%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM503+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 : n018.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 01:49:20 PM UTC 2026
% Result : ContradictoryAxioms 7.17s 1.44s
% Output : CNFRefutation 7.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 21
% Syntax : Number of formulae : 103 ( 36 unt; 0 def)
% Number of atoms : 421 ( 159 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 481 ( 163 ~; 159 |; 129 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 14 con; 0-2 aty)
% Number of variables : 122 ( 0 sgn 66 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(m__2362,hypothesis,
( doDivides0(xr,sdtasdt0(xn,xm))
& ? [X1] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) )
& ? [X1] :
( sdtpldt0(xr,X1) = xk
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
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/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
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(m__2306,hypothesis,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
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/sandbox2/benchmark/theBenchmark.p',m__1860) ).
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(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/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(mMonMul,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& X2 != X3
& X1 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X1,X2) != sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& sdtlseqdt0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(m__2287,hypothesis,
( sdtlseqdt0(xm,xp)
& ? [X1] :
( sdtpldt0(xm,X1) = xp
& aNaturalNumber0(X1) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [X1] :
( sdtpldt0(xn,X1) = xp
& aNaturalNumber0(X1) )
& xn != xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
fof(m__2389,hypothesis,
( sdtlseqdt0(xp,xk)
& ? [X1] :
( sdtpldt0(xp,X1) = xk
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2389) ).
fof(m__1870,hypothesis,
~ ( sdtlseqdt0(xp,xn)
| ? [X1] :
( sdtpldt0(xp,X1) = xn
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(m__2315,hypothesis,
~ ( xk = sz10
| xk = sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).
fof(m__2075,hypothesis,
~ ( sdtlseqdt0(xp,xm)
| ? [X1] :
( sdtpldt0(xp,X1) = xm
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2075) ).
fof(c_0_21,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])])]) ).
fof(c_0_22,hypothesis,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xr,esk14_0)
& aNaturalNumber0(esk14_0)
& sdtpldt0(xr,esk13_0) = xk
& aNaturalNumber0(esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2362])]) ).
fof(c_0_23,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_24,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mLETotal]) ).
fof(c_0_25,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])])]) ).
cnf(c_0_26,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_27,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_29,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_30,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_31,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xr,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_32,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_23])])])])])]) ).
fof(c_0_33,plain,
! [X50,X51] :
( ( ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X50)
| sdtlseqdt0(X50,X51)
| sdtlseqdt0(X51,X50) )
& ( ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X50)
| sdtlseqdt0(X50,X51)
| X51 != X50 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
fof(c_0_34,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_35,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_36,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,hypothesis,
sdtasdt0(xm,xn) = sdtasdt0(xp,xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29])]) ).
cnf(c_0_38,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,hypothesis,
sdtasdt0(xr,esk14_0) = sdtasdt0(xp,xk),
inference(rw,[status(thm)],[c_0_31,c_0_26]) ).
cnf(c_0_40,hypothesis,
aNaturalNumber0(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_41,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
fof(c_0_44,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_45,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_34])])])])])]) ).
cnf(c_0_46,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_47,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(xp,xk),X1) = sdtasdt0(xm,sdtasdt0(xn,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_28]),c_0_29])]) ).
cnf(c_0_48,hypothesis,
aNaturalNumber0(sdtasdt0(xp,xk)),
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_49,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_50,plain,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& X2 != X3
& X1 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X1,X2) != sdtasdt0(X1,X3) ) ) ),
inference(fof_simplification,[status(thm)],[mMonMul]) ).
fof(c_0_51,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_52,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,xk)
| sdtlseqdt0(xk,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_53,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
inference(fof_simplification,[status(thm)],[mMonMul2]) ).
fof(c_0_54,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_44])])])])]) ).
cnf(c_0_55,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_56,hypothesis,
sdtasdt0(xm,sdtasdt0(xn,sz00)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_49])]) ).
fof(c_0_57,plain,
! [X45,X46] :
( X45 = X46
| ~ sdtlseqdt0(X46,X45)
| ~ sdtlseqdt0(X45,X46)
| ~ aNaturalNumber0(X46)
| ~ aNaturalNumber0(X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])])]) ).
fof(c_0_58,plain,
! [X55,X56,X57] :
( ( ~ aNaturalNumber0(X57)
| ~ aNaturalNumber0(X56)
| ~ aNaturalNumber0(X55)
| ~ sdtlseqdt0(X56,X57)
| X56 = X57
| X55 = sz00
| sdtlseqdt0(sdtasdt0(X56,X55),sdtasdt0(X57,X55)) )
& ( ~ aNaturalNumber0(X57)
| ~ aNaturalNumber0(X56)
| ~ aNaturalNumber0(X55)
| ~ sdtlseqdt0(X56,X57)
| X56 = X57
| X55 = sz00
| sdtasdt0(X56,X55) != sdtasdt0(X57,X55) )
& ( ~ aNaturalNumber0(X57)
| ~ aNaturalNumber0(X56)
| ~ aNaturalNumber0(X55)
| ~ sdtlseqdt0(X56,X57)
| X56 = X57
| X55 = sz00
| sdtlseqdt0(sdtasdt0(X55,X56),sdtasdt0(X55,X57)) )
& ( ~ aNaturalNumber0(X57)
| ~ aNaturalNumber0(X56)
| ~ aNaturalNumber0(X55)
| ~ sdtlseqdt0(X56,X57)
| X56 = X57
| X55 = sz00
| sdtasdt0(X55,X56) != sdtasdt0(X55,X57) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])])]) ).
fof(c_0_59,hypothesis,
( sdtlseqdt0(xm,xp)
& ? [X1] :
( sdtpldt0(xm,X1) = xp
& aNaturalNumber0(X1) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [X1] :
( sdtpldt0(xn,X1) = xp
& aNaturalNumber0(X1) )
& xn != xp ),
inference(fof_simplification,[status(thm)],[m__2287]) ).
cnf(c_0_60,plain,
( ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_61,hypothesis,
( sdtlseqdt0(xk,xn)
| sdtlseqdt0(xn,xk) ),
inference(spm,[status(thm)],[c_0_52,c_0_28]) ).
fof(c_0_62,hypothesis,
( sdtlseqdt0(xp,xk)
& sdtpldt0(xp,esk15_0) = xk
& aNaturalNumber0(esk15_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2389])]) ).
fof(c_0_63,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])])])]) ).
fof(c_0_64,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_53])])]) ).
cnf(c_0_65,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| X1 = sz00
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_66,hypothesis,
sdtasdt0(xp,esk9_0) = sdtasdt0(xp,xk),
inference(rw,[status(thm)],[c_0_55,c_0_26]) ).
cnf(c_0_67,hypothesis,
aNaturalNumber0(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_68,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_69,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_70,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(xp,xk),X1) = sdtasdt0(xn,sdtasdt0(xm,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_26]),c_0_29]),c_0_28])]) ).
cnf(c_0_71,hypothesis,
sdtasdt0(xm,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_46]),c_0_28])]) ).
cnf(c_0_72,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_73,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X3)
| X1 = X3
| X2 = sz00
| sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_74,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| X2 = sz00
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_75,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| X2 = X3
| X1 = sz00
| sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_76,hypothesis,
( sdtlseqdt0(xm,xp)
& sdtpldt0(xm,esk11_0) = xp
& aNaturalNumber0(esk11_0)
& xm != xp
& sdtlseqdt0(xn,xp)
& sdtpldt0(xn,esk10_0) = xp
& aNaturalNumber0(esk10_0)
& xn != xp ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_59])])]) ).
cnf(c_0_77,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,xk)
| sdtlseqdt0(X1,xn)
| sdtlseqdt0(xn,xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_28]),c_0_43])]) ).
cnf(c_0_78,hypothesis,
sdtlseqdt0(xp,xk),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_79,hypothesis,
~ sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
fof(c_0_80,hypothesis,
( xk != sz10
& xk != sz00 ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2315])]) ).
cnf(c_0_81,hypothesis,
( sdtpldt0(xp,X1) != xn
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_82,hypothesis,
sdtpldt0(xp,esk15_0) = xk,
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_83,hypothesis,
aNaturalNumber0(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_84,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_85,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xp,X1) != sdtasdt0(xp,xk)
| X1 = esk9_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_68])]),c_0_69]) ).
cnf(c_0_86,hypothesis,
sdtasdt0(xn,sz00) = sz00,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_70]),c_0_48]),c_0_49])]),c_0_71]) ).
cnf(c_0_87,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(sdtasdt0(X3,X1),sdtasdt0(X2,X1))
| X2 = X3
| X1 = sz00 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_38]),c_0_38]),c_0_74]) ).
cnf(c_0_88,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(xn,X1)
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xm,X1))
| xn = X1
| sz00 = xm ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_37]),c_0_28]),c_0_29])]) ).
cnf(c_0_89,hypothesis,
sdtlseqdt0(xm,xp),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_90,hypothesis,
sdtlseqdt0(xn,xk),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_68])]),c_0_79]) ).
cnf(c_0_91,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_92,hypothesis,
xm != xp,
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_93,hypothesis,
xk != xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83])]) ).
cnf(c_0_94,hypothesis,
( sdtlseqdt0(xp,sdtasdt0(xp,xk))
| esk9_0 = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_66]),c_0_68]),c_0_67])]) ).
cnf(c_0_95,hypothesis,
esk9_0 = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_85]),c_0_43])]) ).
cnf(c_0_96,hypothesis,
sdtasdt0(sz00,xn) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_86]),c_0_49]),c_0_28])]) ).
cnf(c_0_97,hypothesis,
sz00 = xm,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),c_0_68]),c_0_43]),c_0_29]),c_0_90])]),c_0_91]),c_0_92]),c_0_93]) ).
fof(c_0_98,hypothesis,
! [X103] :
( ~ sdtlseqdt0(xp,xm)
& ( sdtpldt0(xp,X103) != xm
| ~ aNaturalNumber0(X103) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2075])])])]) ).
cnf(c_0_99,hypothesis,
sdtlseqdt0(xp,sdtasdt0(xp,xk)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95]),c_0_91]) ).
cnf(c_0_100,hypothesis,
sdtasdt0(xp,xk) = xm,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97]),c_0_37]),c_0_97]) ).
cnf(c_0_101,hypothesis,
~ sdtlseqdt0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_102,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_100]),c_0_101]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM503+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 02:37:59 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 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
% 7.17/1.44 % Version: 3.5.1
% 7.17/1.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 7.17/1.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.17/1.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 7.17/1.44 % Starting new_bool_3 with 300s (1) cores
% 7.17/1.44 % Starting new_bool_1 with 300s (1) cores
% 7.17/1.44 % Starting sh5l with 300s (1) cores
% 7.17/1.44 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 784775 completed with status 0
% 7.17/1.44 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 7.17/1.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 7.17/1.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.17/1.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 7.17/1.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.17/1.44 % No SInE strategy applied
% 7.17/1.44 % Search class: FGHSF-FSLM32-SFFFFFNN
% 7.17/1.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.17/1.44 % Starting SubtermCWHack with 136s (1) cores
% 7.17/1.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 7.17/1.44 % Starting G-E--_107_C41_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 7.17/1.44 % Starting new_bool_3 with 136s (1) cores
% 7.17/1.44 % Starting U----_116_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN1 with 136s (1) cores
% 7.17/1.44 % SubtermCWHack with pid 784782 completed with status 0
% 7.17/1.44 % Result found by SubtermCWHack
% 7.17/1.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 7.17/1.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.17/1.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 7.17/1.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.17/1.44 % No SInE strategy applied
% 7.17/1.44 % Search class: FGHSF-FSLM32-SFFFFFNN
% 7.17/1.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.17/1.44 % Starting SubtermCWHack with 136s (1) cores
% 7.17/1.44 % Preprocessing time : 0.002 s
% 7.17/1.44
% 7.17/1.44 % Proof found!
% 7.17/1.44 % SZS status ContradictoryAxioms
% 7.17/1.44 % SZS output start CNFRefutation
% See solution above
% 7.17/1.44 % Parsed axioms : 51
% 7.17/1.44 % Removed by relevancy pruning/SinE : 0
% 7.17/1.44 % Initial clauses : 247
% 7.17/1.44 % Removed in clause preprocessing : 3
% 7.17/1.44 % Initial clauses in saturation : 244
% 7.17/1.44 % Processed clauses : 6991
% 7.17/1.44 % ...of these trivial : 245
% 7.17/1.44 % ...subsumed : 3462
% 7.17/1.44 % ...remaining for further processing : 3284
% 7.17/1.44 % Other redundant clauses eliminated : 430
% 7.17/1.44 % Clauses deleted for lack of memory : 0
% 7.17/1.44 % Backward-subsumed : 697
% 7.17/1.44 % Backward-rewritten : 1269
% 7.17/1.44 % Generated clauses : 51756
% 7.17/1.44 % ...of the previous two non-redundant : 46749
% 7.17/1.44 % ...aggressively subsumed : 0
% 7.17/1.44 % Contextual simplify-reflections : 100
% 7.17/1.44 % Paramodulations : 51275
% 7.17/1.44 % Factorizations : 3
% 7.17/1.44 % NegExts : 0
% 7.17/1.44 % Equation resolutions : 446
% 7.17/1.44 % Disequality decompositions : 0
% 7.17/1.44 % Total rewrite steps : 58757
% 7.17/1.44 % ...of those cached : 58484
% 7.17/1.44 % Propositional unsat checks : 0
% 7.17/1.44 % Propositional check models : 0
% 7.17/1.44 % Propositional check unsatisfiable : 0
% 7.17/1.44 % Propositional clauses : 0
% 7.17/1.44 % Propositional clauses after purity: 0
% 7.17/1.44 % Propositional unsat core size : 0
% 7.17/1.44 % Propositional preprocessing time : 0.000
% 7.17/1.44 % Propositional encoding time : 0.000
% 7.17/1.44 % Propositional solver time : 0.000
% 7.17/1.44 % Success case prop preproc time : 0.000
% 7.17/1.44 % Success case prop encoding time : 0.000
% 7.17/1.44 % Success case prop solver time : 0.000
% 7.17/1.44 % Current number of processed clauses : 1275
% 7.17/1.44 % Positive orientable unit clauses : 273
% 7.17/1.44 % Positive unorientable unit clauses: 0
% 7.17/1.44 % Negative unit clauses : 56
% 7.17/1.44 % Non-unit-clauses : 946
% 7.17/1.44 % Current number of unprocessed clauses: 39217
% 7.17/1.44 % ...number of literals in the above : 242589
% 7.17/1.44 % Current number of archived formulas : 0
% 7.17/1.44 % Current number of archived clauses : 1998
% 7.17/1.44 % Clause-clause subsumption calls (NU) : 885923
% 7.17/1.44 % Rec. Clause-clause subsumption calls : 307622
% 7.17/1.44 % Non-unit clause-clause subsumptions : 3494
% 7.17/1.44 % Unit Clause-clause subsumption calls : 46849
% 7.17/1.44 % Rewrite failures with RHS unbound : 0
% 7.17/1.44 % BW rewrite match attempts : 1162
% 7.17/1.44 % BW rewrite match successes : 92
% 7.17/1.44 % Condensation attempts : 0
% 7.17/1.44 % Condensation successes : 0
% 7.17/1.44 % Termbank termtop insertions : 1046977
% 7.17/1.44 % Search garbage collected termcells : 2480
% 7.17/1.44
% 7.17/1.44 % -------------------------------------------------
% 7.17/1.44 % User time : 0.920 s
% 7.17/1.44 % System time : 0.034 s
% 7.17/1.44 % Total time : 0.953 s
% 7.17/1.44 % Maximum resident set size: 4164 pages
% 7.17/1.44
% 7.17/1.44 % -------------------------------------------------
% 7.17/1.44 % User time : 4.539 s
% 7.17/1.44 % System time : 0.170 s
% 7.17/1.44 % Total time : 4.709 s
% 7.17/1.44 % Maximum resident set size: 4864 pages
% 7.17/1.44 % E exiting
%------------------------------------------------------------------------------