%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM512+1 : 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 : n009.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 0.09s 0.46s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 64 ( 17 unt; 0 def)
% Number of atoms : 261 ( 110 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 326 ( 129 ~; 141 |; 35 &)
% ( 4 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
& sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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__2342,hypothesis,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
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/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
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(m__2487,hypothesis,
doDivides0(xr,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2487) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(m__1860,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mDefPrime,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( ! [X2] :
( ( doDivides0(X2,X1)
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(c_0_13,negated_conjecture,
~ ( sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
& sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_14,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]) ).
fof(c_0_15,negated_conjecture,
( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
| sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])]) ).
fof(c_0_16,plain,
! [X81,X82,X83] :
( sdtasdt0(X83,sdtsldt0(X82,X81)) = sdtsldt0(sdtasdt0(X83,X82),X81)
| ~ aNaturalNumber0(X83)
| ~ doDivides0(X81,X82)
| X81 = sz00
| ~ aNaturalNumber0(X82)
| ~ aNaturalNumber0(X81) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
cnf(c_0_17,negated_conjecture,
( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
| sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,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_16]) ).
cnf(c_0_19,hypothesis,
doDivides0(xr,xk),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_20,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_21,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
fof(c_0_22,plain,
! [X15,X16] :
( sdtasdt0(X15,X16) = sdtasdt0(X16,X15)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_23,negated_conjecture,
( ~ aNaturalNumber0(xk)
| sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm)
| sdtasdt0(sdtasdt0(xp,sdtsldt0(xk,xr)),xr) != sdtasdt0(xn,xm)
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20]),c_0_21])]) ).
cnf(c_0_24,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_26,plain,
! [X17,X18,X19] :
( sdtasdt0(sdtasdt0(X17,X18),X19) = sdtasdt0(X17,sdtasdt0(X18,X19))
| ~ aNaturalNumber0(X19)
| ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
cnf(c_0_27,negated_conjecture,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtasdt0(sdtasdt0(xm,sdtsldt0(xn,xr)),xr) != sdtasdt0(xn,xm)
| sdtasdt0(sdtasdt0(xp,sdtsldt0(xk,xr)),xr) != sdtasdt0(xn,xm)
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_28,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_29,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]) ).
cnf(c_0_30,negated_conjecture,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtasdt0(xm,sdtasdt0(sdtsldt0(xn,xr),xr)) != sdtasdt0(xn,xm)
| sdtasdt0(sdtasdt0(xp,sdtsldt0(xk,xr)),xr) != sdtasdt0(xn,xm)
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_21]),c_0_25])]) ).
fof(c_0_31,plain,
! [X67,X68,X69] :
( ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 = sdtsldt0(X68,X67)
| X68 != sdtasdt0(X67,X69)
| ~ aNaturalNumber0(X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| X68 = sdtasdt0(X67,X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| aNaturalNumber0(X69) ) ),
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_29])])])])]) ).
cnf(c_0_32,negated_conjecture,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtasdt0(xm,sdtasdt0(sdtsldt0(xn,xr),xr)) != sdtasdt0(xn,xm)
| sdtasdt0(xp,sdtasdt0(sdtsldt0(xk,xr),xr)) != sdtasdt0(xn,xm)
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_28]),c_0_21]),c_0_20])]) ).
cnf(c_0_33,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_31]) ).
cnf(c_0_34,negated_conjecture,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtasdt0(xm,sdtasdt0(xr,sdtsldt0(xn,xr))) != sdtasdt0(xn,xm)
| sdtasdt0(xp,sdtasdt0(sdtsldt0(xk,xr),xr)) != sdtasdt0(xn,xm)
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_24]),c_0_21])]) ).
cnf(c_0_35,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| X1 = sz00
| sdtasdt0(X1,sdtsldt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_36,hypothesis,
doDivides0(xr,xn),
inference(split_conjunct,[status(thm)],[m__2487]) ).
cnf(c_0_37,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_38,negated_conjecture,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtasdt0(xm,xn) != sdtasdt0(xn,xm)
| sdtasdt0(xp,sdtasdt0(sdtsldt0(xk,xr),xr)) != sdtasdt0(xn,xm)
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_21]),c_0_37])]) ).
cnf(c_0_39,negated_conjecture,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtasdt0(xm,xn) != sdtasdt0(xn,xm)
| sdtasdt0(xp,sdtasdt0(xr,sdtsldt0(xk,xr))) != sdtasdt0(xn,xm)
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_24]),c_0_21])]) ).
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_31]) ).
cnf(c_0_41,negated_conjecture,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtasdt0(xm,xn) != sdtasdt0(xn,xm)
| sdtasdt0(xp,xk) != sdtasdt0(xn,xm)
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_35]),c_0_19]),c_0_21])]) ).
cnf(c_0_42,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(sdtsldt0(X2,X1))
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_40]) ).
cnf(c_0_43,negated_conjecture,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtasdt0(xm,xn) != sdtasdt0(xn,xm)
| sdtasdt0(xp,xk) != sdtasdt0(xn,xm)
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_19]),c_0_21])]) ).
cnf(c_0_44,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_45,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
fof(c_0_46,plain,
! [X7,X8] :
( aNaturalNumber0(sdtasdt0(X7,X8))
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
fof(c_0_47,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( ! [X2] :
( ( doDivides0(X2,X1)
& aNaturalNumber0(X2) )
=> ( X2 = X1
| X2 = sz10 ) )
& X1 != sz10
& X1 != sz00 ) ) ),
inference(fof_simplification,[status(thm)],[mDefPrime]) ).
cnf(c_0_48,negated_conjecture,
( ~ aNaturalNumber0(xk)
| sdtasdt0(xm,xn) != sdtasdt0(xn,xm)
| sdtasdt0(xp,xk) != sdtasdt0(xn,xm)
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_42]),c_0_36]),c_0_21]),c_0_37])]) ).
cnf(c_0_49,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| xp = sz00
| sdtasdt0(xp,xk) = sdtasdt0(xn,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_44]),c_0_45]),c_0_20])]) ).
cnf(c_0_50,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_51,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| aNaturalNumber0(xk)
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_44]),c_0_45]),c_0_20])]) ).
fof(c_0_52,plain,
! [X84,X85] :
( ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| esk3_1(X84) != X84 )
& ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| esk3_1(X84) != sz10 )
& ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| doDivides0(esk3_1(X84),X84) )
& ( ~ aNaturalNumber0(X84)
| isPrime0(X84)
| X84 = sz10
| X84 = sz00
| aNaturalNumber0(esk3_1(X84)) )
& ( ~ aNaturalNumber0(X84)
| ~ isPrime0(X84)
| X85 = X84
| X85 = sz10
| ~ doDivides0(X85,X84)
| ~ aNaturalNumber0(X85) )
& ( ~ aNaturalNumber0(X84)
| ~ isPrime0(X84)
| X84 != sz10 )
& ( ~ aNaturalNumber0(X84)
| ~ isPrime0(X84)
| X84 != 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_47])])])])])]) ).
cnf(c_0_53,negated_conjecture,
( ~ aNaturalNumber0(xk)
| sdtasdt0(xp,xk) != sdtasdt0(xn,xm)
| xr = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_24]),c_0_37]),c_0_25])]) ).
cnf(c_0_54,hypothesis,
( xp = sz00
| sdtasdt0(xp,xk) = sdtasdt0(xn,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_25]),c_0_37])]) ).
cnf(c_0_55,hypothesis,
( aNaturalNumber0(xk)
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_50]),c_0_25]),c_0_37])]) ).
cnf(c_0_56,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_57,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_58,hypothesis,
isPrime0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_59,hypothesis,
( xr = sz00
| xp = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_60,plain,
~ isPrime0(sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_56]),c_0_57])]) ).
cnf(c_0_61,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_62,hypothesis,
xp = sz00,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).
cnf(c_0_63,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62]),c_0_60]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM512+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 02:36:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.46 % Version: 3.5.1
% 0.09/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.46 % Starting sh5l with 300s (1) cores
% 0.09/0.46 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 661224 completed with status 0
% 0.09/0.46 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.09/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.46 % No SInE strategy applied
% 0.09/0.46 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.09/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.09/0.46 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 0.09/0.46 % Starting new_bool_3 with 136s (1) cores
% 0.09/0.46 % SAT001_MinMin_p005000_rr_RG with pid 661232 completed with status 0
% 0.09/0.46 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.09/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.46 % No SInE strategy applied
% 0.09/0.46 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.09/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.09/0.46 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.09/0.46 % Preprocessing time : 0.001 s
% 0.09/0.46 % Presaturation interreduction done
% 0.09/0.46
% 0.09/0.46 % Proof found!
% 0.09/0.46 % SZS status Theorem
% 0.09/0.46 % SZS output start CNFRefutation
% See solution above
% 0.09/0.46 % Parsed axioms : 54
% 0.09/0.46 % Removed by relevancy pruning/SinE : 0
% 0.09/0.46 % Initial clauses : 99
% 0.09/0.46 % Removed in clause preprocessing : 3
% 0.09/0.46 % Initial clauses in saturation : 96
% 0.09/0.46 % Processed clauses : 400
% 0.09/0.46 % ...of these trivial : 1
% 0.09/0.46 % ...subsumed : 88
% 0.09/0.46 % ...remaining for further processing : 311
% 0.09/0.46 % Other redundant clauses eliminated : 35
% 0.09/0.46 % Clauses deleted for lack of memory : 0
% 0.09/0.46 % Backward-subsumed : 23
% 0.09/0.46 % Backward-rewritten : 68
% 0.09/0.46 % Generated clauses : 958
% 0.09/0.46 % ...of the previous two non-redundant : 893
% 0.09/0.46 % ...aggressively subsumed : 0
% 0.09/0.46 % Contextual simplify-reflections : 23
% 0.09/0.46 % Paramodulations : 918
% 0.09/0.46 % Factorizations : 1
% 0.09/0.46 % NegExts : 0
% 0.09/0.46 % Equation resolutions : 39
% 0.09/0.46 % Disequality decompositions : 0
% 0.09/0.46 % Total rewrite steps : 681
% 0.09/0.46 % ...of those cached : 667
% 0.09/0.46 % Propositional unsat checks : 0
% 0.09/0.46 % Propositional check models : 0
% 0.09/0.46 % Propositional check unsatisfiable : 0
% 0.09/0.46 % Propositional clauses : 0
% 0.09/0.46 % Propositional clauses after purity: 0
% 0.09/0.46 % Propositional unsat core size : 0
% 0.09/0.46 % Propositional preprocessing time : 0.000
% 0.09/0.46 % Propositional encoding time : 0.000
% 0.09/0.46 % Propositional solver time : 0.000
% 0.09/0.46 % Success case prop preproc time : 0.000
% 0.09/0.46 % Success case prop encoding time : 0.000
% 0.09/0.46 % Success case prop solver time : 0.000
% 0.09/0.46 % Current number of processed clauses : 121
% 0.09/0.46 % Positive orientable unit clauses : 13
% 0.09/0.46 % Positive unorientable unit clauses: 0
% 0.09/0.46 % Negative unit clauses : 6
% 0.09/0.46 % Non-unit-clauses : 102
% 0.09/0.46 % Current number of unprocessed clauses: 642
% 0.09/0.46 % ...number of literals in the above : 3932
% 0.09/0.46 % Current number of archived formulas : 0
% 0.09/0.46 % Current number of archived clauses : 179
% 0.09/0.46 % Clause-clause subsumption calls (NU) : 5583
% 0.09/0.46 % Rec. Clause-clause subsumption calls : 970
% 0.09/0.46 % Non-unit clause-clause subsumptions : 130
% 0.09/0.46 % Unit Clause-clause subsumption calls : 100
% 0.09/0.46 % Rewrite failures with RHS unbound : 0
% 0.09/0.46 % BW rewrite match attempts : 2
% 0.09/0.46 % BW rewrite match successes : 2
% 0.09/0.46 % Condensation attempts : 0
% 0.09/0.46 % Condensation successes : 0
% 0.09/0.46 % Termbank termtop insertions : 27566
% 0.09/0.46 % Search garbage collected termcells : 1365
% 0.09/0.46
% 0.09/0.46 % -------------------------------------------------
% 0.09/0.46 % User time : 0.030 s
% 0.09/0.46 % System time : 0.005 s
% 0.09/0.46 % Total time : 0.034 s
% 0.09/0.46 % Maximum resident set size: 3948 pages
% 0.09/0.46
% 0.09/0.46 % -------------------------------------------------
% 0.09/0.46 % User time : 0.121 s
% 0.09/0.46 % System time : 0.025 s
% 0.09/0.46 % Total time : 0.146 s
% 0.09/0.46 % Maximum resident set size: 4864 pages
% 0.09/0.46 % E exiting
%------------------------------------------------------------------------------