%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM563+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 : n015.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 01:49:35 PM UTC 2026
% Result : Theorem 0.84s 0.68s
% Output : CNFRefutation 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 13 unt; 0 def)
% Number of atoms : 306 ( 55 equ)
% Maximal formula atoms : 88 ( 5 avg)
% Number of connectives : 397 ( 151 ~; 145 |; 75 &)
% ( 3 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 77 ( 1 sgn 42 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( xK = sz00
=> ? [X1] :
( ? [X2] :
( ! [X3] :
( ( aElementOf0(X3,slbdtsldtrb0(X2,xK))
& sbrdtbr0(X3) = xK
& aSubsetOf0(X3,X2)
& ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,X2) )
& aSet0(X3) )
=> sdtlpdtrp0(xc,X3) = X1 )
& isCountable0(X2)
& ( aSubsetOf0(X2,xS)
| ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,xS) )
& aSet0(X2) ) ) )
& aElementOf0(X1,xT) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mCardEmpty,axiom,
! [X1] :
( aSet0(X1)
=> ( sbrdtbr0(X1) = sz00
<=> X1 = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
fof(m__3453,hypothesis,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ! [X1] :
( aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
=> aElementOf0(X1,xT) )
& ! [X1] :
( aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [X2] :
( sdtlpdtrp0(xc,X2) = X1
& aElementOf0(X2,szDzozmdt0(xc)) ) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ! [X1] :
( ( ( sbrdtbr0(X1) = xK
& ( aSubsetOf0(X1,xS)
| ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) )
& aSet0(X1) ) ) )
=> aElementOf0(X1,szDzozmdt0(xc)) )
& ( aElementOf0(X1,szDzozmdt0(xc))
=> ( sbrdtbr0(X1) = xK
& aSubsetOf0(X1,xS)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) )
& aSet0(X1) ) ) )
& aFunction0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
fof(mSelNSet,axiom,
! [X1] :
( ( ~ isFinite0(X1)
& aSet0(X1) )
=> ! [X2] :
( aElementOf0(X2,szNzAzT0)
=> slbdtsldtrb0(X1,X2) != slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelNSet) ).
fof(mCountNFin,axiom,
! [X1] :
( ( isCountable0(X1)
& aSet0(X1) )
=> ~ isFinite0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(m__3435,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(mDomSet,axiom,
! [X1] :
( aFunction0(X1)
=> aSet0(szDzozmdt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDomSet) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( ~ ? [X2] : aElementOf0(X2,X1)
& aSet0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(mSubRefl,axiom,
! [X1] :
( aSet0(X1)
=> aSubsetOf0(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
fof(c_0_10,negated_conjecture,
~ ( xK = sz00
=> ? [X1] :
( ? [X2] :
( ! [X3] :
( ( aElementOf0(X3,slbdtsldtrb0(X2,xK))
& sbrdtbr0(X3) = xK
& aSubsetOf0(X3,X2)
& ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,X2) )
& aSet0(X3) )
=> sdtlpdtrp0(xc,X3) = X1 )
& isCountable0(X2)
& ( aSubsetOf0(X2,xS)
| ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,xS) )
& aSet0(X2) ) ) )
& aElementOf0(X1,xT) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_11,plain,
! [X101] :
( ( ~ aSet0(X101)
| sbrdtbr0(X101) = sz00
| X101 != slcrc0 )
& ( ~ aSet0(X101)
| X101 = slcrc0
| sbrdtbr0(X101) != sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardEmpty])])])]) ).
fof(c_0_12,negated_conjecture,
! [X36,X37,X40] :
( ( ~ aElementOf0(X36,xT)
| ~ isCountable0(X37)
| ~ aSubsetOf0(X37,xS)
| sdtlpdtrp0(xc,esk13_2(X36,X37)) != X36 )
& ( ~ aElementOf0(X36,xT)
| ~ isCountable0(X37)
| ~ aSubsetOf0(X37,xS)
| aElementOf0(esk13_2(X36,X37),slbdtsldtrb0(X37,xK)) )
& ( ~ aElementOf0(X36,xT)
| ~ isCountable0(X37)
| ~ aSubsetOf0(X37,xS)
| sbrdtbr0(esk13_2(X36,X37)) = xK )
& ( ~ aElementOf0(X36,xT)
| ~ isCountable0(X37)
| ~ aSubsetOf0(X37,xS)
| aSubsetOf0(esk13_2(X36,X37),X37) )
& ( ~ aElementOf0(X36,xT)
| ~ isCountable0(X37)
| ~ aSubsetOf0(X37,xS)
| aElementOf0(X40,X37)
| ~ aElementOf0(X40,esk13_2(X36,X37)) )
& ( ~ aElementOf0(X36,xT)
| ~ isCountable0(X37)
| ~ aSubsetOf0(X37,xS)
| aSet0(esk13_2(X36,X37)) )
& ( ~ aElementOf0(X36,xT)
| ~ isCountable0(X37)
| ~ aSet0(X37)
| ~ aElementOf0(esk12_2(X36,X37),xS)
| sdtlpdtrp0(xc,esk13_2(X36,X37)) != X36 )
& ( ~ aElementOf0(X36,xT)
| ~ isCountable0(X37)
| ~ aSet0(X37)
| ~ aElementOf0(esk12_2(X36,X37),xS)
| aElementOf0(esk13_2(X36,X37),slbdtsldtrb0(X37,xK)) )
& ( ~ aElementOf0(X36,xT)
| ~ isCountable0(X37)
| ~ aSet0(X37)
| ~ aElementOf0(esk12_2(X36,X37),xS)
| sbrdtbr0(esk13_2(X36,X37)) = xK )
& ( ~ aElementOf0(X36,xT)
| ~ isCountable0(X37)
| ~ aSet0(X37)
| ~ aElementOf0(esk12_2(X36,X37),xS)
| aSubsetOf0(esk13_2(X36,X37),X37) )
& ( ~ aElementOf0(X36,xT)
| ~ isCountable0(X37)
| ~ aSet0(X37)
| ~ aElementOf0(esk12_2(X36,X37),xS)
| aElementOf0(X40,X37)
| ~ aElementOf0(X40,esk13_2(X36,X37)) )
& ( ~ aElementOf0(X36,xT)
| ~ isCountable0(X37)
| ~ aSet0(X37)
| ~ aElementOf0(esk12_2(X36,X37),xS)
| aSet0(esk13_2(X36,X37)) )
& ( ~ aElementOf0(X36,xT)
| ~ isCountable0(X37)
| ~ aSet0(X37)
| aElementOf0(esk12_2(X36,X37),X37)
| sdtlpdtrp0(xc,esk13_2(X36,X37)) != X36 )
& ( ~ aElementOf0(X36,xT)
| ~ isCountable0(X37)
| ~ aSet0(X37)
| aElementOf0(esk12_2(X36,X37),X37)
| aElementOf0(esk13_2(X36,X37),slbdtsldtrb0(X37,xK)) )
& ( ~ aElementOf0(X36,xT)
| ~ isCountable0(X37)
| ~ aSet0(X37)
| aElementOf0(esk12_2(X36,X37),X37)
| sbrdtbr0(esk13_2(X36,X37)) = xK )
& ( ~ aElementOf0(X36,xT)
| ~ isCountable0(X37)
| ~ aSet0(X37)
| aElementOf0(esk12_2(X36,X37),X37)
| aSubsetOf0(esk13_2(X36,X37),X37) )
& ( ~ aElementOf0(X36,xT)
| ~ isCountable0(X37)
| ~ aSet0(X37)
| aElementOf0(esk12_2(X36,X37),X37)
| aElementOf0(X40,X37)
| ~ aElementOf0(X40,esk13_2(X36,X37)) )
& ( ~ aElementOf0(X36,xT)
| ~ isCountable0(X37)
| ~ aSet0(X37)
| aElementOf0(esk12_2(X36,X37),X37)
| aSet0(esk13_2(X36,X37)) )
& xK = 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_10])])])])])]) ).
fof(c_0_13,hypothesis,
! [X9,X10,X11,X13,X15,X16,X17] :
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ( aElementOf0(X17,xT)
| ~ aElementOf0(X17,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ( aElementOf0(X15,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| sdtlpdtrp0(xc,X16) != X15
| ~ aElementOf0(X16,szDzozmdt0(xc)) )
& ( ~ aElementOf0(X13,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| sdtlpdtrp0(xc,esk2_1(X13)) = X13 )
& ( ~ aElementOf0(X13,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(esk2_1(X13),szDzozmdt0(xc)) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ( aElementOf0(X11,szDzozmdt0(xc))
| sbrdtbr0(X11) != xK
| ~ aSubsetOf0(X11,xS) )
& ( aElementOf0(X11,szDzozmdt0(xc))
| sbrdtbr0(X11) != xK
| ~ aSet0(X11)
| ~ aElementOf0(esk1_1(X11),xS) )
& ( aElementOf0(X11,szDzozmdt0(xc))
| sbrdtbr0(X11) != xK
| ~ aSet0(X11)
| aElementOf0(esk1_1(X11),X11) )
& ( ~ aElementOf0(X9,szDzozmdt0(xc))
| sbrdtbr0(X9) = xK )
& ( ~ aElementOf0(X9,szDzozmdt0(xc))
| aSubsetOf0(X9,xS) )
& ( ~ aElementOf0(X9,szDzozmdt0(xc))
| aElementOf0(X10,xS)
| ~ aElementOf0(X10,X9) )
& ( ~ aElementOf0(X9,szDzozmdt0(xc))
| aSet0(X9) )
& aFunction0(xc) ),
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)],[m__3453])])])])])])]) ).
cnf(c_0_14,plain,
( ~ aSet0(X1)
| sbrdtbr0(X1) != sz00
| X1 = slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
xK = sz00,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xc))
| sbrdtbr0(X1) = xK ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,hypothesis,
( ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(esk2_1(X1),szDzozmdt0(xc)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xc))
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( ~ aSet0(X1)
| sbrdtbr0(X1) != xK
| X1 = slcrc0 ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,hypothesis,
( ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| sbrdtbr0(esk2_1(X1)) = xK ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,hypothesis,
( ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aSet0(esk2_1(X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
fof(c_0_22,plain,
! [X1] :
( ( ~ isFinite0(X1)
& aSet0(X1) )
=> ! [X2] :
( aElementOf0(X2,szNzAzT0)
=> slbdtsldtrb0(X1,X2) != slcrc0 ) ),
inference(fof_simplification,[status(thm)],[mSelNSet]) ).
cnf(c_0_23,hypothesis,
( sdtlpdtrp0(xc,X1) != X2
| ~ aElementOf0(X1,szDzozmdt0(xc))
| aElementOf0(X2,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,hypothesis,
( ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| sdtlpdtrp0(xc,esk2_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_25,hypothesis,
( ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| esk2_1(X1) = slcrc0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
fof(c_0_26,plain,
! [X1] :
( ( isCountable0(X1)
& aSet0(X1) )
=> ~ isFinite0(X1) ),
inference(fof_simplification,[status(thm)],[mCountNFin]) ).
fof(c_0_27,plain,
! [X90,X91] :
( slbdtsldtrb0(X90,X91) != slcrc0
| ~ aElementOf0(X91,szNzAzT0)
| isFinite0(X90)
| ~ aSet0(X90) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
cnf(c_0_28,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
fof(c_0_29,hypothesis,
! [X8] :
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ( aElementOf0(X8,szNzAzT0)
| ~ aElementOf0(X8,xS) )
& aSet0(xS) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3435])])])]) ).
cnf(c_0_30,hypothesis,
( ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(X1,xT) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_31,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,X1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_32,hypothesis,
( ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| sdtlpdtrp0(xc,slcrc0) = X1 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_33,plain,
! [X78] :
( aSet0(szDzozmdt0(X78))
| ~ aFunction0(X78) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDomSet])])]) ).
fof(c_0_34,plain,
! [X46] :
( ~ isFinite0(X46)
| ~ isCountable0(X46)
| ~ aSet0(X46) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).
cnf(c_0_35,plain,
( slbdtsldtrb0(X1,X2) != slcrc0
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X1)
| isFinite0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,hypothesis,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_37,plain,
aElementOf0(xK,szNzAzT0),
inference(rw,[status(thm)],[c_0_28,c_0_15]) ).
cnf(c_0_38,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,X1),xT) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xc))
| sdtlpdtrp0(xc,slcrc0) = sdtlpdtrp0(xc,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
fof(c_0_41,plain,
! [X116,X117,X118] :
( ( X118 = slcrc0
| aElementOf0(esk24_1(X118),X118)
| ~ aSet0(X118) )
& ( X116 != slcrc0
| ~ aElementOf0(X117,X116) )
& ( X116 != slcrc0
| aSet0(X116) ) ),
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)],[mDefEmp])])])])])])]) ).
cnf(c_0_42,plain,
( ~ aFunction0(X1)
| aSet0(szDzozmdt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,hypothesis,
aFunction0(xc),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_44,plain,
( ~ isFinite0(X1)
| ~ isCountable0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_45,hypothesis,
( szDzozmdt0(xc) != slcrc0
| isFinite0(xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38])]) ).
cnf(c_0_46,hypothesis,
isCountable0(xS),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_47,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
( ~ aSet0(X1)
| X1 = slcrc0
| aElementOf0(esk24_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,hypothesis,
aSet0(szDzozmdt0(xc)),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,hypothesis,
szDzozmdt0(xc) != slcrc0,
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_38])]) ).
cnf(c_0_51,negated_conjecture,
( ~ aElementOf0(X1,xT)
| ~ isCountable0(X2)
| ~ aSubsetOf0(X2,xS)
| sdtlpdtrp0(xc,esk13_2(X1,X2)) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_52,hypothesis,
aElementOf0(sdtlpdtrp0(xc,slcrc0),xT),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( ~ aElementOf0(X1,xT)
| ~ isCountable0(X2)
| ~ aSubsetOf0(X2,xS)
| aElementOf0(esk13_2(X1,X2),slbdtsldtrb0(X2,xK)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_54,hypothesis,
( ~ aElementOf0(esk13_2(sdtlpdtrp0(xc,slcrc0),X1),szDzozmdt0(xc))
| ~ isCountable0(X1)
| ~ aSubsetOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_40])]),c_0_52])]) ).
cnf(c_0_55,hypothesis,
( ~ aElementOf0(X1,xT)
| ~ aSubsetOf0(xS,xS)
| aElementOf0(esk13_2(X1,xS),szDzozmdt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_36]),c_0_46])]) ).
fof(c_0_56,plain,
! [X55] :
( aSubsetOf0(X55,X55)
| ~ aSet0(X55) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])])]) ).
cnf(c_0_57,hypothesis,
~ aSubsetOf0(xS,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_46]),c_0_52])]) ).
cnf(c_0_58,plain,
( ~ aSet0(X1)
| aSubsetOf0(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_59,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM563+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 02:43:21 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.84/0.68 % Version: 3.5.1
% 0.84/0.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.84/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.84/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.84/0.68 % Starting new_bool_3 with 300s (1) cores
% 0.84/0.68 % Starting new_bool_1 with 300s (1) cores
% 0.84/0.68 % Starting sh5l with 300s (1) cores
% 0.84/0.68 % new_bool_1 with pid 383925 completed with status 0
% 0.84/0.68 % Result found by new_bool_1
% 0.84/0.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.84/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.84/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.84/0.68 % Starting new_bool_3 with 300s (1) cores
% 0.84/0.68 % Starting new_bool_1 with 300s (1) cores
% 0.84/0.68 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.84/0.68 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.84/0.68 % Search class: FGHSF-SMLM32-SFFFFFNN
% 0.84/0.68 % partial match(1): FGHSF-SMLM33-SFFFFFNN
% 0.84/0.68 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.84/0.68 % Starting SubtermCWHack with 28s (1) cores
% 0.84/0.68 % SubtermCWHack with pid 383954 completed with status 0
% 0.84/0.68 % Result found by SubtermCWHack
% 0.84/0.68 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.84/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.84/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.84/0.68 % Starting new_bool_3 with 300s (1) cores
% 0.84/0.68 % Starting new_bool_1 with 300s (1) cores
% 0.84/0.68 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.84/0.68 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.84/0.68 % Search class: FGHSF-SMLM32-SFFFFFNN
% 0.84/0.68 % partial match(1): FGHSF-SMLM33-SFFFFFNN
% 0.84/0.68 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.84/0.68 % Starting SubtermCWHack with 28s (1) cores
% 0.84/0.68 % Preprocessing time : 0.082 s
% 0.84/0.68
% 0.84/0.68 % Proof found!
% 0.84/0.68 % SZS status Theorem
% 0.84/0.68 % SZS output start CNFRefutation
% See solution above
% 0.84/0.69 % Parsed axioms : 78
% 0.84/0.69 % Removed by relevancy pruning/SinE : 17
% 0.84/0.69 % Initial clauses : 4104
% 0.84/0.69 % Removed in clause preprocessing : 7
% 0.84/0.69 % Initial clauses in saturation : 4097
% 0.84/0.69 % Processed clauses : 392
% 0.84/0.69 % ...of these trivial : 6
% 0.84/0.69 % ...subsumed : 139
% 0.84/0.69 % ...remaining for further processing : 247
% 0.84/0.69 % Other redundant clauses eliminated : 21
% 0.84/0.69 % Clauses deleted for lack of memory : 0
% 0.84/0.69 % Backward-subsumed : 9
% 0.84/0.69 % Backward-rewritten : 8
% 0.84/0.69 % Generated clauses : 741
% 0.84/0.69 % ...of the previous two non-redundant : 594
% 0.84/0.69 % ...aggressively subsumed : 0
% 0.84/0.69 % Contextual simplify-reflections : 13
% 0.84/0.69 % Paramodulations : 718
% 0.84/0.69 % Factorizations : 0
% 0.84/0.69 % NegExts : 0
% 0.84/0.69 % Equation resolutions : 22
% 0.84/0.69 % Disequality decompositions : 0
% 0.84/0.69 % Total rewrite steps : 507
% 0.84/0.69 % ...of those cached : 477
% 0.84/0.69 % Propositional unsat checks : 0
% 0.84/0.69 % Propositional check models : 0
% 0.84/0.69 % Propositional check unsatisfiable : 0
% 0.84/0.69 % Propositional clauses : 0
% 0.84/0.69 % Propositional clauses after purity: 0
% 0.84/0.69 % Propositional unsat core size : 0
% 0.84/0.69 % Propositional preprocessing time : 0.000
% 0.84/0.69 % Propositional encoding time : 0.000
% 0.84/0.69 % Propositional solver time : 0.000
% 0.84/0.69 % Success case prop preproc time : 0.000
% 0.84/0.69 % Success case prop encoding time : 0.000
% 0.84/0.69 % Success case prop solver time : 0.000
% 0.84/0.69 % Current number of processed clauses : 213
% 0.84/0.69 % Positive orientable unit clauses : 35
% 0.84/0.69 % Positive unorientable unit clauses: 0
% 0.84/0.69 % Negative unit clauses : 9
% 0.84/0.69 % Non-unit-clauses : 169
% 0.84/0.69 % Current number of unprocessed clauses: 4282
% 0.84/0.69 % ...number of literals in the above : 51855
% 0.84/0.69 % Current number of archived formulas : 0
% 0.84/0.69 % Current number of archived clauses : 19
% 0.84/0.69 % Clause-clause subsumption calls (NU) : 5900
% 0.84/0.69 % Rec. Clause-clause subsumption calls : 3761
% 0.84/0.69 % Non-unit clause-clause subsumptions : 123
% 0.84/0.69 % Unit Clause-clause subsumption calls : 198
% 0.84/0.69 % Rewrite failures with RHS unbound : 0
% 0.84/0.69 % BW rewrite match attempts : 6
% 0.84/0.69 % BW rewrite match successes : 6
% 0.84/0.69 % Condensation attempts : 0
% 0.84/0.69 % Condensation successes : 0
% 0.84/0.69 % Termbank termtop insertions : 337384
% 0.84/0.69 % Search garbage collected termcells : 25433
% 0.84/0.69
% 0.84/0.69 % -------------------------------------------------
% 0.84/0.69 % User time : 0.212 s
% 0.84/0.69 % System time : 0.023 s
% 0.84/0.69 % Total time : 0.235 s
% 0.84/0.69 % Maximum resident set size: 15272 pages
% 0.84/0.69
% 0.84/0.69 % -------------------------------------------------
% 0.84/0.69 % User time : 0.216 s
% 0.84/0.69 % System time : 0.028 s
% 0.84/0.69 % Total time : 0.244 s
% 0.84/0.69 % Maximum resident set size: 4864 pages
% 0.84/0.69 % E exiting
%------------------------------------------------------------------------------