%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM518+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 : n008.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 01:49:24 PM UTC 2026
% Result : Theorem 1.36s 0.64s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 64 ( 22 unt; 0 def)
% Number of atoms : 284 ( 96 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 313 ( 93 ~; 107 |; 94 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 73 ( 0 sgn 39 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( doDivides0(xp,xm)
| ? [X1] :
( xm = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
| doDivides0(xp,xn)
| ? [X1] :
( xn = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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(m__2645,hypothesis,
( ( doDivides0(xp,xm)
& ? [X1] :
( xm = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) )
| ( doDivides0(xp,sdtsldt0(xn,xr))
& ? [X1] :
( sdtsldt0(xn,xr) = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2645) ).
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(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__2487,hypothesis,
( doDivides0(xr,xn)
& ? [X1] :
( xn = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2487) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(m__1870,hypothesis,
~ ( sdtlseqdt0(xp,xn)
| ? [X1] :
( sdtpldt0(xp,X1) = xn
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(c_0_14,negated_conjecture,
~ ( doDivides0(xp,xm)
| ? [X1] :
( xm = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
| doDivides0(xp,xn)
| ? [X1] :
( xn = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
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,hypothesis,
( ( doDivides0(xp,sdtsldt0(xn,xr))
| doDivides0(xp,xm) )
& ( doDivides0(xp,sdtsldt0(xn,xr))
| xm = sdtasdt0(xp,esk22_0) )
& ( doDivides0(xp,sdtsldt0(xn,xr))
| aNaturalNumber0(esk22_0) )
& ( sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0)
| doDivides0(xp,xm) )
& ( sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0)
| xm = sdtasdt0(xp,esk22_0) )
& ( sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0)
| aNaturalNumber0(esk22_0) )
& ( aNaturalNumber0(esk21_0)
| doDivides0(xp,xm) )
& ( aNaturalNumber0(esk21_0)
| xm = sdtasdt0(xp,esk22_0) )
& ( aNaturalNumber0(esk21_0)
| aNaturalNumber0(esk22_0) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| doDivides0(xp,xm) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| xm = sdtasdt0(xp,esk22_0) )
& ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| aNaturalNumber0(esk22_0) )
& ( aNaturalNumber0(sdtsldt0(xn,xr))
| doDivides0(xp,xm) )
& ( aNaturalNumber0(sdtsldt0(xn,xr))
| xm = sdtasdt0(xp,esk22_0) )
& ( aNaturalNumber0(sdtsldt0(xn,xr))
| aNaturalNumber0(esk22_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2645])])]) ).
fof(c_0_19,negated_conjecture,
! [X119,X120] :
( ~ doDivides0(xp,xm)
& ( xm != sdtasdt0(xp,X120)
| ~ aNaturalNumber0(X120) )
& ~ doDivides0(xp,xn)
& ( xn != sdtasdt0(xp,X119)
| ~ aNaturalNumber0(X119) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[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,hypothesis,
( isPrime0(xr)
& ! [X1] :
( ( ( doDivides0(X1,xr)
| ? [X2] :
( xr = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( X1 = xr
| X1 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X1] :
( xk = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) )
& aNaturalNumber0(xr) ),
inference(fof_simplification,[status(thm)],[m__2342]) ).
fof(c_0_24,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_25,hypothesis,
( sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0)
| doDivides0(xp,xm) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
~ doDivides0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,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_28,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_29,hypothesis,
( doDivides0(xr,xn)
& xn = sdtasdt0(xr,esk18_0)
& aNaturalNumber0(esk18_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2487])]) ).
fof(c_0_30,hypothesis,
! [X107,X108] :
( isPrime0(xr)
& ( X107 = xr
| X107 = sz10
| ~ aNaturalNumber0(X107)
| ~ doDivides0(X107,xr) )
& ( X107 = xr
| X107 = sz10
| ~ aNaturalNumber0(X107)
| xr != sdtasdt0(X107,X108)
| ~ aNaturalNumber0(X108) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,esk12_0)
& aNaturalNumber0(esk12_0)
& aNaturalNumber0(xr) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])])])]) ).
cnf(c_0_31,hypothesis,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,hypothesis,
sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0),
inference(sr,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,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_27]),c_0_22]),c_0_28]) ).
cnf(c_0_34,hypothesis,
xn = sdtasdt0(xr,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,hypothesis,
aNaturalNumber0(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,hypothesis,
xr != sz00,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_38,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
inference(fof_simplification,[status(thm)],[mMonMul2]) ).
fof(c_0_39,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_40,hypothesis,
sdtlseqdt0(sdtasdt0(xp,esk21_0),xn),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_41,hypothesis,
sdtasdt0(xp,esk21_0) = esk18_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_33,c_0_34]),c_0_32]),c_0_35]),c_0_36])]),c_0_37]) ).
fof(c_0_42,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_38])])]) ).
cnf(c_0_43,hypothesis,
( aNaturalNumber0(esk21_0)
| doDivides0(xp,xm) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_44,plain,
( ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,hypothesis,
sdtlseqdt0(esk18_0,xn),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_47,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_49,hypothesis,
aNaturalNumber0(esk21_0),
inference(sr,[status(thm)],[c_0_43,c_0_26]) ).
fof(c_0_50,hypothesis,
! [X102] :
( ~ sdtlseqdt0(xp,xn)
& ( sdtpldt0(xp,X102) != xn
| ~ aNaturalNumber0(X102) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1870])])])]) ).
cnf(c_0_51,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,esk18_0)
| sdtlseqdt0(X1,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_36])]) ).
cnf(c_0_52,hypothesis,
( sdtlseqdt0(xp,esk18_0)
| esk21_0 = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_41]),c_0_48]),c_0_49])]) ).
cnf(c_0_53,hypothesis,
~ sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_54,plain,
! [X23] :
( ( ~ aNaturalNumber0(X23)
| sz00 = sdtasdt0(sz00,X23) )
& ( ~ aNaturalNumber0(X23)
| sdtasdt0(X23,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])])]) ).
cnf(c_0_55,hypothesis,
esk21_0 = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_48])]),c_0_53]) ).
cnf(c_0_56,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_57,hypothesis,
sdtasdt0(xp,sz00) = esk18_0,
inference(rw,[status(thm)],[c_0_41,c_0_55]) ).
cnf(c_0_58,hypothesis,
esk18_0 = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_48])]) ).
cnf(c_0_59,negated_conjecture,
( xn != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_60,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_61,hypothesis,
sdtasdt0(xr,sz00) = xn,
inference(rw,[status(thm)],[c_0_34,c_0_58]) ).
cnf(c_0_62,negated_conjecture,
sz00 != xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_56]),c_0_60]),c_0_48])]) ).
cnf(c_0_63,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_61]),c_0_35])]),c_0_62]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM518+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n008.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 02:37:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 1.36/0.64 % Version: 3.5.1
% 1.36/0.64 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.36/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.36/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.36/0.64 % Starting new_bool_3 with 300s (1) cores
% 1.36/0.64 % Starting new_bool_1 with 300s (1) cores
% 1.36/0.64 % Starting sh5l with 300s (1) cores
% 1.36/0.64 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 4158004 completed with status 0
% 1.36/0.64 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.36/0.64 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.36/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.36/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.36/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.36/0.64 % No SInE strategy applied
% 1.36/0.64 % Search class: FGHSF-FSLM32-SFFFFFNN
% 1.36/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.36/0.64 % Starting SubtermCWHack with 136s (1) cores
% 1.36/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.36/0.64 % Starting G-E--_107_C41_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 1.36/0.64 % Starting new_bool_3 with 136s (1) cores
% 1.36/0.64 % Starting U----_116_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN1 with 136s (1) cores
% 1.36/0.64 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 4158012 completed with status 0
% 1.36/0.64 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.36/0.64 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.36/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.36/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.36/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.36/0.64 % No SInE strategy applied
% 1.36/0.64 % Search class: FGHSF-FSLM32-SFFFFFNN
% 1.36/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.36/0.64 % Starting SubtermCWHack with 136s (1) cores
% 1.36/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.36/0.64 % Preprocessing time : 0.004 s
% 1.36/0.64 % Presaturation interreduction done
% 1.36/0.64
% 1.36/0.64 % Proof found!
% 1.36/0.64 % SZS status Theorem
% 1.36/0.64 % SZS output start CNFRefutation
% See solution above
% 1.36/0.64 % Parsed axioms : 56
% 1.36/0.64 % Removed by relevancy pruning/SinE : 0
% 1.36/0.64 % Initial clauses : 288
% 1.36/0.64 % Removed in clause preprocessing : 3
% 1.36/0.64 % Initial clauses in saturation : 285
% 1.36/0.64 % Processed clauses : 727
% 1.36/0.64 % ...of these trivial : 26
% 1.36/0.64 % ...subsumed : 69
% 1.36/0.64 % ...remaining for further processing : 632
% 1.36/0.64 % Other redundant clauses eliminated : 163
% 1.36/0.64 % Clauses deleted for lack of memory : 0
% 1.36/0.64 % Backward-subsumed : 3
% 1.36/0.64 % Backward-rewritten : 50
% 1.36/0.64 % Generated clauses : 4799
% 1.36/0.64 % ...of the previous two non-redundant : 4511
% 1.36/0.64 % ...aggressively subsumed : 0
% 1.36/0.64 % Contextual simplify-reflections : 6
% 1.36/0.64 % Paramodulations : 4585
% 1.36/0.64 % Factorizations : 2
% 1.36/0.64 % NegExts : 0
% 1.36/0.64 % Equation resolutions : 212
% 1.36/0.64 % Disequality decompositions : 0
% 1.36/0.64 % Total rewrite steps : 6969
% 1.36/0.64 % ...of those cached : 6907
% 1.36/0.64 % Propositional unsat checks : 0
% 1.36/0.64 % Propositional check models : 0
% 1.36/0.64 % Propositional check unsatisfiable : 0
% 1.36/0.64 % Propositional clauses : 0
% 1.36/0.64 % Propositional clauses after purity: 0
% 1.36/0.64 % Propositional unsat core size : 0
% 1.36/0.64 % Propositional preprocessing time : 0.000
% 1.36/0.64 % Propositional encoding time : 0.000
% 1.36/0.64 % Propositional solver time : 0.000
% 1.36/0.64 % Success case prop preproc time : 0.000
% 1.36/0.64 % Success case prop encoding time : 0.000
% 1.36/0.64 % Success case prop solver time : 0.000
% 1.36/0.64 % Current number of processed clauses : 309
% 1.36/0.64 % Positive orientable unit clauses : 71
% 1.36/0.64 % Positive unorientable unit clauses: 0
% 1.36/0.64 % Negative unit clauses : 23
% 1.36/0.64 % Non-unit-clauses : 215
% 1.36/0.64 % Current number of unprocessed clauses: 4159
% 1.36/0.64 % ...number of literals in the above : 31294
% 1.36/0.64 % Current number of archived formulas : 0
% 1.36/0.64 % Current number of archived clauses : 312
% 1.36/0.64 % Clause-clause subsumption calls (NU) : 64077
% 1.36/0.64 % Rec. Clause-clause subsumption calls : 414
% 1.36/0.64 % Non-unit clause-clause subsumptions : 28
% 1.36/0.64 % Unit Clause-clause subsumption calls : 5936
% 1.36/0.64 % Rewrite failures with RHS unbound : 0
% 1.36/0.64 % BW rewrite match attempts : 12
% 1.36/0.64 % BW rewrite match successes : 12
% 1.36/0.64 % Condensation attempts : 0
% 1.36/0.64 % Condensation successes : 0
% 1.36/0.64 % Termbank termtop insertions : 190741
% 1.36/0.64 % Search garbage collected termcells : 2565
% 1.36/0.64
% 1.36/0.64 % -------------------------------------------------
% 1.36/0.64 % User time : 0.188 s
% 1.36/0.64 % System time : 0.010 s
% 1.36/0.64 % Total time : 0.198 s
% 1.36/0.64 % Maximum resident set size: 4224 pages
% 1.36/0.64
% 1.36/0.64 % -------------------------------------------------
% 1.36/0.64 % User time : 0.723 s
% 1.36/0.64 % System time : 0.043 s
% 1.36/0.64 % Total time : 0.765 s
% 1.36/0.64 % Maximum resident set size: 4608 pages
% 1.36/0.64 % E exiting
%------------------------------------------------------------------------------