%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM528+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 01:55:22 PM UTC 2026
% Result : Theorem 0.36s 0.72s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 20
% Syntax : Number of formulae : 96 ( 25 unt; 0 def)
% Number of atoms : 338 ( 129 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 378 ( 136 ~; 137 |; 78 &)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 53 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2987,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
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(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__3046,hypothesis,
( doDivides0(xp,xn)
& ? [X1] :
( xn = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [X1] :
( sdtasdt0(xn,xn) = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
fof(m__3082,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3082) ).
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(m__3059,hypothesis,
( xq = sdtsldt0(xn,xp)
& xn = sdtasdt0(xp,xq)
& aNaturalNumber0(xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
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(m__,conjecture,
( ( sdtlseqdt0(xm,xn)
| ? [X1] :
( sdtpldt0(xm,X1) = xn
& aNaturalNumber0(X1) ) )
& xm != xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__3152,hypothesis,
( ( sdtlseqdt0(xn,xm)
| ? [X1] :
( sdtpldt0(xn,X1) = xm
& aNaturalNumber0(X1) ) )
=> ( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
& ? [X1] :
( sdtpldt0(sdtasdt0(xn,xn),X1) = sdtasdt0(xm,xm)
& aNaturalNumber0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3152) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
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(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(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X2 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__3025,hypothesis,
( isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( xp = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xp
| X1 = sz10 ) )
& xp != sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).
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(c_0_20,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_simplification,[status(thm)],[m__2987]) ).
fof(c_0_21,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_22,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])])]) ).
fof(c_0_23,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_nnf,[status(thm)],[c_0_20]) ).
fof(c_0_24,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_21])])])])]) ).
fof(c_0_25,hypothesis,
( doDivides0(xp,xn)
& xn = sdtasdt0(xp,esk8_0)
& aNaturalNumber0(esk8_0)
& doDivides0(xp,sdtasdt0(xn,xn))
& sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0)
& aNaturalNumber0(esk7_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__3046])]) ).
cnf(c_0_26,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(split_conjunct,[status(thm)],[m__3082]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_29,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mLETotal]) ).
cnf(c_0_30,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| X1 = sz00
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,hypothesis,
sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,hypothesis,
aNaturalNumber0(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xq,xq))
| aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_35,hypothesis,
aNaturalNumber0(xq),
inference(split_conjunct,[status(thm)],[m__3059]) ).
fof(c_0_36,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
inference(fof_simplification,[status(thm)],[mMonMul2]) ).
fof(c_0_37,negated_conjecture,
~ ( ( sdtlseqdt0(xm,xn)
| ? [X1] :
( sdtpldt0(xm,X1) = xn
& aNaturalNumber0(X1) ) )
& xm != xn ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_38,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_29])])])]) ).
fof(c_0_39,hypothesis,
! [X103] :
( ( ~ sdtlseqdt0(xn,xm)
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) )
& ( ~ sdtlseqdt0(xn,xm)
| sdtpldt0(sdtasdt0(xn,xn),esk9_0) = sdtasdt0(xm,xm) )
& ( ~ sdtlseqdt0(xn,xm)
| aNaturalNumber0(esk9_0) )
& ( sdtpldt0(xn,X103) != xm
| ~ aNaturalNumber0(X103)
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) )
& ( sdtpldt0(xn,X103) != xm
| ~ aNaturalNumber0(X103)
| sdtpldt0(sdtasdt0(xn,xn),esk9_0) = sdtasdt0(xm,xm) )
& ( sdtpldt0(xn,X103) != xm
| ~ aNaturalNumber0(X103)
| aNaturalNumber0(esk9_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3152])])])])])]) ).
fof(c_0_40,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_41,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xp,X1) != sdtasdt0(xn,xn)
| X1 = esk7_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_28])]),c_0_33]) ).
cnf(c_0_42,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_43,hypothesis,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_26]),c_0_35])]) ).
fof(c_0_44,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_36])])]) ).
fof(c_0_45,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_46,negated_conjecture,
~ ( ( sdtlseqdt0(xm,xn)
| ? [X1] :
( sdtpldt0(xm,X1) = xn
& aNaturalNumber0(X1) ) )
& xm != xn ),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
cnf(c_0_47,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_48,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_49,hypothesis,
( sdtpldt0(xn,X1) != xm
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_50,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_52,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_53,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])])]) ).
cnf(c_0_54,hypothesis,
( ~ sdtlseqdt0(xn,xm)
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_55,hypothesis,
sdtasdt0(xm,xm) = esk7_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_56,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_57,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_58,negated_conjecture,
! [X105] :
( ( xm = xn
| ~ sdtlseqdt0(xm,xn) )
& ( xm = xn
| sdtpldt0(xm,X105) != xn
| ~ aNaturalNumber0(X105) ) ),
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_46])])])])]) ).
cnf(c_0_59,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(xm,X1)
| sdtlseqdt0(X1,xm) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_60,hypothesis,
( xm != xn
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52])]) ).
cnf(c_0_61,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_62,hypothesis,
( ~ sdtlseqdt0(xn,xm)
| sdtlseqdt0(sdtasdt0(xn,xn),esk7_0) ),
inference(rw,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_63,hypothesis,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_31]),c_0_32]),c_0_28])]) ).
cnf(c_0_64,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| X1 = sz00 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
fof(c_0_65,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_66,negated_conjecture,
( ~ sdtlseqdt0(xm,xn)
| xm = xn ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_67,hypothesis,
( sdtlseqdt0(xn,xm)
| sdtlseqdt0(xm,xn) ),
inference(spm,[status(thm)],[c_0_59,c_0_52]) ).
cnf(c_0_68,hypothesis,
( xm != xn
| sdtlseqdt0(sdtasdt0(xn,xn),esk7_0) ),
inference(rw,[status(thm)],[c_0_60,c_0_55]) ).
cnf(c_0_69,hypothesis,
( ~ sdtlseqdt0(xn,xm)
| ~ sdtlseqdt0(esk7_0,sdtasdt0(xn,xn))
| sdtasdt0(xn,xn) = esk7_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]),c_0_32])]) ).
cnf(c_0_70,hypothesis,
sdtlseqdt0(esk7_0,sdtasdt0(xn,xn)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_31]),c_0_32]),c_0_28])]),c_0_33]) ).
cnf(c_0_71,plain,
( ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_72,negated_conjecture,
( sdtlseqdt0(xn,xm)
| xm = xn ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(xn,X1)
| sdtlseqdt0(X1,xn) ),
inference(spm,[status(thm)],[c_0_47,c_0_52]) ).
cnf(c_0_74,hypothesis,
( ~ sdtlseqdt0(esk7_0,sdtasdt0(xn,xn))
| xm != xn
| sdtasdt0(xn,xn) = esk7_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_68]),c_0_63]),c_0_32])]) ).
cnf(c_0_75,hypothesis,
( ~ sdtlseqdt0(xn,xm)
| sdtasdt0(xn,xn) = esk7_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]) ).
cnf(c_0_76,negated_conjecture,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,xn)
| sdtlseqdt0(X1,xm)
| xm = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_48]),c_0_52])]) ).
cnf(c_0_77,hypothesis,
sdtlseqdt0(xn,xn),
inference(spm,[status(thm)],[c_0_73,c_0_52]) ).
cnf(c_0_78,hypothesis,
( xm != xn
| sdtasdt0(xn,xn) = esk7_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_70])]) ).
fof(c_0_79,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_80,negated_conjecture,
sdtasdt0(xn,xn) = esk7_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),c_0_52])]),c_0_78]) ).
cnf(c_0_81,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_82,hypothesis,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_83,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
fof(c_0_84,hypothesis,
( isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( xp = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xp
| X1 = sz10 ) )
& xp != sz10 ),
inference(fof_simplification,[status(thm)],[m__3025]) ).
cnf(c_0_85,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| X2 = sz00
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_86,hypothesis,
sdtasdt0(xp,esk7_0) = esk7_0,
inference(rw,[status(thm)],[c_0_31,c_0_80]) ).
cnf(c_0_87,hypothesis,
esk7_0 != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_55]),c_0_48])]),c_0_82]) ).
fof(c_0_88,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_89,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_83]) ).
fof(c_0_90,hypothesis,
! [X99,X100] :
( 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 ),
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_84])])])])]) ).
cnf(c_0_91,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,esk7_0) != esk7_0
| xp = X1 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_32]),c_0_28])]),c_0_87]) ).
cnf(c_0_92,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_93,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_94,hypothesis,
xp != sz10,
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_95,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_32])]),c_0_94]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM528+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n011.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 02:37:55 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.51 Running first-order theorem proving
% 0.27/0.51 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
% 0.36/0.72 % Version: 3.5.1
% 0.36/0.72 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.36/0.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.36/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.36/0.72 % Starting new_bool_3 with 300s (1) cores
% 0.36/0.72 % Starting new_bool_1 with 300s (1) cores
% 0.36/0.72 % Starting sh5l with 300s (1) cores
% 0.36/0.72 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 785818 completed with status 0
% 0.36/0.72 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.36/0.72 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.36/0.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.36/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.36/0.72 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.36/0.72 % No SInE strategy applied
% 0.36/0.72 % Search class: FGHSF-FSMM32-SFFFFFNN
% 0.36/0.72 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.36/0.72 % Starting SubtermCWHack with 136s (1) cores
% 0.36/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.36/0.72 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S0Y with 136s (1) cores
% 0.36/0.72 % Starting new_bool_3 with 136s (1) cores
% 0.36/0.72 % Starting new_bool_1 with 136s (1) cores
% 0.36/0.72 % G-E--_208_C18_F1_AE_CS_SP_PS_S0Y with pid 785826 completed with status 0
% 0.36/0.72 % Result found by G-E--_208_C18_F1_AE_CS_SP_PS_S0Y
% 0.36/0.72 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.36/0.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.36/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.36/0.72 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.36/0.72 % No SInE strategy applied
% 0.36/0.72 % Search class: FGHSF-FSMM32-SFFFFFNN
% 0.36/0.72 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.36/0.72 % Starting SubtermCWHack with 136s (1) cores
% 0.36/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.36/0.72 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S0Y with 136s (1) cores
% 0.36/0.72 % Preprocessing time : 0.002 s
% 0.36/0.72 % Presaturation interreduction done
% 0.36/0.72
% 0.36/0.72 % Proof found!
% 0.36/0.72 % SZS status Theorem
% 0.36/0.72 % SZS output start CNFRefutation
% See solution above
% 0.36/0.72 % Parsed axioms : 48
% 0.36/0.72 % Removed by relevancy pruning/SinE : 0
% 0.36/0.72 % Initial clauses : 107
% 0.36/0.72 % Removed in clause preprocessing : 3
% 0.36/0.72 % Initial clauses in saturation : 104
% 0.36/0.72 % Processed clauses : 1881
% 0.36/0.72 % ...of these trivial : 22
% 0.36/0.72 % ...subsumed : 1024
% 0.36/0.72 % ...remaining for further processing : 835
% 0.36/0.72 % Other redundant clauses eliminated : 32
% 0.36/0.72 % Clauses deleted for lack of memory : 0
% 0.36/0.72 % Backward-subsumed : 190
% 0.36/0.72 % Backward-rewritten : 191
% 0.36/0.72 % Generated clauses : 4684
% 0.36/0.72 % ...of the previous two non-redundant : 4152
% 0.36/0.72 % ...aggressively subsumed : 0
% 0.36/0.72 % Contextual simplify-reflections : 60
% 0.36/0.72 % Paramodulations : 4605
% 0.36/0.72 % Factorizations : 1
% 0.36/0.72 % NegExts : 0
% 0.36/0.72 % Equation resolutions : 78
% 0.36/0.72 % Disequality decompositions : 0
% 0.36/0.72 % Total rewrite steps : 5406
% 0.36/0.72 % ...of those cached : 5355
% 0.36/0.72 % Propositional unsat checks : 0
% 0.36/0.72 % Propositional check models : 0
% 0.36/0.72 % Propositional check unsatisfiable : 0
% 0.36/0.72 % Propositional clauses : 0
% 0.36/0.72 % Propositional clauses after purity: 0
% 0.36/0.72 % Propositional unsat core size : 0
% 0.36/0.72 % Propositional preprocessing time : 0.000
% 0.36/0.72 % Propositional encoding time : 0.000
% 0.36/0.72 % Propositional solver time : 0.000
% 0.36/0.72 % Success case prop preproc time : 0.000
% 0.36/0.72 % Success case prop encoding time : 0.000
% 0.36/0.72 % Success case prop solver time : 0.000
% 0.36/0.72 % Current number of processed clauses : 354
% 0.36/0.72 % Positive orientable unit clauses : 46
% 0.36/0.72 % Positive unorientable unit clauses: 0
% 0.36/0.72 % Negative unit clauses : 13
% 0.36/0.72 % Non-unit-clauses : 295
% 0.36/0.72 % Current number of unprocessed clauses: 2193
% 0.36/0.72 % ...number of literals in the above : 11279
% 0.36/0.72 % Current number of archived formulas : 0
% 0.36/0.72 % Current number of archived clauses : 480
% 0.36/0.72 % Clause-clause subsumption calls (NU) : 35348
% 0.36/0.72 % Rec. Clause-clause subsumption calls : 15461
% 0.36/0.72 % Non-unit clause-clause subsumptions : 853
% 0.36/0.72 % Unit Clause-clause subsumption calls : 1486
% 0.36/0.72 % Rewrite failures with RHS unbound : 0
% 0.36/0.72 % BW rewrite match attempts : 27
% 0.36/0.72 % BW rewrite match successes : 27
% 0.36/0.72 % Condensation attempts : 0
% 0.36/0.72 % Condensation successes : 0
% 0.36/0.72 % Termbank termtop insertions : 77635
% 0.36/0.72 % Search garbage collected termcells : 1715
% 0.36/0.72
% 0.36/0.72 % -------------------------------------------------
% 0.36/0.72 % User time : 0.140 s
% 0.36/0.72 % System time : 0.011 s
% 0.36/0.72 % Total time : 0.151 s
% 0.36/0.72 % Maximum resident set size: 3952 pages
% 0.36/0.72
% 0.36/0.72 % -------------------------------------------------
% 0.36/0.72 % User time : 0.537 s
% 0.36/0.72 % System time : 0.041 s
% 0.36/0.72 % Total time : 0.577 s
% 0.36/0.72 % Maximum resident set size: 4864 pages
% 0.36/0.72 % E exiting
%------------------------------------------------------------------------------