%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM518+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 : n017.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 01:55:20 PM UTC 2026
% Result : Theorem 0.76s 0.57s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 20
% Syntax : Number of formulae : 104 ( 36 unt; 0 def)
% Number of atoms : 466 ( 185 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 519 ( 157 ~; 185 |; 142 &)
% ( 3 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 13 con; 0-2 aty)
% Number of variables : 108 ( 0 sgn 60 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__1860,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X1] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
& isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( xp = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xp
| X1 = sz10 ) )
& xp != sz10
& xp != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(mPrimDiv,axiom,
! [X1] :
( ( X1 != sz10
& X1 != sz00
& aNaturalNumber0(X1) )
=> ? [X2] :
( isPrime0(X2)
& doDivides0(X2,X1)
& aNaturalNumber0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimDiv) ).
fof(mDefPrime,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( ! [X2] :
( ( doDivides0(X2,X1)
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(m__,conjecture,
( doDivides0(xp,xm)
| ? [X1] :
( xm = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
| doDivides0(xp,xn)
| ? [X1] :
( xn = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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__2342,hypothesis,
( isPrime0(xr)
& ! [X1] :
( ( ( doDivides0(X1,xr)
| ? [X2] :
( xr = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xr
| X1 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X1] :
( xk = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) )
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(m__2645,hypothesis,
( ( doDivides0(xp,xm)
& ? [X1] :
( xm = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) )
| ( doDivides0(xp,sdtsldt0(xn,xr))
& ? [X1] :
( sdtsldt0(xn,xr) = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2645) ).
fof(m__2487,hypothesis,
( doDivides0(xr,xn)
& ? [X1] :
( xn = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2487) ).
fof(m__2504,hypothesis,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& ? [X1] :
( sdtpldt0(sdtsldt0(xn,xr),X1) = xn
& aNaturalNumber0(X1) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& ~ ( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> sdtsldt0(xn,xr) = xn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2504) ).
fof(mDivMin,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,sdtpldt0(X2,X3))
& doDivides0(X1,X2) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivMin) ).
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(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(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__1870,hypothesis,
~ ( sdtlseqdt0(xp,xn)
| ? [X1] :
( sdtpldt0(xp,X1) = xn
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
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_20,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X1] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
& isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( xp = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xp
| X1 = sz10 ) )
& xp != sz10
& xp != sz00 ),
inference(fof_simplification,[status(thm)],[m__1860]) ).
fof(c_0_21,plain,
! [X1] :
( ( X1 != sz10
& X1 != sz00
& aNaturalNumber0(X1) )
=> ? [X2] :
( isPrime0(X2)
& doDivides0(X2,X1)
& aNaturalNumber0(X2) ) ),
inference(fof_simplification,[status(thm)],[mPrimDiv]) ).
fof(c_0_22,hypothesis,
! [X99,X100] :
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,esk9_0)
& aNaturalNumber0(esk9_0)
& isPrime0(xp)
& ( X99 = xp
| X99 = sz10
| ~ aNaturalNumber0(X99)
| ~ doDivides0(X99,xp) )
& ( X99 = xp
| X99 = sz10
| ~ aNaturalNumber0(X99)
| xp != sdtasdt0(X99,X100)
| ~ aNaturalNumber0(X100) )
& xp != sz10
& xp != sz00 ),
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_20])])])])])]) ).
fof(c_0_23,plain,
! [X89] :
( ( X89 = sz10
| X89 = sz00
| ~ aNaturalNumber0(X89)
| isPrime0(esk4_1(X89)) )
& ( X89 = sz10
| X89 = sz00
| ~ aNaturalNumber0(X89)
| doDivides0(esk4_1(X89),X89) )
& ( X89 = sz10
| X89 = sz00
| ~ aNaturalNumber0(X89)
| aNaturalNumber0(esk4_1(X89)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])]) ).
fof(c_0_24,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( ! [X2] :
( ( doDivides0(X2,X1)
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) ) ),
inference(fof_simplification,[status(thm)],[mDefPrime]) ).
fof(c_0_25,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
cnf(c_0_26,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xp)
| X1 = xp
| X1 = sz10 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz10
| X1 = sz00
| doDivides0(esk4_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_29,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,hypothesis,
xp != sz10,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_31,plain,
! [X86,X87] :
( ( ~ aNaturalNumber0(X86)
| isPrime0(X86)
| X86 = sz10
| X86 = sz00
| esk3_1(X86) != X86 )
& ( ~ aNaturalNumber0(X86)
| isPrime0(X86)
| X86 = sz10
| X86 = sz00
| esk3_1(X86) != sz10 )
& ( ~ aNaturalNumber0(X86)
| isPrime0(X86)
| X86 = sz10
| X86 = sz00
| doDivides0(esk3_1(X86),X86) )
& ( ~ aNaturalNumber0(X86)
| isPrime0(X86)
| X86 = sz10
| X86 = sz00
| aNaturalNumber0(esk3_1(X86)) )
& ( ~ aNaturalNumber0(X86)
| ~ isPrime0(X86)
| X87 = X86
| X87 = sz10
| ~ doDivides0(X87,X86)
| ~ aNaturalNumber0(X87) )
& ( ~ aNaturalNumber0(X86)
| ~ isPrime0(X86)
| X86 != sz10 )
& ( ~ aNaturalNumber0(X86)
| ~ isPrime0(X86)
| X86 != sz00 ) ),
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_24])])])])])]) ).
fof(c_0_32,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_25]) ).
fof(c_0_33,negated_conjecture,
~ ( doDivides0(xp,xm)
| ? [X1] :
( xm = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
| doDivides0(xp,xn)
| ? [X1] :
( xn = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_34,hypothesis,
( ~ aNaturalNumber0(esk4_1(xp))
| esk4_1(xp) = sz10
| esk4_1(xp) = xp ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]),c_0_29]),c_0_30]) ).
cnf(c_0_35,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz10
| X1 = sz00
| aNaturalNumber0(esk4_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_36,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz10 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_38,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]) ).
fof(c_0_39,hypothesis,
( isPrime0(xr)
& ! [X1] :
( ( ( doDivides0(X1,xr)
| ? [X2] :
( xr = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xr
| X1 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X1] :
( xk = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) )
& aNaturalNumber0(xr) ),
inference(fof_simplification,[status(thm)],[m__2342]) ).
fof(c_0_40,hypothesis,
( ( doDivides0(xp,sdtsldt0(xn,xr))
| doDivides0(xp,xm) )
& ( doDivides0(xp,sdtsldt0(xn,xr))
| xm = sdtasdt0(xp,esk22_0) )
& ( doDivides0(xp,sdtsldt0(xn,xr))
| aNaturalNumber0(esk22_0) )
& ( sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0)
| doDivides0(xp,xm) )
& ( sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0)
| xm = sdtasdt0(xp,esk22_0) )
& ( sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0)
| aNaturalNumber0(esk22_0) )
& ( aNaturalNumber0(esk21_0)
| doDivides0(xp,xm) )
& ( aNaturalNumber0(esk21_0)
| xm = sdtasdt0(xp,esk22_0) )
& ( aNaturalNumber0(esk21_0)
| aNaturalNumber0(esk22_0) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| doDivides0(xp,xm) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| xm = sdtasdt0(xp,esk22_0) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| aNaturalNumber0(esk22_0) )
& ( aNaturalNumber0(sdtsldt0(xn,xr))
| doDivides0(xp,xm) )
& ( aNaturalNumber0(sdtsldt0(xn,xr))
| xm = sdtasdt0(xp,esk22_0) )
& ( aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(esk22_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2645])])]) ).
fof(c_0_41,negated_conjecture,
! [X119,X120] :
( ~ doDivides0(xp,xm)
& ( xm != sdtasdt0(xp,X120)
| ~ aNaturalNumber0(X120) )
& ~ doDivides0(xp,xn)
& ( xn != sdtasdt0(xp,X119)
| ~ aNaturalNumber0(X119) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])]) ).
cnf(c_0_42,plain,
( ~ aNaturalNumber0(X1)
| X1 = sz10
| X1 = sz00
| isPrime0(esk4_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_43,hypothesis,
( esk4_1(xp) = xp
| esk4_1(xp) = sz10 ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_28])]),c_0_29]),c_0_30]) ).
cnf(c_0_44,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_36]),c_0_37])]) ).
fof(c_0_45,plain,
! [X30,X31,X32] :
( ( ~ aNaturalNumber0(X30)
| X30 = sz00
| ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X31)
| X31 = X32
| sdtasdt0(X31,X30) != sdtasdt0(X32,X30) )
& ( ~ aNaturalNumber0(X30)
| X30 = sz00
| ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X31)
| X31 = X32
| sdtasdt0(X30,X31) != sdtasdt0(X30,X32) ) ),
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_38])])])])]) ).
fof(c_0_46,hypothesis,
( doDivides0(xr,xn)
& xn = sdtasdt0(xr,esk18_0)
& aNaturalNumber0(esk18_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2487])]) ).
fof(c_0_47,hypothesis,
! [X107,X108] :
( isPrime0(xr)
& ( X107 = xr
| X107 = sz10
| ~ aNaturalNumber0(X107)
| ~ doDivides0(X107,xr) )
& ( X107 = xr
| X107 = sz10
| ~ aNaturalNumber0(X107)
| xr != sdtasdt0(X107,X108)
| ~ aNaturalNumber0(X108) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,esk12_0)
& aNaturalNumber0(esk12_0)
& aNaturalNumber0(xr) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])])])]) ).
fof(c_0_48,hypothesis,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& sdtpldt0(sdtsldt0(xn,xr),esk19_0) = xn
& aNaturalNumber0(esk19_0)
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& sdtsldt0(xn,xr) != xn
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2504])])])]) ).
cnf(c_0_49,hypothesis,
( sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0)
| doDivides0(xp,xm) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,negated_conjecture,
~ doDivides0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_51,plain,
! [X78,X79,X80] :
( doDivides0(X78,X80)
| ~ doDivides0(X78,sdtpldt0(X79,X80))
| ~ doDivides0(X78,X79)
| ~ aNaturalNumber0(X80)
| ~ aNaturalNumber0(X79)
| ~ aNaturalNumber0(X78) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivMin])])]) ).
cnf(c_0_52,hypothesis,
esk4_1(xp) = xp,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_28])]),c_0_29]),c_0_30]),c_0_44]) ).
cnf(c_0_53,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| X1 = sz00
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_54,hypothesis,
xn = sdtasdt0(xr,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,hypothesis,
aNaturalNumber0(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_56,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_57,hypothesis,
xr != sz00,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_58,hypothesis,
xn = sdtasdt0(xr,sdtsldt0(xn,xr)),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_59,hypothesis,
sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0),
inference(sr,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_60,hypothesis,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_61,plain,
( ~ doDivides0(X1,sdtpldt0(X2,X3))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_62,hypothesis,
doDivides0(xp,xp),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_52]),c_0_28])]),c_0_29]),c_0_30]) ).
fof(c_0_63,plain,
! [X16] :
( ( ~ aNaturalNumber0(X16)
| X16 = sdtpldt0(sz00,X16) )
& ( ~ aNaturalNumber0(X16)
| sdtpldt0(X16,sz00) = X16 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])])]) ).
cnf(c_0_64,hypothesis,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_65,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xr,X1) != xn
| X1 = esk18_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_55]),c_0_56])]),c_0_57]) ).
cnf(c_0_66,hypothesis,
sdtasdt0(xr,sdtasdt0(xp,esk21_0)) = xn,
inference(rw,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_67,hypothesis,
aNaturalNumber0(sdtasdt0(xp,esk21_0)),
inference(rw,[status(thm)],[c_0_60,c_0_59]) ).
fof(c_0_68,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
inference(fof_simplification,[status(thm)],[mMonMul2]) ).
fof(c_0_69,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])])])])])]) ).
cnf(c_0_70,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(xp,sdtpldt0(xp,X1))
| doDivides0(xp,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_28])]) ).
cnf(c_0_71,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_72,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_73,plain,
! [X47,X48,X49] :
( sdtlseqdt0(X47,X49)
| ~ sdtlseqdt0(X48,X49)
| ~ sdtlseqdt0(X47,X48)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X48)
| ~ aNaturalNumber0(X47) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])])]) ).
cnf(c_0_74,hypothesis,
sdtlseqdt0(sdtasdt0(xp,esk21_0),xn),
inference(rw,[status(thm)],[c_0_64,c_0_59]) ).
cnf(c_0_75,hypothesis,
sdtasdt0(xp,esk21_0) = esk18_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67])]) ).
fof(c_0_76,plain,
! [X59,X60] :
( sdtlseqdt0(X60,sdtasdt0(X60,X59))
| X59 = sz00
| ~ aNaturalNumber0(X60)
| ~ aNaturalNumber0(X59) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_68])])]) ).
cnf(c_0_77,hypothesis,
( aNaturalNumber0(esk21_0)
| doDivides0(xp,xm) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_78,plain,
! [X35,X36] :
( X36 = sz00
| X35 = sz00
| sdtasdt0(X35,X36) != sz00
| ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])])]) ).
cnf(c_0_79,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X1 = sdtasdt0(X2,esk2_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_80,hypothesis,
doDivides0(xp,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_62]),c_0_72]),c_0_28])]) ).
cnf(c_0_81,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_82,plain,
( ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_83,hypothesis,
sdtlseqdt0(esk18_0,xn),
inference(rw,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_84,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_85,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_86,hypothesis,
aNaturalNumber0(esk21_0),
inference(sr,[status(thm)],[c_0_77,c_0_50]) ).
fof(c_0_87,hypothesis,
! [X102] :
( ~ sdtlseqdt0(xp,xn)
& ( sdtpldt0(xp,X102) != xn
| ~ aNaturalNumber0(X102) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1870])])])]) ).
cnf(c_0_88,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_89,hypothesis,
sdtasdt0(xp,esk2_2(xp,sz00)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_28]),c_0_72])]) ).
cnf(c_0_90,hypothesis,
aNaturalNumber0(esk2_2(xp,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_80]),c_0_72]),c_0_28])]) ).
cnf(c_0_91,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,esk18_0)
| sdtlseqdt0(X1,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]),c_0_55])]) ).
cnf(c_0_92,hypothesis,
( sdtlseqdt0(xp,esk18_0)
| esk21_0 = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_75]),c_0_28]),c_0_86])]) ).
cnf(c_0_93,hypothesis,
~ sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_94,hypothesis,
esk2_2(xp,sz00) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]),c_0_28])]),c_0_29]) ).
cnf(c_0_95,hypothesis,
esk21_0 = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_28])]),c_0_93]) ).
cnf(c_0_96,hypothesis,
sdtasdt0(xp,sz00) = sz00,
inference(rw,[status(thm)],[c_0_89,c_0_94]) ).
fof(c_0_97,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_98,hypothesis,
esk18_0 = sz00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_95]),c_0_96]) ).
cnf(c_0_99,negated_conjecture,
( xn != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_100,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_101,hypothesis,
sdtasdt0(xr,sz00) = xn,
inference(rw,[status(thm)],[c_0_54,c_0_98]) ).
cnf(c_0_102,negated_conjecture,
sz00 != xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_72]),c_0_28])]) ).
cnf(c_0_103,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_56])]),c_0_102]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM518+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n017.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 02:31:57 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.76/0.57 % Version: 3.5.1
% 0.76/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.76/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.76/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.76/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.76/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.76/0.57 % Starting sh5l with 300s (1) cores
% 0.76/0.57 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1233440 completed with status 0
% 0.76/0.57 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.76/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.76/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.76/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.76/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.76/0.57 % No SInE strategy applied
% 0.76/0.57 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.76/0.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.76/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.76/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.76/0.57 % Starting G-E--_107_C41_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.76/0.57 % Starting new_bool_3 with 136s (1) cores
% 0.76/0.57 % Starting U----_116_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN1 with 136s (1) cores
% 0.76/0.57 % new_bool_3 with pid 1233449 completed with status 0
% 0.76/0.57 % Result found by new_bool_3
% 0.76/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.76/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.76/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.76/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.76/0.57 % No SInE strategy applied
% 0.76/0.57 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.76/0.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.76/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.76/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.76/0.57 % Starting G-E--_107_C41_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.76/0.57 % Starting new_bool_3 with 136s (1) cores
% 0.76/0.57 % Preprocessing time : 0.006 s
% 0.76/0.57 % Presaturation interreduction done
% 0.76/0.57
% 0.76/0.57 % Proof found!
% 0.76/0.57 % SZS status Theorem
% 0.76/0.57 % SZS output start CNFRefutation
% See solution above
% 0.76/0.57 % Parsed axioms : 56
% 0.76/0.57 % Removed by relevancy pruning/SinE : 0
% 0.76/0.57 % Initial clauses : 288
% 0.76/0.57 % Removed in clause preprocessing : 3
% 0.76/0.57 % Initial clauses in saturation : 285
% 0.76/0.57 % Processed clauses : 892
% 0.76/0.57 % ...of these trivial : 36
% 0.76/0.57 % ...subsumed : 179
% 0.76/0.57 % ...remaining for further processing : 677
% 0.76/0.57 % Other redundant clauses eliminated : 19
% 0.76/0.57 % Clauses deleted for lack of memory : 0
% 0.76/0.57 % Backward-subsumed : 7
% 0.76/0.57 % Backward-rewritten : 120
% 0.76/0.57 % Generated clauses : 1615
% 0.76/0.57 % ...of the previous two non-redundant : 1513
% 0.76/0.57 % ...aggressively subsumed : 0
% 0.76/0.57 % Contextual simplify-reflections : 8
% 0.76/0.57 % Paramodulations : 1587
% 0.76/0.57 % Factorizations : 4
% 0.76/0.57 % NegExts : 0
% 0.76/0.57 % Equation resolutions : 23
% 0.76/0.57 % Disequality decompositions : 0
% 0.76/0.57 % Total rewrite steps : 2577
% 0.76/0.57 % ...of those cached : 2468
% 0.76/0.57 % Propositional unsat checks : 0
% 0.76/0.57 % Propositional check models : 0
% 0.76/0.57 % Propositional check unsatisfiable : 0
% 0.76/0.57 % Propositional clauses : 0
% 0.76/0.57 % Propositional clauses after purity: 0
% 0.76/0.57 % Propositional unsat core size : 0
% 0.76/0.57 % Propositional preprocessing time : 0.000
% 0.76/0.57 % Propositional encoding time : 0.000
% 0.76/0.57 % Propositional solver time : 0.000
% 0.76/0.57 % Success case prop preproc time : 0.000
% 0.76/0.57 % Success case prop encoding time : 0.000
% 0.76/0.57 % Success case prop solver time : 0.000
% 0.76/0.57 % Current number of processed clauses : 279
% 0.76/0.57 % Positive orientable unit clauses : 123
% 0.76/0.57 % Positive unorientable unit clauses: 0
% 0.76/0.57 % Negative unit clauses : 25
% 0.76/0.57 % Non-unit-clauses : 131
% 0.76/0.57 % Current number of unprocessed clauses: 1133
% 0.76/0.57 % ...number of literals in the above : 5049
% 0.76/0.57 % Current number of archived formulas : 0
% 0.76/0.57 % Current number of archived clauses : 387
% 0.76/0.57 % Clause-clause subsumption calls (NU) : 36862
% 0.76/0.57 % Rec. Clause-clause subsumption calls : 1299
% 0.76/0.57 % Non-unit clause-clause subsumptions : 76
% 0.76/0.57 % Unit Clause-clause subsumption calls : 2126
% 0.76/0.57 % Rewrite failures with RHS unbound : 0
% 0.76/0.57 % BW rewrite match attempts : 29
% 0.76/0.57 % BW rewrite match successes : 26
% 0.76/0.57 % Condensation attempts : 0
% 0.76/0.57 % Condensation successes : 0
% 0.76/0.57 % Termbank termtop insertions : 50797
% 0.76/0.57 % Search garbage collected termcells : 2565
% 0.76/0.57
% 0.76/0.57 % -------------------------------------------------
% 0.76/0.57 % User time : 0.138 s
% 0.76/0.57 % System time : 0.008 s
% 0.76/0.57 % Total time : 0.146 s
% 0.76/0.57 % Maximum resident set size: 4224 pages
% 0.76/0.57
% 0.76/0.57 % -------------------------------------------------
% 0.76/0.57 % User time : 0.631 s
% 0.76/0.57 % System time : 0.034 s
% 0.76/0.57 % Total time : 0.665 s
% 0.76/0.57 % Maximum resident set size: 4608 pages
% 0.76/0.57 % E exiting
%------------------------------------------------------------------------------