%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM580+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 : n010.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 01:55:34 PM UTC 2026
% Result : Theorem 2.06s 6.40s
% Output : CNFRefutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 44 ( 13 unt; 0 def)
% Number of atoms : 244 ( 41 equ)
% Maximal formula atoms : 52 ( 5 avg)
% Number of connectives : 300 ( 100 ~; 97 |; 71 &)
% ( 9 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 60 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__3989_02,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( X1 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989_02) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( X4 != X2
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(m__3671,hypothesis,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__3989,hypothesis,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989) ).
fof(m__,conjecture,
( ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( X1 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
=> sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mCardCons,axiom,
! [X1] :
( ( isFinite0(X1)
& aSet0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardCons) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(m__3533,hypothesis,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3533) ).
fof(mCardNum,axiom,
! [X1] :
( aSet0(X1)
=> ( aElementOf0(sbrdtbr0(X1),szNzAzT0)
<=> isFinite0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
fof(c_0_10,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( X1 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(fof_simplification,[status(thm)],[m__3989_02]) ).
fof(c_0_11,plain,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( X4 != X2
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
inference(fof_simplification,[status(thm)],[mDefDiff]) ).
fof(c_0_12,hypothesis,
! [X212,X213] :
( ( ~ aElementOf0(X212,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X212)) )
& ( ~ aElementOf0(X212,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X212),szNzAzT0) )
& ( ~ aElementOf0(X212,szNzAzT0)
| aElementOf0(X213,szNzAzT0)
| ~ aElementOf0(X213,sdtlpdtrp0(xN,X212)) )
& ( ~ aElementOf0(X212,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X212)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3671])])])])]) ).
fof(c_0_13,hypothesis,
! [X221,X222,X223] :
( aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElementOf0(X223,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X223,xQ) )
& aSet0(xQ)
& ( aElementOf0(X222,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| X222 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X222,sdtlpdtrp0(xN,xi))
| ~ aElement0(X222) )
& ( ~ aElementOf0(X222,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| X222 != szmzizndt0(sdtlpdtrp0(xN,xi)) )
& ( ~ aElementOf0(X222,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElementOf0(X222,sdtlpdtrp0(xN,xi)) )
& ( ~ aElementOf0(X222,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElement0(X222) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X221)
| ~ aElementOf0(X221,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
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_10])])])])]) ).
fof(c_0_14,plain,
! [X40,X41,X42,X43,X44,X45] :
( ( ~ aElement0(X41)
| ~ aSet0(X40)
| X45 = sdtmndt0(X40,X41)
| ~ aSet0(X45)
| aElementOf0(esk4_3(X40,X41,X45),X45)
| esk4_3(X40,X41,X45) != X41 )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X45 = sdtmndt0(X40,X41)
| ~ aSet0(X45)
| aElementOf0(esk4_3(X40,X41,X45),X45)
| aElementOf0(esk4_3(X40,X41,X45),X40) )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X45 = sdtmndt0(X40,X41)
| ~ aSet0(X45)
| aElementOf0(esk4_3(X40,X41,X45),X45)
| aElement0(esk4_3(X40,X41,X45)) )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X45 = sdtmndt0(X40,X41)
| ~ aSet0(X45)
| esk4_3(X40,X41,X45) = X41
| ~ aElementOf0(esk4_3(X40,X41,X45),X40)
| ~ aElement0(esk4_3(X40,X41,X45))
| ~ aElementOf0(esk4_3(X40,X41,X45),X45) )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X42 != sdtmndt0(X40,X41)
| aElementOf0(X44,X42)
| X44 = X41
| ~ aElementOf0(X44,X40)
| ~ aElement0(X44) )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X42 != sdtmndt0(X40,X41)
| ~ aElementOf0(X43,X42)
| X43 != X41 )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X42 != sdtmndt0(X40,X41)
| ~ aElementOf0(X43,X42)
| aElementOf0(X43,X40) )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X42 != sdtmndt0(X40,X41)
| ~ aElementOf0(X43,X42)
| aElement0(X43) )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X42 != sdtmndt0(X40,X41)
| aSet0(X42) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])])])]) ).
fof(c_0_15,plain,
! [X10,X11] :
( aElement0(X11)
| ~ aElementOf0(X11,X10)
| ~ aSet0(X10) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
cnf(c_0_16,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X2))
| aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,hypothesis,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,hypothesis,
aElementOf0(xi,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3989]) ).
fof(c_0_19,negated_conjecture,
~ ( ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( X1 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
=> sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_20,plain,
! [X1] :
( ( isFinite0(X1)
& aSet0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[mCardCons]) ).
cnf(c_0_21,plain,
( ~ aElement0(X2)
| ~ aSet0(X4)
| X3 != sdtmndt0(X4,X2)
| ~ aElementOf0(X1,X3)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,hypothesis,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),szNzAzT0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_24,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
fof(c_0_25,negated_conjecture,
! [X224,X225] :
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK
& ( aElementOf0(X225,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X225)
| X225 != szmzizndt0(sdtlpdtrp0(xN,xi)) )
& ( aElementOf0(X225,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X225)
| ~ aElementOf0(X225,xQ) )
& ( ~ aElementOf0(X225,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| X225 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X225,xQ) )
& ( ~ aElementOf0(X225,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElement0(X225) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X224)
| ~ aElementOf0(X224,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
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_19])])])])]) ).
fof(c_0_26,plain,
! [X86,X87] :
( sbrdtbr0(sdtpldt0(X86,X87)) = szszuzczcdt0(sbrdtbr0(X86))
| aElementOf0(X87,X86)
| ~ aElement0(X87)
| ~ isFinite0(X86)
| ~ aSet0(X86) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
cnf(c_0_27,plain,
( ~ aSet0(X2)
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtmndt0(X2,X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_21])]) ).
cnf(c_0_28,hypothesis,
( ~ aElementOf0(X1,xQ)
| aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_29,hypothesis,
aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_30,negated_conjecture,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
( ~ aElement0(X2)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1))
| aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,hypothesis,
sbrdtbr0(xQ) = xk,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_33,hypothesis,
szszuzczcdt0(xk) = xK,
inference(split_conjunct,[status(thm)],[m__3533]) ).
cnf(c_0_34,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_35,hypothesis,
( ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_36,negated_conjecture,
( ~ isFinite0(xQ)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33]),c_0_29]),c_0_34])]) ).
fof(c_0_37,plain,
! [X84] :
( ( ~ aSet0(X84)
| aElementOf0(sbrdtbr0(X84),szNzAzT0)
| ~ isFinite0(X84) )
& ( ~ aSet0(X84)
| isFinite0(X84)
| ~ aElementOf0(sbrdtbr0(X84),szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardNum])])])]) ).
cnf(c_0_38,hypothesis,
( ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ isFinite0(xQ) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
( ~ aSet0(X1)
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| isFinite0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_40,hypothesis,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3533]) ).
cnf(c_0_41,hypothesis,
~ aSet0(sdtlpdtrp0(xN,xi)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_32]),c_0_40]),c_0_34])]) ).
cnf(c_0_42,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_43,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM580+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/5.68 % Computer : n010.cluster.edu
% 0.19/5.68 % Model : x86_64 x86_64
% 0.19/5.68 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.68 % Memory : 8046.5625MB
% 0.19/5.68 % OS : Linux 6.8.0-71-generic
% 0.19/5.68 % CPULimit : 300
% 0.19/5.68 % WCLimit : 300
% 0.19/5.68 % DateTime : Mon Sep 21 02:41:47 UTC 2026
% 0.19/5.68 % CPUTime :
% 0.19/5.68 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/5.76 Running first-order theorem proving
% 0.24/5.76 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
% 2.06/6.40 % Version: 3.5.1
% 2.06/6.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.06/6.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.06/6.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.06/6.40 % Starting new_bool_3 with 300s (1) cores
% 2.06/6.40 % Starting new_bool_1 with 300s (1) cores
% 2.06/6.40 % Starting sh5l with 300s (1) cores
% 2.06/6.40 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 4061797 completed with status 0
% 2.06/6.40 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 2.06/6.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.06/6.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.06/6.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.06/6.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.06/6.40 % No SInE strategy applied
% 2.06/6.40 % Search class: FGHSF-SMLM32-MFFFFFNN
% 2.06/6.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.06/6.40 % Starting SubtermCWHack with 136s (1) cores
% 2.06/6.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 2.06/6.40 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 2.06/6.40 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 2.06/6.40 % Starting new_bool_3 with 136s (1) cores
% 2.06/6.40 % SubtermCWHack with pid 4061802 completed with status 0
% 2.06/6.40 % Result found by SubtermCWHack
% 2.06/6.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.06/6.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.06/6.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.06/6.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.06/6.40 % No SInE strategy applied
% 2.06/6.40 % Search class: FGHSF-SMLM32-MFFFFFNN
% 2.06/6.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.06/6.40 % Starting SubtermCWHack with 136s (1) cores
% 2.06/6.40 % Preprocessing time : 0.087 s
% 2.06/6.40
% 2.06/6.40 % Proof found!
% 2.06/6.40 % SZS status Theorem
% 2.06/6.40 % SZS output start CNFRefutation
% See solution above
% 2.06/6.40 % Parsed axioms : 87
% 2.06/6.40 % Removed by relevancy pruning/SinE : 0
% 2.06/6.40 % Initial clauses : 4207
% 2.06/6.40 % Removed in clause preprocessing : 7
% 2.06/6.40 % Initial clauses in saturation : 4200
% 2.06/6.40 % Processed clauses : 369
% 2.06/6.40 % ...of these trivial : 1
% 2.06/6.40 % ...subsumed : 59
% 2.06/6.40 % ...remaining for further processing : 309
% 2.06/6.40 % Other redundant clauses eliminated : 30
% 2.06/6.40 % Clauses deleted for lack of memory : 0
% 2.06/6.40 % Backward-subsumed : 31
% 2.06/6.40 % Backward-rewritten : 5
% 2.06/6.40 % Generated clauses : 511
% 2.06/6.40 % ...of the previous two non-redundant : 418
% 2.06/6.40 % ...aggressively subsumed : 0
% 2.06/6.40 % Contextual simplify-reflections : 7
% 2.06/6.40 % Paramodulations : 480
% 2.06/6.40 % Factorizations : 0
% 2.06/6.40 % NegExts : 0
% 2.06/6.40 % Equation resolutions : 31
% 2.06/6.40 % Disequality decompositions : 0
% 2.06/6.40 % Total rewrite steps : 351
% 2.06/6.40 % ...of those cached : 308
% 2.06/6.40 % Propositional unsat checks : 0
% 2.06/6.40 % Propositional check models : 0
% 2.06/6.40 % Propositional check unsatisfiable : 0
% 2.06/6.40 % Propositional clauses : 0
% 2.06/6.40 % Propositional clauses after purity: 0
% 2.06/6.40 % Propositional unsat core size : 0
% 2.06/6.40 % Propositional preprocessing time : 0.000
% 2.06/6.40 % Propositional encoding time : 0.000
% 2.06/6.40 % Propositional solver time : 0.000
% 2.06/6.40 % Success case prop preproc time : 0.000
% 2.06/6.40 % Success case prop encoding time : 0.000
% 2.06/6.40 % Success case prop solver time : 0.000
% 2.06/6.40 % Current number of processed clauses : 247
% 2.06/6.40 % Positive orientable unit clauses : 56
% 2.06/6.40 % Positive unorientable unit clauses: 0
% 2.06/6.40 % Negative unit clauses : 18
% 2.06/6.40 % Non-unit-clauses : 173
% 2.06/6.40 % Current number of unprocessed clauses: 4242
% 2.06/6.40 % ...number of literals in the above : 51654
% 2.06/6.40 % Current number of archived formulas : 0
% 2.06/6.40 % Current number of archived clauses : 38
% 2.06/6.40 % Clause-clause subsumption calls (NU) : 4120
% 2.06/6.40 % Rec. Clause-clause subsumption calls : 2699
% 2.06/6.40 % Non-unit clause-clause subsumptions : 51
% 2.06/6.40 % Unit Clause-clause subsumption calls : 700
% 2.06/6.40 % Rewrite failures with RHS unbound : 0
% 2.06/6.40 % BW rewrite match attempts : 7
% 2.06/6.40 % BW rewrite match successes : 7
% 2.06/6.40 % Condensation attempts : 0
% 2.06/6.40 % Condensation successes : 0
% 2.06/6.40 % Termbank termtop insertions : 342202
% 2.06/6.40 % Search garbage collected termcells : 27133
% 2.06/6.40
% 2.06/6.40 % -------------------------------------------------
% 2.06/6.40 % User time : 0.562 s
% 2.06/6.40 % System time : 0.034 s
% 2.06/6.40 % Total time : 0.596 s
% 2.06/6.40 % Maximum resident set size: 14780 pages
% 2.06/6.40
% 2.06/6.40 % -------------------------------------------------
% 2.06/6.40 % User time : 1.007 s
% 2.06/6.40 % System time : 0.088 s
% 2.06/6.40 % Total time : 1.094 s
% 2.06/6.40 % Maximum resident set size: 4864 pages
% 2.06/6.40 % E exiting
%------------------------------------------------------------------------------