%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM511+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 : n014.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 01:55:18 PM UTC 2026
% Result : Theorem 11.31s 2.09s
% Output : CNFRefutation 11.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 73 ( 27 unt; 0 def)
% Number of atoms : 306 ( 121 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 349 ( 116 ~; 121 |; 83 &)
% ( 3 <=>; 26 =>; 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 : 16 ( 16 usr; 12 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 45 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
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(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
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(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mDivAsso,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( aNaturalNumber0(X3)
=> sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivAsso) ).
fof(m__,conjecture,
( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ? [X1] :
( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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__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/sandbox/benchmark/theBenchmark.p',m__2362) ).
fof(m__2306,hypothesis,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
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(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(c_0_13,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_14,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_15,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefQuot]) ).
fof(c_0_16,plain,
! [X33,X34,X36] :
( ( ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X33)
| doDivides0(X33,X34)
| X34 != sdtasdt0(X33,X36)
| ~ aNaturalNumber0(X36) )
& ( ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X33)
| ~ doDivides0(X33,X34)
| X34 = sdtasdt0(X33,esk16_2(X33,X34)) )
& ( ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X33)
| ~ doDivides0(X33,X34)
| aNaturalNumber0(esk16_2(X33,X34)) ) ),
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_17,plain,
! [X48,X49] :
( aNaturalNumber0(sdtasdt0(X48,X49))
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X48) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
fof(c_0_18,plain,
! [X59,X60,X61] :
( ( ~ aNaturalNumber0(X59)
| X59 = sz00
| ~ aNaturalNumber0(X61)
| ~ aNaturalNumber0(X60)
| X60 = X61
| sdtasdt0(X60,X59) != sdtasdt0(X61,X59) )
& ( ~ aNaturalNumber0(X59)
| X59 = sz00
| ~ aNaturalNumber0(X61)
| ~ aNaturalNumber0(X60)
| X60 = X61
| sdtasdt0(X59,X60) != sdtasdt0(X59,X61) ) ),
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_13])])])])]) ).
fof(c_0_19,hypothesis,
! [X22,X23] :
( isPrime0(xr)
& ( X22 = xr
| X22 = sz10
| ~ aNaturalNumber0(X22)
| ~ doDivides0(X22,xr) )
& ( X22 = xr
| X22 = sz10
| ~ aNaturalNumber0(X22)
| xr != sdtasdt0(X22,X23)
| ~ aNaturalNumber0(X23) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,esk8_0)
& aNaturalNumber0(esk8_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_14])])])])])]) ).
fof(c_0_20,plain,
! [X108,X109,X110] :
( ( ~ aNaturalNumber0(X109)
| ~ aNaturalNumber0(X108)
| ~ doDivides0(X108,X109)
| X108 = sz00
| X110 = sdtsldt0(X109,X108)
| X109 != sdtasdt0(X108,X110)
| ~ aNaturalNumber0(X110) )
& ( ~ aNaturalNumber0(X109)
| ~ aNaturalNumber0(X108)
| ~ doDivides0(X108,X109)
| X108 = sz00
| X110 != sdtsldt0(X109,X108)
| X109 = sdtasdt0(X108,X110) )
& ( ~ aNaturalNumber0(X109)
| ~ aNaturalNumber0(X108)
| ~ doDivides0(X108,X109)
| X108 = sz00
| X110 != sdtsldt0(X109,X108)
| aNaturalNumber0(X110) ) ),
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_15])])])])]) ).
cnf(c_0_21,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( aNaturalNumber0(X3)
=> sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1) ) ) ),
inference(fof_simplification,[status(thm)],[mDivAsso]) ).
cnf(c_0_24,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| X1 = sz00
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,hypothesis,
xk = sdtasdt0(xr,esk8_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,hypothesis,
aNaturalNumber0(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,hypothesis,
xr != sz00,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2)
| X2 = sz00
| X1 = sdtasdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_30,negated_conjecture,
~ ( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ? [X1] :
( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_31,hypothesis,
( doDivides0(xr,xn)
& xn = sdtasdt0(xr,esk14_0)
& aNaturalNumber0(esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2487])]) ).
cnf(c_0_32,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| X3 = sz00
| X1 = sdtsldt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_33,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_21]),c_0_22]) ).
fof(c_0_34,hypothesis,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xr,esk10_0)
& aNaturalNumber0(esk10_0)
& sdtpldt0(xr,esk9_0) = xk
& aNaturalNumber0(esk9_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2362])]) ).
fof(c_0_35,plain,
! [X111,X112,X113] :
( sdtasdt0(X113,sdtsldt0(X112,X111)) = sdtsldt0(sdtasdt0(X113,X112),X111)
| ~ aNaturalNumber0(X113)
| ~ doDivides0(X111,X112)
| X111 = sz00
| ~ aNaturalNumber0(X112)
| ~ aNaturalNumber0(X111) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
cnf(c_0_36,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xr,X1) != xk
| X1 = esk8_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27])]),c_0_28]) ).
cnf(c_0_37,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| X1 = sz00
| sdtasdt0(X1,sdtsldt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_38,hypothesis,
doDivides0(xr,xk),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_39,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_40,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X1 != sdtsldt0(X2,X3)
| X3 = sz00
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_41,negated_conjecture,
! [X31] :
( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
& ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,X31)
| ~ aNaturalNumber0(X31) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])]) ).
fof(c_0_42,plain,
! [X50,X51] :
( sdtasdt0(X50,X51) = sdtasdt0(X51,X50)
| ~ aNaturalNumber0(X51)
| ~ aNaturalNumber0(X50) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
fof(c_0_43,hypothesis,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& sdtpldt0(sdtsldt0(xn,xr),esk15_0) = xn
& aNaturalNumber0(esk15_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_44,hypothesis,
xn = sdtasdt0(xr,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_45,hypothesis,
aNaturalNumber0(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_46,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = sz00
| sdtsldt0(sdtasdt0(X1,X2),X1) = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_32]),c_0_22]),c_0_33]) ).
cnf(c_0_47,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xr,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_48,hypothesis,
aNaturalNumber0(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_49,plain,
( ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1)
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_50,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_51,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_52,hypothesis,
( ~ aNaturalNumber0(sdtsldt0(xk,xr))
| sdtsldt0(xk,xr) = esk8_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_27])]),c_0_28])]),c_0_38]),c_0_39])]) ).
cnf(c_0_53,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(sdtsldt0(X2,X1))
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_40]) ).
cnf(c_0_54,negated_conjecture,
~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_55,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_56,hypothesis,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_57,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_58,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xr,X1) != xn
| X1 = esk14_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_44]),c_0_45]),c_0_27])]),c_0_28]) ).
cnf(c_0_59,hypothesis,
xn = sdtasdt0(xr,sdtsldt0(xn,xr)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_60,hypothesis,
sdtsldt0(sdtasdt0(xn,xm),xr) = esk10_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_27]),c_0_48])]),c_0_28]) ).
cnf(c_0_61,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xk)
| X1 = sz00
| sdtsldt0(sdtasdt0(xn,xm),X1) = sdtasdt0(xp,sdtsldt0(xk,X1)) ),
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_39])]) ).
cnf(c_0_62,hypothesis,
sdtsldt0(xk,xr) = esk8_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_38]),c_0_27]),c_0_39])]),c_0_28]) ).
cnf(c_0_63,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xm,sdtsldt0(xn,xr))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_57])]) ).
cnf(c_0_64,hypothesis,
sdtsldt0(xn,xr) = esk14_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_56])]) ).
cnf(c_0_65,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X3,X1)
| X3 = sz00
| sdtsldt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X2,sdtsldt0(X1,X3)) ),
inference(spm,[status(thm)],[c_0_49,c_0_55]) ).
cnf(c_0_66,hypothesis,
doDivides0(xr,xn),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_67,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_68,hypothesis,
sdtasdt0(xp,esk8_0) = esk10_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_38]),c_0_27])]),c_0_28]) ).
cnf(c_0_69,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xm,esk14_0)),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_70,hypothesis,
sdtasdt0(xm,esk14_0) = esk10_0,
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_60,c_0_65]),c_0_64]),c_0_66]),c_0_57]),c_0_67]),c_0_27])]),c_0_28]) ).
cnf(c_0_71,hypothesis,
doDivides0(xp,esk10_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_68]),c_0_51]),c_0_26])]) ).
cnf(c_0_72,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70]),c_0_71])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM511+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.53 % Computer : n014.cluster.edu
% 0.11/0.53 % Model : x86_64 x86_64
% 0.11/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.53 % Memory : 8046.5625MB
% 0.11/0.53 % OS : Linux 6.8.0-71-generic
% 0.11/0.53 % CPULimit : 300
% 0.11/0.53 % WCLimit : 300
% 0.11/0.53 % DateTime : Mon Sep 21 02:36:20 UTC 2026
% 0.11/0.54 % CPUTime :
% 0.11/0.54 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.57 Running first-order theorem proving
% 0.11/0.57 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
% 11.31/2.09 % Version: 3.5.1
% 11.31/2.09 % Preprocessing class: FSLSSMSSSSSNFFN.
% 11.31/2.09 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.31/2.09 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 11.31/2.09 % Starting new_bool_3 with 300s (1) cores
% 11.31/2.09 % Starting new_bool_1 with 300s (1) cores
% 11.31/2.09 % Starting sh5l with 300s (1) cores
% 11.31/2.09 % new_bool_3 with pid 2961289 completed with status 0
% 11.31/2.09 % Result found by new_bool_3
% 11.31/2.09 % Preprocessing class: FSLSSMSSSSSNFFN.
% 11.31/2.09 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.31/2.09 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 11.31/2.09 % Starting new_bool_3 with 300s (1) cores
% 11.31/2.09 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 11.31/2.09 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 11.31/2.09 % Search class: FGHSF-FSLM32-SFFFFFNN
% 11.31/2.09 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 11.31/2.09 % Starting SubtermCWHack with 31s (1) cores
% 11.31/2.09 % SubtermCWHack with pid 2961293 completed with status 0
% 11.31/2.09 % Result found by SubtermCWHack
% 11.31/2.09 % Preprocessing class: FSLSSMSSSSSNFFN.
% 11.31/2.09 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.31/2.09 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 11.31/2.09 % Starting new_bool_3 with 300s (1) cores
% 11.31/2.09 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 11.31/2.09 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 11.31/2.09 % Search class: FGHSF-FSLM32-SFFFFFNN
% 11.31/2.09 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 11.31/2.09 % Starting SubtermCWHack with 31s (1) cores
% 11.31/2.09 % Preprocessing time : 0.003 s
% 11.31/2.09
% 11.31/2.09 % Proof found!
% 11.31/2.09 % SZS status Theorem
% 11.31/2.09 % SZS output start CNFRefutation
% See solution above
% 11.31/2.09 % Parsed axioms : 54
% 11.31/2.09 % Removed by relevancy pruning/SinE : 1
% 11.31/2.09 % Initial clauses : 265
% 11.31/2.09 % Removed in clause preprocessing : 3
% 11.31/2.09 % Initial clauses in saturation : 262
% 11.31/2.09 % Processed clauses : 7635
% 11.31/2.09 % ...of these trivial : 266
% 11.31/2.09 % ...subsumed : 3596
% 11.31/2.09 % ...remaining for further processing : 3773
% 11.31/2.09 % Other redundant clauses eliminated : 420
% 11.31/2.09 % Clauses deleted for lack of memory : 0
% 11.31/2.09 % Backward-subsumed : 792
% 11.31/2.09 % Backward-rewritten : 327
% 11.31/2.09 % Generated clauses : 61921
% 11.31/2.09 % ...of the previous two non-redundant : 54175
% 11.31/2.09 % ...aggressively subsumed : 0
% 11.31/2.09 % Contextual simplify-reflections : 175
% 11.31/2.09 % Paramodulations : 61448
% 11.31/2.09 % Factorizations : 2
% 11.31/2.09 % NegExts : 0
% 11.31/2.09 % Equation resolutions : 435
% 11.31/2.09 % Disequality decompositions : 0
% 11.31/2.09 % Total rewrite steps : 72686
% 11.31/2.09 % ...of those cached : 72385
% 11.31/2.09 % Propositional unsat checks : 0
% 11.31/2.09 % Propositional check models : 0
% 11.31/2.09 % Propositional check unsatisfiable : 0
% 11.31/2.09 % Propositional clauses : 0
% 11.31/2.09 % Propositional clauses after purity: 0
% 11.31/2.09 % Propositional unsat core size : 0
% 11.31/2.09 % Propositional preprocessing time : 0.000
% 11.31/2.09 % Propositional encoding time : 0.000
% 11.31/2.09 % Propositional solver time : 0.000
% 11.31/2.09 % Success case prop preproc time : 0.000
% 11.31/2.09 % Success case prop encoding time : 0.000
% 11.31/2.09 % Success case prop solver time : 0.000
% 11.31/2.09 % Current number of processed clauses : 2610
% 11.31/2.09 % Positive orientable unit clauses : 360
% 11.31/2.09 % Positive unorientable unit clauses: 0
% 11.31/2.09 % Negative unit clauses : 109
% 11.31/2.09 % Non-unit-clauses : 2141
% 11.31/2.09 % Current number of unprocessed clauses: 46141
% 11.31/2.09 % ...number of literals in the above : 288778
% 11.31/2.09 % Current number of archived formulas : 0
% 11.31/2.09 % Current number of archived clauses : 1155
% 11.31/2.09 % Clause-clause subsumption calls (NU) : 1394900
% 11.31/2.09 % Rec. Clause-clause subsumption calls : 447235
% 11.31/2.09 % Non-unit clause-clause subsumptions : 3729
% 11.31/2.09 % Unit Clause-clause subsumption calls : 47067
% 11.31/2.09 % Rewrite failures with RHS unbound : 0
% 11.31/2.09 % BW rewrite match attempts : 1002
% 11.31/2.09 % BW rewrite match successes : 89
% 11.31/2.09 % Condensation attempts : 0
% 11.31/2.09 % Condensation successes : 0
% 11.31/2.09 % Termbank termtop insertions : 1275895
% 11.31/2.09 % Search garbage collected termcells : 2444
% 11.31/2.09
% 11.31/2.09 % -------------------------------------------------
% 11.31/2.09 % User time : 1.411 s
% 11.31/2.09 % System time : 0.048 s
% 11.31/2.09 % Total time : 1.459 s
% 11.31/2.09 % Maximum resident set size: 4220 pages
% 11.31/2.09
% 11.31/2.09 % -------------------------------------------------
% 11.31/2.09 % User time : 1.415 s
% 11.31/2.09 % System time : 0.052 s
% 11.31/2.09 % Total time : 1.466 s
% 11.31/2.09 % Maximum resident set size: 4608 pages
% 11.31/2.09 % E exiting
%------------------------------------------------------------------------------