%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM511+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 : 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 01:49:22 PM UTC 2026
% Result : Theorem 11.38s 1.98s
% Output : CNFRefutation 11.38s
% 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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2487,hypothesis,
( doDivides0(xr,xn)
& ? [X1] :
( xn = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',m__2306) ).
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__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/sandbox2/benchmark/theBenchmark.p',m__2504) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/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,
! [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])])])])])]) ).
fof(c_0_17,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_18,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_13])])])])]) ).
fof(c_0_19,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_14])])])])])]) ).
fof(c_0_20,plain,
! [X69,X70,X71] :
( ( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X69)
| ~ doDivides0(X69,X70)
| X69 = sz00
| X71 = sdtsldt0(X70,X69)
| X70 != sdtasdt0(X69,X71)
| ~ aNaturalNumber0(X71) )
& ( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X69)
| ~ doDivides0(X69,X70)
| X69 = sz00
| X71 != sdtsldt0(X70,X69)
| X70 = sdtasdt0(X69,X71) )
& ( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X69)
| ~ doDivides0(X69,X70)
| X69 = sz00
| X71 != sdtsldt0(X70,X69)
| aNaturalNumber0(X71) ) ),
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,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,hypothesis,
aNaturalNumber0(esk12_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,esk18_0)
& aNaturalNumber0(esk18_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,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_35,plain,
! [X83,X84,X85] :
( sdtasdt0(X85,sdtsldt0(X84,X83)) = sdtsldt0(sdtasdt0(X85,X84),X83)
| ~ aNaturalNumber0(X85)
| ~ doDivides0(X83,X84)
| X83 = sz00
| ~ aNaturalNumber0(X84)
| ~ aNaturalNumber0(X83) ),
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 = esk12_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,
! [X116] :
( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
& ( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,X116)
| ~ aNaturalNumber0(X116) )
& 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,
! [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_43,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_44,hypothesis,
xn = sdtasdt0(xr,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_45,hypothesis,
aNaturalNumber0(esk18_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,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_48,hypothesis,
aNaturalNumber0(esk14_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) = esk12_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 = esk18_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) = esk14_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) = esk12_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) = esk18_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,esk12_0) = esk14_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,esk18_0)),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_70,hypothesis,
sdtasdt0(xm,esk18_0) = esk14_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,esk14_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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 02:36:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 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
% 11.38/1.98 % Version: 3.5.1
% 11.38/1.98 % Preprocessing class: FSLSSMSSSSSNFFN.
% 11.38/1.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.38/1.98 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 11.38/1.98 % Starting new_bool_3 with 300s (1) cores
% 11.38/1.98 % Starting new_bool_1 with 300s (1) cores
% 11.38/1.98 % Starting sh5l with 300s (1) cores
% 11.38/1.98 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2961313 completed with status 0
% 11.38/1.98 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 11.38/1.98 % Preprocessing class: FSLSSMSSSSSNFFN.
% 11.38/1.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.38/1.98 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 11.38/1.98 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 11.38/1.98 % No SInE strategy applied
% 11.38/1.98 % Search class: FGHSF-FSLM32-SFFFFFNN
% 11.38/1.98 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 11.38/1.98 % Starting SubtermCWHack with 136s (1) cores
% 11.38/1.98 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 11.38/1.98 % Starting G-E--_107_C41_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 11.38/1.98 % Starting new_bool_3 with 136s (1) cores
% 11.38/1.98 % Starting U----_116_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN1 with 136s (1) cores
% 11.38/1.98 % SubtermCWHack with pid 2961317 completed with status 0
% 11.38/1.98 % Result found by SubtermCWHack
% 11.38/1.98 % Preprocessing class: FSLSSMSSSSSNFFN.
% 11.38/1.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.38/1.98 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 11.38/1.98 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 11.38/1.98 % No SInE strategy applied
% 11.38/1.98 % Search class: FGHSF-FSLM32-SFFFFFNN
% 11.38/1.98 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 11.38/1.98 % Starting SubtermCWHack with 136s (1) cores
% 11.38/1.98 % Preprocessing time : 0.004 s
% 11.38/1.98
% 11.38/1.98 % Proof found!
% 11.38/1.98 % SZS status Theorem
% 11.38/1.98 % SZS output start CNFRefutation
% See solution above
% 11.38/1.98 % Parsed axioms : 54
% 11.38/1.98 % Removed by relevancy pruning/SinE : 0
% 11.38/1.98 % Initial clauses : 268
% 11.38/1.98 % Removed in clause preprocessing : 3
% 11.38/1.98 % Initial clauses in saturation : 265
% 11.38/1.98 % Processed clauses : 7910
% 11.38/1.98 % ...of these trivial : 297
% 11.38/1.98 % ...subsumed : 3741
% 11.38/1.98 % ...remaining for further processing : 3872
% 11.38/1.98 % Other redundant clauses eliminated : 445
% 11.38/1.98 % Clauses deleted for lack of memory : 0
% 11.38/1.98 % Backward-subsumed : 779
% 11.38/1.98 % Backward-rewritten : 331
% 11.38/1.98 % Generated clauses : 63975
% 11.38/1.98 % ...of the previous two non-redundant : 55942
% 11.38/1.98 % ...aggressively subsumed : 0
% 11.38/1.98 % Contextual simplify-reflections : 177
% 11.38/1.98 % Paramodulations : 63477
% 11.38/1.98 % Factorizations : 2
% 11.38/1.98 % NegExts : 0
% 11.38/1.98 % Equation resolutions : 460
% 11.38/1.98 % Disequality decompositions : 0
% 11.38/1.98 % Total rewrite steps : 75114
% 11.38/1.98 % ...of those cached : 74772
% 11.38/1.98 % Propositional unsat checks : 0
% 11.38/1.98 % Propositional check models : 0
% 11.38/1.98 % Propositional check unsatisfiable : 0
% 11.38/1.98 % Propositional clauses : 0
% 11.38/1.98 % Propositional clauses after purity: 0
% 11.38/1.98 % Propositional unsat core size : 0
% 11.38/1.98 % Propositional preprocessing time : 0.000
% 11.38/1.98 % Propositional encoding time : 0.000
% 11.38/1.98 % Propositional solver time : 0.000
% 11.38/1.98 % Success case prop preproc time : 0.000
% 11.38/1.98 % Success case prop encoding time : 0.000
% 11.38/1.98 % Success case prop solver time : 0.000
% 11.38/1.98 % Current number of processed clauses : 2715
% 11.38/1.98 % Positive orientable unit clauses : 418
% 11.38/1.98 % Positive unorientable unit clauses: 0
% 11.38/1.98 % Negative unit clauses : 116
% 11.38/1.98 % Non-unit-clauses : 2181
% 11.38/1.98 % Current number of unprocessed clauses: 47598
% 11.38/1.98 % ...number of literals in the above : 297174
% 11.38/1.98 % Current number of archived formulas : 0
% 11.38/1.98 % Current number of archived clauses : 1146
% 11.38/1.98 % Clause-clause subsumption calls (NU) : 1320004
% 11.38/1.98 % Rec. Clause-clause subsumption calls : 419373
% 11.38/1.98 % Non-unit clause-clause subsumptions : 3853
% 11.38/1.98 % Unit Clause-clause subsumption calls : 73277
% 11.38/1.98 % Rewrite failures with RHS unbound : 0
% 11.38/1.98 % BW rewrite match attempts : 1296
% 11.38/1.98 % BW rewrite match successes : 103
% 11.38/1.98 % Condensation attempts : 0
% 11.38/1.98 % Condensation successes : 0
% 11.38/1.98 % Termbank termtop insertions : 1316168
% 11.38/1.98 % Search garbage collected termcells : 2491
% 11.38/1.98
% 11.38/1.98 % -------------------------------------------------
% 11.38/1.98 % User time : 1.453 s
% 11.38/1.98 % System time : 0.046 s
% 11.38/1.98 % Total time : 1.499 s
% 11.38/1.98 % Maximum resident set size: 4220 pages
% 11.38/1.98
% 11.38/1.98 % -------------------------------------------------
% 11.38/1.98 % User time : 7.012 s
% 11.38/1.98 % System time : 0.251 s
% 11.38/1.98 % Total time : 7.262 s
% 11.38/1.98 % Maximum resident set size: 4608 pages
% 11.38/1.98 % E exiting
%------------------------------------------------------------------------------