67,plain,
( ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_68,negated_conjecture,
sdtasdt0(sz00,esk9_1(xk)) = xk,
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_69,negated_conjecture,
aNaturalNumber0(esk9_1(xk)),
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_66,c_0_25]),c_0_26])])]),c_0_32])]),c_0_33]),c_0_34]) ).
cnf(c_0_70,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69])]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM483+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.48 % Computer : n011.cluster.edu
% 0.19/0.48 % Model : x86_64 x86_64
% 0.19/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.48 % Memory : 8046.5625MB
% 0.19/0.48 % OS : Linux 6.8.0-71-generic
% 0.19/0.49 % CPULimit : 300
% 0.19/0.49 % WCLimit : 300
% 0.19/0.49 % DateTime : Mon Sep 21 02:33:55 UTC 2026
% 0.19/0.49 % CPUTime :
% 0.19/0.49 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.56 Running first-order theorem proving
% 0.23/0.56 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
% 0.29/0.78 % Version: 3.5.1
% 0.29/0.78 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.29/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.29/0.78 % Starting new_bool_3 with 300s (1) cores
% 0.29/0.78 % Starting new_bool_1 with 300s (1) cores
% 0.29/0.78 % Starting sh5l with 300s (1) cores
% 0.29/0.78 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 780139 completed with status 0
% 0.29/0.78 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.29/0.78 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.29/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.29/0.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.29/0.78 % No SInE strategy applied
% 0.29/0.78 % Search class: FGHSF-FSMM21-SFFFFFNN
% 0.29/0.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.29/0.78 % Starting SubtermCWHack with 136s (1) cores
% 0.29/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.29/0.78 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.29/0.78 % Starting new_bool_3 with 136s (1) cores
% 0.29/0.78 % Starting new_bool_1 with 136s (1) cores
% 0.29/0.78 % new_bool_1 with pid 780148 completed with status 0
% 0.29/0.78 % Result found by new_bool_1
% 0.29/0.78 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.29/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.29/0.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.29/0.78 % No SInE strategy applied
% 0.29/0.78 % Search class: FGHSF-FSMM21-SFFFFFNN
% 0.29/0.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.29/0.78 % Starting SubtermCWHack with 136s (1) cores
% 0.29/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.29/0.78 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.29/0.78 % Starting new_bool_3 with 136s (1) cores
% 0.29/0.78 % Starting new_bool_1 with 136s (1) cores
% 0.29/0.78 % Preprocessing time : 0.004 s
% 0.29/0.78 % Presaturation interreduction done
% 0.29/0.78
% 0.29/0.78 % Proof found!
% 0.29/0.78 % SZS status Theorem
% 0.29/0.78 % SZS output start CNFRefutation
% See solution above
% 0.29/0.78 % Parsed axioms : 42
% 0.29/0.78 % Removed by relevancy pruning/SinE : 0
% 0.29/0.78 % Initial clauses : 100
% 0.29/0.78 % Removed in clause preprocessing : 3
% 0.29/0.78 % Initial clauses in saturation : 97
% 0.29/0.78 % Processed clauses : 1126
% 0.29/0.78 % ...of these trivial : 11
% 0.29/0.78 % ...subsumed : 556
% 0.29/0.78 % ...remaining for further processing : 559
% 0.29/0.78 % Other redundant clauses eliminated : 38
% 0.29/0.78 % Clauses deleted for lack of memory : 0
% 0.29/0.78 % Backward-subsumed : 74
% 0.29/0.78 % Backward-rewritten : 78
% 0.29/0.78 % Generated clauses : 2595
% 0.29/0.78 % ...of the previous two non-redundant : 2196
% 0.29/0.78 % ...aggressively subsumed : 0
% 0.29/0.78 % Contextual simplify-reflections : 89
% 0.29/0.78 % Paramodulations : 2543
% 0.29/0.78 % Factorizations : 9
% 0.29/0.78 % NegExts : 0
% 0.29/0.78 % Equation resolutions : 43
% 0.29/0.78 % Disequality decompositions : 0
% 0.29/0.78 % Total rewrite steps : 2959
% 0.29/0.78 % ...of those cached : 2896
% 0.29/0.78 % Propositional unsat checks : 0
% 0.29/0.78 % Propositional check models : 0
% 0.29/0.78 % Propositional check unsatisfiable : 0
% 0.29/0.78 % Propositional clauses : 0
% 0.29/0.78 % Propositional clauses after purity: 0
% 0.29/0.78 % Propositional unsat core size : 0
% 0.29/0.78 % Propositional preprocessing time : 0.000
% 0.29/0.78 % Propositional encoding time : 0.000
% 0.29/0.78 % Propositional solver time : 0.000
% 0.29/0.78 % Success case prop preproc time : 0.000
% 0.29/0.78 % Success case prop encoding time : 0.000
% 0.29/0.78 % Success case prop solver time : 0.000
% 0.29/0.78 % Current number of processed clauses : 304
% 0.29/0.78 % Positive orientable unit clauses : 50
% 0.29/0.78 % Positive unorientable unit clauses: 0
% 0.29/0.78 % Negative unit clauses : 18
% 0.29/0.78 % Non-unit-clauses : 236
% 0.29/0.78 % Current number of unprocessed clauses: 1128
% 0.29/0.78 % ...number of literals in the above : 5468
% 0.29/0.78 % Current number of archived formulas : 0
% 0.29/0.78 % Current number of archived clauses : 244
% 0.29/0.78 % Clause-clause subsumption calls (NU) : 12598
% 0.29/0.78 % Rec. Clause-clause subsumption calls : 3146
% 0.29/0.78 % Non-unit clause-clause subsumptions : 439
% 0.29/0.78 % Unit Clause-clause subsumption calls : 1689
% 0.29/0.78 % Rewrite failures with RHS unbound : 0
% 0.29/0.78 % BW rewrite match attempts : 22
% 0.29/0.78 % BW rewrite match successes : 20
% 0.29/0.78 % Condensation attempts : 0
% 0.29/0.78 % Condensation successes : 0
% 0.29/0.78 % Termbank termtop insertions : 52921
% 0.29/0.78 % Search garbage collected termcells : 1695
% 0.29/0.78
% 0.29/0.78 % -------------------------------------------------
% 0.29/0.78 % User time : 0.150 s
% 0.29/0.78 % System time : 0.012 s
% 0.29/0.78 % Total time : 0.162 s
% 0.29/0.78 % Maximum resident set size: 3684 pages
% 0.29/0.78
% 0.29/0.78 % -------------------------------------------------
% 0.29/0.78 % User time : 0.436 s
% 0.29/0.78 % System time : 0.034 s
% 0.29/0.78 % Total time : 0.470 s
% 0.29/0.78 % Maximum resident set size: 4864 pages
% 0.29/0.78 % E exiting
%------------------------------------------------------------------------------