%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM563+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 : n001.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 01:49:34 PM UTC 2026
% Result : Theorem 0.14s 5.50s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 75 ( 21 unt; 0 def)
% Number of atoms : 255 ( 50 equ)
% Maximal formula atoms : 39 ( 3 avg)
% Number of connectives : 314 ( 134 ~; 123 |; 34 &)
% ( 5 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 92 ( 0 sgn 44 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mCountNFin,axiom,
! [X1] :
( ( isCountable0(X1)
& aSet0(X1) )
=> ~ isFinite0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin) ).
fof(m__,conjecture,
( xK = sz00
=> ? [X1] :
( ? [X2] :
( ! [X3] :
( aElementOf0(X3,slbdtsldtrb0(X2,xK))
=> sdtlpdtrp0(xc,X3) = X1 )
& isCountable0(X2)
& aSubsetOf0(X2,xS) )
& aElementOf0(X1,xT) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(mDefSel,axiom,
! [X1,X2] :
( ( aElementOf0(X2,szNzAzT0)
& aSet0(X1) )
=> ! [X3] :
( X3 = slbdtsldtrb0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( sbrdtbr0(X4) = X2
& aSubsetOf0(X4,X1) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(mSelNSet,axiom,
! [X1] :
( ( ~ isFinite0(X1)
& aSet0(X1) )
=> ! [X2] :
( aElementOf0(X2,szNzAzT0)
=> slbdtsldtrb0(X1,X2) != slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSelNSet) ).
fof(m__3435,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(m__3453,hypothesis,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3453) ).
fof(mDomSet,axiom,
! [X1] :
( aFunction0(X1)
=> aSet0(szDzozmdt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDomSet) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( ~ ? [X2] : aElementOf0(X2,X1)
& aSet0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(mCardEmpty,axiom,
! [X1] :
( aSet0(X1)
=> ( sbrdtbr0(X1) = sz00
<=> X1 = slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
fof(m__3291,hypothesis,
( isFinite0(xT)
& aSet0(xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3291) ).
fof(mImgRng,axiom,
! [X1] :
( aFunction0(X1)
=> ! [X2] :
( aElementOf0(X2,szDzozmdt0(X1))
=> aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgRng) ).
fof(mSubRefl,axiom,
! [X1] :
( aSet0(X1)
=> aSubsetOf0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
fof(c_0_15,plain,
! [X1] :
( ( isCountable0(X1)
& aSet0(X1) )
=> ~ isFinite0(X1) ),
inference(fof_simplification,[status(thm)],[mCountNFin]) ).
fof(c_0_16,negated_conjecture,
~ ( xK = sz00
=> ? [X1] :
( ? [X2] :
( ! [X3] :
( aElementOf0(X3,slbdtsldtrb0(X2,xK))
=> sdtlpdtrp0(xc,X3) = X1 )
& isCountable0(X2)
& aSubsetOf0(X2,xS) )
& aElementOf0(X1,xT) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_17,plain,
! [X21] :
( ~ isFinite0(X21)
| ~ isCountable0(X21)
| ~ aSet0(X21) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_18,plain,
! [X25,X26,X27,X28] :
( ( ~ aSet0(X25)
| aSubsetOf0(X28,X25)
| ~ aSet0(X28)
| ~ aElementOf0(esk4_2(X25,X28),X25) )
& ( ~ aSet0(X25)
| aSubsetOf0(X28,X25)
| ~ aSet0(X28)
| aElementOf0(esk4_2(X25,X28),X28) )
& ( ~ aSet0(X25)
| ~ aSubsetOf0(X26,X25)
| aElementOf0(X27,X25)
| ~ aElementOf0(X27,X26) )
& ( ~ aSet0(X25)
| ~ aSubsetOf0(X26,X25)
| aSet0(X26) ) ),
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)],[mDefSub])])])])])])]) ).
fof(c_0_19,plain,
! [X56,X57,X58,X59,X60,X61] :
( ( ~ aElementOf0(X57,szNzAzT0)
| ~ aSet0(X56)
| X61 = slbdtsldtrb0(X56,X57)
| ~ aSet0(X61)
| aElementOf0(esk10_3(X56,X57,X61),X61)
| sbrdtbr0(esk10_3(X56,X57,X61)) = X57 )
& ( ~ aElementOf0(X57,szNzAzT0)
| ~ aSet0(X56)
| X61 = slbdtsldtrb0(X56,X57)
| ~ aSet0(X61)
| aElementOf0(esk10_3(X56,X57,X61),X61)
| aSubsetOf0(esk10_3(X56,X57,X61),X56) )
& ( ~ aElementOf0(X57,szNzAzT0)
| ~ aSet0(X56)
| X61 = slbdtsldtrb0(X56,X57)
| ~ aSet0(X61)
| sbrdtbr0(esk10_3(X56,X57,X61)) != X57
| ~ aSubsetOf0(esk10_3(X56,X57,X61),X56)
| ~ aElementOf0(esk10_3(X56,X57,X61),X61) )
& ( ~ aElementOf0(X57,szNzAzT0)
| ~ aSet0(X56)
| X58 != slbdtsldtrb0(X56,X57)
| aElementOf0(X60,X58)
| sbrdtbr0(X60) != X57
| ~ aSubsetOf0(X60,X56) )
& ( ~ aElementOf0(X57,szNzAzT0)
| ~ aSet0(X56)
| X58 != slbdtsldtrb0(X56,X57)
| ~ aElementOf0(X59,X58)
| sbrdtbr0(X59) = X57 )
& ( ~ aElementOf0(X57,szNzAzT0)
| ~ aSet0(X56)
| X58 != slbdtsldtrb0(X56,X57)
| ~ aElementOf0(X59,X58)
| aSubsetOf0(X59,X56) )
& ( ~ aElementOf0(X57,szNzAzT0)
| ~ aSet0(X56)
| X58 != slbdtsldtrb0(X56,X57)
| aSet0(X58) ) ),
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)],[mDefSel])])])])])])]) ).
fof(c_0_20,negated_conjecture,
! [X13,X14] :
( ( ~ aElementOf0(X13,xT)
| ~ isCountable0(X14)
| ~ aSubsetOf0(X14,xS)
| sdtlpdtrp0(xc,esk3_2(X13,X14)) != X13 )
& ( ~ aElementOf0(X13,xT)
| ~ isCountable0(X14)
| ~ aSubsetOf0(X14,xS)
| aElementOf0(esk3_2(X13,X14),slbdtsldtrb0(X14,xK)) )
& 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_16])])])])])]) ).
fof(c_0_21,plain,
! [X1] :
( ( ~ isFinite0(X1)
& aSet0(X1) )
=> ! [X2] :
( aElementOf0(X2,szNzAzT0)
=> slbdtsldtrb0(X1,X2) != slcrc0 ) ),
inference(fof_simplification,[status(thm)],[mSelNSet]) ).
cnf(c_0_22,plain,
( ~ isFinite0(X1)
| ~ isCountable0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,hypothesis,
isCountable0(xS),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_24,plain,
( ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_26,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_27,plain,
( ~ aElementOf0(X4,szNzAzT0)
| ~ aSet0(X2)
| X3 != slbdtsldtrb0(X2,X4)
| ~ aElementOf0(X1,X3)
| aSubsetOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,hypothesis,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_29,negated_conjecture,
xK = sz00,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,negated_conjecture,
( ~ aElementOf0(X1,xT)
| ~ isCountable0(X2)
| ~ aSubsetOf0(X2,xS)
| aElementOf0(esk3_2(X1,X2),slbdtsldtrb0(X2,xK)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_31,plain,
! [X53] :
( aSet0(szDzozmdt0(X53))
| ~ aFunction0(X53) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDomSet])])]) ).
fof(c_0_32,plain,
! [X65,X66] :
( slbdtsldtrb0(X65,X66) != slcrc0
| ~ aElementOf0(X66,szNzAzT0)
| isFinite0(X65)
| ~ aSet0(X65) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
cnf(c_0_33,hypothesis,
( ~ aSet0(xS)
| ~ isFinite0(xS) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_34,hypothesis,
aSet0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_35,plain,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X4)
| X3 != slbdtsldtrb0(X4,X2)
| ~ aElementOf0(X1,X3)
| sbrdtbr0(X1) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_36,plain,
( ~ aSet0(X2)
| ~ aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X1,slbdtsldtrb0(X2,X3))
| aSubsetOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_37,hypothesis,
slbdtsldtrb0(xS,sz00) = szDzozmdt0(xc),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_38,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_39,negated_conjecture,
( ~ aElementOf0(X1,xT)
| ~ isCountable0(X2)
| ~ aSubsetOf0(X2,xS)
| aElementOf0(esk3_2(X1,X2),slbdtsldtrb0(X2,sz00)) ),
inference(rw,[status(thm)],[c_0_30,c_0_29]) ).
fof(c_0_40,plain,
! [X84,X85,X86] :
( ( X86 = slcrc0
| aElementOf0(esk13_1(X86),X86)
| ~ aSet0(X86) )
& ( X84 != slcrc0
| ~ aElementOf0(X85,X84) )
& ( X84 != slcrc0
| aSet0(X84) ) ),
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_41,plain,
( ~ aFunction0(X1)
| aSet0(szDzozmdt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,hypothesis,
aFunction0(xc),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_43,plain,
( slbdtsldtrb0(X1,X2) != slcrc0
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X1)
| isFinite0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_44,hypothesis,
~ isFinite0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
fof(c_0_45,plain,
! [X83] :
( ( ~ aSet0(X83)
| sbrdtbr0(X83) = sz00
| X83 != slcrc0 )
& ( ~ aSet0(X83)
| X83 = slcrc0
| sbrdtbr0(X83) != sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardEmpty])])])]) ).
cnf(c_0_46,plain,
( ~ aSet0(X3)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,slbdtsldtrb0(X3,X2))
| sbrdtbr0(X1) = X2 ),
inference(er,[status(thm)],[c_0_35]) ).
cnf(c_0_47,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xc))
| aSubsetOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_34])]) ).
cnf(c_0_48,hypothesis,
( ~ aElementOf0(X1,xT)
| ~ aSubsetOf0(xS,xS)
| aElementOf0(esk3_2(X1,xS),szDzozmdt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_37]),c_0_23])]) ).
cnf(c_0_49,plain,
( ~ aSet0(X1)
| X1 = slcrc0
| aElementOf0(esk13_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,hypothesis,
aSet0(szDzozmdt0(xc)),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_51,hypothesis,
szDzozmdt0(xc) != slcrc0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_37]),c_0_38]),c_0_34])]),c_0_44]) ).
cnf(c_0_52,plain,
( ~ aSet0(X1)
| sbrdtbr0(X1) != sz00
| X1 = slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xc))
| sbrdtbr0(X1) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_37]),c_0_38]),c_0_34])]) ).
cnf(c_0_54,hypothesis,
( ~ aElementOf0(X1,xT)
| ~ aSubsetOf0(xS,xS)
| aSubsetOf0(esk3_2(X1,xS),xS) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,hypothesis,
aSubsetOf0(esk13_1(szDzozmdt0(xc)),xS),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_49]),c_0_50])]),c_0_51]) ).
cnf(c_0_56,hypothesis,
( ~ aSet0(X1)
| ~ aElementOf0(X1,szDzozmdt0(xc))
| X1 = slcrc0 ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,hypothesis,
( ~ aElementOf0(X1,xT)
| ~ aSubsetOf0(xS,xS)
| aSet0(esk3_2(X1,xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_54]),c_0_34])]) ).
cnf(c_0_58,plain,
( ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_59,hypothesis,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_60,hypothesis,
aSet0(xT),
inference(split_conjunct,[status(thm)],[m__3291]) ).
fof(c_0_61,plain,
! [X47,X48] :
( aElementOf0(sdtlpdtrp0(X47,X48),sdtlcdtrc0(X47,szDzozmdt0(X47)))
| ~ aElementOf0(X48,szDzozmdt0(X47))
| ~ aFunction0(X47) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mImgRng])])])]) ).
cnf(c_0_62,hypothesis,
aSet0(esk13_1(szDzozmdt0(xc))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_55]),c_0_34])]) ).
cnf(c_0_63,negated_conjecture,
( ~ aElementOf0(X1,xT)
| ~ isCountable0(X2)
| ~ aSubsetOf0(X2,xS)
| sdtlpdtrp0(xc,esk3_2(X1,X2)) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_64,hypothesis,
( ~ aElementOf0(X1,xT)
| ~ aSubsetOf0(xS,xS)
| esk3_2(X1,xS) = slcrc0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_48]),c_0_57]) ).
cnf(c_0_65,hypothesis,
( ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(X1,xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60])]) ).
cnf(c_0_66,plain,
( ~ aElementOf0(X2,szDzozmdt0(X1))
| ~ aFunction0(X1)
| aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_67,hypothesis,
esk13_1(szDzozmdt0(xc)) = slcrc0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_49]),c_0_62]),c_0_50])]),c_0_51]) ).
cnf(c_0_68,negated_conjecture,
( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ~ aSubsetOf0(xS,xS) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_23])])]) ).
cnf(c_0_69,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,X1),xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_42])]) ).
cnf(c_0_70,hypothesis,
aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_67]),c_0_50])]),c_0_51]) ).
fof(c_0_71,plain,
! [X30] :
( aSubsetOf0(X30,X30)
| ~ aSet0(X30) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])])]) ).
cnf(c_0_72,hypothesis,
~ aSubsetOf0(xS,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]) ).
cnf(c_0_73,plain,
( ~ aSet0(X1)
| aSubsetOf0(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_74,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM563+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/5.37 % Computer : n001.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 02:45:50 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.50 % Version: 3.5.1
% 0.14/5.50 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/5.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/5.50 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.50 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.50 % Starting sh5l with 300s (1) cores
% 0.14/5.50 % new_bool_1 with pid 2020059 completed with status 0
% 0.14/5.50 % Result found by new_bool_1
% 0.14/5.50 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/5.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/5.50 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.50 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.50 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/5.50 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/5.50 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.14/5.50 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.50 % Starting SubtermCWHack with 28s (1) cores
% 0.14/5.50 % SubtermCWHack with pid 2020079 completed with status 0
% 0.14/5.50 % Result found by SubtermCWHack
% 0.14/5.50 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/5.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/5.50 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.50 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.50 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/5.50 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/5.50 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.14/5.50 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.50 % Starting SubtermCWHack with 28s (1) cores
% 0.14/5.50 % Preprocessing time : 0.002 s
% 0.14/5.50
% 0.14/5.50 % Proof found!
% 0.14/5.50 % SZS status Theorem
% 0.14/5.50 % SZS output start CNFRefutation
% See solution above
% 0.14/5.50 % Parsed axioms : 78
% 0.14/5.50 % Removed by relevancy pruning/SinE : 7
% 0.14/5.50 % Initial clauses : 135
% 0.14/5.50 % Removed in clause preprocessing : 7
% 0.14/5.50 % Initial clauses in saturation : 128
% 0.14/5.50 % Processed clauses : 570
% 0.14/5.50 % ...of these trivial : 1
% 0.14/5.50 % ...subsumed : 244
% 0.14/5.50 % ...remaining for further processing : 325
% 0.14/5.50 % Other redundant clauses eliminated : 34
% 0.14/5.50 % Clauses deleted for lack of memory : 0
% 0.14/5.50 % Backward-subsumed : 17
% 0.14/5.50 % Backward-rewritten : 18
% 0.14/5.50 % Generated clauses : 1120
% 0.14/5.50 % ...of the previous two non-redundant : 969
% 0.14/5.50 % ...aggressively subsumed : 0
% 0.14/5.50 % Contextual simplify-reflections : 36
% 0.14/5.50 % Paramodulations : 1089
% 0.14/5.50 % Factorizations : 0
% 0.14/5.50 % NegExts : 0
% 0.14/5.50 % Equation resolutions : 35
% 0.14/5.50 % Disequality decompositions : 0
% 0.14/5.50 % Total rewrite steps : 648
% 0.14/5.50 % ...of those cached : 618
% 0.14/5.50 % Propositional unsat checks : 0
% 0.14/5.50 % Propositional check models : 0
% 0.14/5.50 % Propositional check unsatisfiable : 0
% 0.14/5.50 % Propositional clauses : 0
% 0.14/5.50 % Propositional clauses after purity: 0
% 0.14/5.50 % Propositional unsat core size : 0
% 0.14/5.50 % Propositional preprocessing time : 0.000
% 0.14/5.50 % Propositional encoding time : 0.000
% 0.14/5.50 % Propositional solver time : 0.000
% 0.14/5.50 % Success case prop preproc time : 0.000
% 0.14/5.50 % Success case prop encoding time : 0.000
% 0.14/5.50 % Success case prop solver time : 0.000
% 0.14/5.50 % Current number of processed clauses : 265
% 0.14/5.50 % Positive orientable unit clauses : 29
% 0.14/5.50 % Positive unorientable unit clauses: 0
% 0.14/5.50 % Negative unit clauses : 8
% 0.14/5.50 % Non-unit-clauses : 228
% 0.14/5.50 % Current number of unprocessed clauses: 521
% 0.14/5.50 % ...number of literals in the above : 3061
% 0.14/5.50 % Current number of archived formulas : 0
% 0.14/5.50 % Current number of archived clauses : 35
% 0.14/5.50 % Clause-clause subsumption calls (NU) : 11989
% 0.14/5.50 % Rec. Clause-clause subsumption calls : 4955
% 0.14/5.50 % Non-unit clause-clause subsumptions : 215
% 0.14/5.50 % Unit Clause-clause subsumption calls : 343
% 0.14/5.50 % Rewrite failures with RHS unbound : 0
% 0.14/5.50 % BW rewrite match attempts : 4
% 0.14/5.50 % BW rewrite match successes : 4
% 0.14/5.50 % Condensation attempts : 0
% 0.14/5.50 % Condensation successes : 0
% 0.14/5.50 % Termbank termtop insertions : 30738
% 0.14/5.50 % Search garbage collected termcells : 2885
% 0.14/5.50
% 0.14/5.50 % -------------------------------------------------
% 0.14/5.50 % User time : 0.051 s
% 0.14/5.50 % System time : 0.005 s
% 0.14/5.50 % Total time : 0.056 s
% 0.14/5.50 % Maximum resident set size: 3992 pages
% 0.14/5.50
% 0.14/5.50 % -------------------------------------------------
% 0.14/5.50 % User time : 0.054 s
% 0.14/5.50 % System time : 0.009 s
% 0.14/5.50 % Total time : 0.064 s
% 0.14/5.50 % Maximum resident set size: 4864 pages
% 0.14/5.50 % E exiting
%------------------------------------------------------------------------------