%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM563+1 : 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 : 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 01:55:31 PM UTC 2026
% Result : Theorem 0.56s 0.71s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 79 ( 23 unt; 0 def)
% Number of atoms : 269 ( 52 equ)
% Maximal formula atoms : 39 ( 3 avg)
% Number of connectives : 332 ( 142 ~; 135 |; 34 &)
% ( 5 <=>; 16 =>; 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 : 99 ( 0 sgn 40 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mCountNFin,axiom,
! [X1] :
( ( isCountable0(X1)
& aSet0(X1) )
=> ~ isFinite0(X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',m__) ).
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(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(m__3435,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(m__3453,hypothesis,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( ~ ? [X2] : aElementOf0(X2,X1)
& aSet0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(mCardEmpty,axiom,
! [X1] :
( aSet0(X1)
=> ( sbrdtbr0(X1) = sz00
<=> X1 = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
fof(m__3291,hypothesis,
( isFinite0(xT)
& aSet0(xT) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mImgRng) ).
fof(c_0_13,plain,
! [X1] :
( ( isCountable0(X1)
& aSet0(X1) )
=> ~ isFinite0(X1) ),
inference(fof_simplification,[status(thm)],[mCountNFin]) ).
fof(c_0_14,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_15,plain,
! [X1] :
( ( ~ isFinite0(X1)
& aSet0(X1) )
=> ! [X2] :
( aElementOf0(X2,szNzAzT0)
=> slbdtsldtrb0(X1,X2) != slcrc0 ) ),
inference(fof_simplification,[status(thm)],[mSelNSet]) ).
fof(c_0_16,plain,
! [X17] :
( ~ isFinite0(X17)
| ~ isCountable0(X17)
| ~ aSet0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_17,plain,
! [X19,X20,X21,X22] :
( ( ~ aSet0(X19)
| aSubsetOf0(X22,X19)
| ~ aSet0(X22)
| ~ aElementOf0(esk2_2(X19,X22),X19) )
& ( ~ aSet0(X19)
| aSubsetOf0(X22,X19)
| ~ aSet0(X22)
| aElementOf0(esk2_2(X19,X22),X22) )
& ( ~ aSet0(X19)
| ~ aSubsetOf0(X20,X19)
| aElementOf0(X21,X19)
| ~ aElementOf0(X21,X20) )
& ( ~ aSet0(X19)
| ~ aSubsetOf0(X20,X19)
| aSet0(X20) ) ),
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_18,plain,
! [X120,X121,X122,X123,X124,X125] :
( ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X125 = slbdtsldtrb0(X120,X121)
| ~ aSet0(X125)
| aElementOf0(esk11_3(X120,X121,X125),X125)
| sbrdtbr0(esk11_3(X120,X121,X125)) = X121 )
& ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X125 = slbdtsldtrb0(X120,X121)
| ~ aSet0(X125)
| aElementOf0(esk11_3(X120,X121,X125),X125)
| aSubsetOf0(esk11_3(X120,X121,X125),X120) )
& ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X125 = slbdtsldtrb0(X120,X121)
| ~ aSet0(X125)
| sbrdtbr0(esk11_3(X120,X121,X125)) != X121
| ~ aSubsetOf0(esk11_3(X120,X121,X125),X120)
| ~ aElementOf0(esk11_3(X120,X121,X125),X125) )
& ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X122 != slbdtsldtrb0(X120,X121)
| aElementOf0(X124,X122)
| sbrdtbr0(X124) != X121
| ~ aSubsetOf0(X124,X120) )
& ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X122 != slbdtsldtrb0(X120,X121)
| ~ aElementOf0(X123,X122)
| sbrdtbr0(X123) = X121 )
& ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X122 != slbdtsldtrb0(X120,X121)
| ~ aElementOf0(X123,X122)
| aSubsetOf0(X123,X120) )
& ( ~ aElementOf0(X121,szNzAzT0)
| ~ aSet0(X120)
| X122 != slbdtsldtrb0(X120,X121)
| aSet0(X122) ) ),
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_19,negated_conjecture,
! [X183,X184] :
( ( ~ aElementOf0(X183,xT)
| ~ isCountable0(X184)
| ~ aSubsetOf0(X184,xS)
| sdtlpdtrp0(xc,esk22_2(X183,X184)) != X183 )
& ( ~ aElementOf0(X183,xT)
| ~ isCountable0(X184)
| ~ aSubsetOf0(X184,xS)
| aElementOf0(esk22_2(X183,X184),slbdtsldtrb0(X184,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_14])])])])])]) ).
fof(c_0_20,plain,
! [X129,X130] :
( slbdtsldtrb0(X129,X130) != slcrc0
| ~ aElementOf0(X130,szNzAzT0)
| isFinite0(X129)
| ~ aSet0(X129) ),
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,
( ~ isFinite0(X1)
| ~ isCountable0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,hypothesis,
isCountable0(xS),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_23,plain,
( ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_25,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_26,plain,
( ~ aElementOf0(X4,szNzAzT0)
| ~ aSet0(X2)
| X3 != slbdtsldtrb0(X2,X4)
| ~ aElementOf0(X1,X3)
| aSubsetOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,hypothesis,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_28,negated_conjecture,
xK = sz00,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,negated_conjecture,
( ~ aElementOf0(X1,xT)
| ~ isCountable0(X2)
| ~ aSubsetOf0(X2,xS)
| aElementOf0(esk22_2(X1,X2),slbdtsldtrb0(X2,xK)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,plain,
( ~ aElementOf0(X3,szNzAzT0)
| ~ aSet0(X2)
| X1 != slbdtsldtrb0(X2,X3)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_31,plain,
( slbdtsldtrb0(X1,X2) != slcrc0
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X1)
| isFinite0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_33,hypothesis,
( ~ aSet0(xS)
| ~ isFinite0(xS) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_34,hypothesis,
aSet0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_35,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSubsetOf0(X2,X1)
| aElementOf0(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_36,plain,
( ~ aSet0(X2)
| ~ aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X1,slbdtsldtrb0(X2,X3))
| aSubsetOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_37,hypothesis,
slbdtsldtrb0(xS,sz00) = szDzozmdt0(xc),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_38,negated_conjecture,
( ~ aElementOf0(X1,xT)
| ~ isCountable0(X2)
| ~ aSubsetOf0(X2,xS)
| aElementOf0(esk22_2(X1,X2),slbdtsldtrb0(X2,sz00)) ),
inference(rw,[status(thm)],[c_0_29,c_0_28]) ).
fof(c_0_39,plain,
! [X12,X13,X14] :
( ( X14 = slcrc0
| aElementOf0(esk1_1(X14),X14)
| ~ aSet0(X14) )
& ( X12 != slcrc0
| ~ aElementOf0(X13,X12) )
& ( X12 != slcrc0
| aSet0(X12) ) ),
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_40,plain,
( ~ aSet0(X1)
| ~ aElementOf0(X2,szNzAzT0)
| aSet0(slbdtsldtrb0(X1,X2)) ),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_41,plain,
( ~ aSet0(X1)
| slbdtsldtrb0(X1,sz00) != slcrc0
| isFinite0(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_42,hypothesis,
~ isFinite0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
cnf(c_0_43,plain,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X4)
| X3 != slbdtsldtrb0(X4,X2)
| ~ aElementOf0(X1,X3)
| sbrdtbr0(X1) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_44,hypothesis,
( ~ aSet0(X1)
| aElementOf0(esk2_2(X1,xS),xS)
| aSubsetOf0(xS,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
cnf(c_0_45,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_32]),c_0_34])]) ).
cnf(c_0_46,hypothesis,
( ~ aElementOf0(X1,xT)
| ~ aSubsetOf0(xS,xS)
| aElementOf0(esk22_2(X1,xS),szDzozmdt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_37]),c_0_22])]) ).
cnf(c_0_47,plain,
( ~ aSet0(X1)
| X1 = slcrc0
| aElementOf0(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,hypothesis,
aSet0(szDzozmdt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_37]),c_0_32]),c_0_34])]) ).
cnf(c_0_49,hypothesis,
szDzozmdt0(xc) != slcrc0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_37]),c_0_34])]),c_0_42]) ).
fof(c_0_50,plain,
! [X84] :
( ( ~ aSet0(X84)
| sbrdtbr0(X84) = sz00
| X84 != slcrc0 )
& ( ~ aSet0(X84)
| X84 = slcrc0
| sbrdtbr0(X84) != sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardEmpty])])])]) ).
cnf(c_0_51,plain,
( ~ aSet0(X3)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,slbdtsldtrb0(X3,X2))
| sbrdtbr0(X1) = X2 ),
inference(er,[status(thm)],[c_0_43]) ).
cnf(c_0_52,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(esk2_2(X1,X2),X1)
| aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_53,hypothesis,
( aElementOf0(esk2_2(xS,xS),xS)
| aSubsetOf0(xS,xS) ),
inference(spm,[status(thm)],[c_0_44,c_0_34]) ).
cnf(c_0_54,hypothesis,
( ~ aElementOf0(X1,xT)
| ~ aSubsetOf0(xS,xS)
| aSubsetOf0(esk22_2(X1,xS),xS) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_55,hypothesis,
aElementOf0(esk1_1(szDzozmdt0(xc)),szDzozmdt0(xc)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_56,plain,
( ~ aSet0(X1)
| sbrdtbr0(X1) != sz00
| X1 = slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_57,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_51,c_0_37]),c_0_32]),c_0_34])]) ).
cnf(c_0_58,hypothesis,
aSubsetOf0(xS,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_34])]) ).
cnf(c_0_59,hypothesis,
( ~ aElementOf0(X1,xT)
| ~ aSubsetOf0(xS,xS)
| aSet0(esk22_2(X1,xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_54]),c_0_34])]) ).
cnf(c_0_60,hypothesis,
aSubsetOf0(esk1_1(szDzozmdt0(xc)),xS),
inference(spm,[status(thm)],[c_0_45,c_0_55]) ).
cnf(c_0_61,hypothesis,
( ~ aSet0(X1)
| ~ aElementOf0(X1,szDzozmdt0(xc))
| X1 = slcrc0 ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,hypothesis,
( ~ aElementOf0(X1,xT)
| aElementOf0(esk22_2(X1,xS),szDzozmdt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_58])]) ).
cnf(c_0_63,hypothesis,
( ~ aElementOf0(X1,xT)
| aSet0(esk22_2(X1,xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_58])]) ).
cnf(c_0_64,plain,
( ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_65,hypothesis,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_66,hypothesis,
aSet0(xT),
inference(split_conjunct,[status(thm)],[m__3291]) ).
fof(c_0_67,plain,
! [X164,X165] :
( aElementOf0(sdtlpdtrp0(X164,X165),sdtlcdtrc0(X164,szDzozmdt0(X164)))
| ~ aElementOf0(X165,szDzozmdt0(X164))
| ~ aFunction0(X164) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mImgRng])])])]) ).
cnf(c_0_68,hypothesis,
aSet0(esk1_1(szDzozmdt0(xc))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_60]),c_0_34])]) ).
cnf(c_0_69,negated_conjecture,
( ~ aElementOf0(X1,xT)
| ~ isCountable0(X2)
| ~ aSubsetOf0(X2,xS)
| sdtlpdtrp0(xc,esk22_2(X1,X2)) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_70,hypothesis,
( ~ aElementOf0(X1,xT)
| esk22_2(X1,xS) = slcrc0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_71,hypothesis,
( ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(X1,xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66])]) ).
cnf(c_0_72,plain,
( ~ aElementOf0(X2,szDzozmdt0(X1))
| ~ aFunction0(X1)
| aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_73,hypothesis,
aFunction0(xc),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_74,hypothesis,
esk1_1(szDzozmdt0(xc)) = slcrc0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_55]),c_0_68])]) ).
cnf(c_0_75,negated_conjecture,
~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_58]),c_0_22])])]) ).
cnf(c_0_76,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,X1),xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
cnf(c_0_77,hypothesis,
aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(rw,[status(thm)],[c_0_55,c_0_74]) ).
cnf(c_0_78,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM563+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n009.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 02:40:13 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.53 Running first-order theorem proving
% 0.22/0.53 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
% 0.56/0.71 % Version: 3.5.1
% 0.56/0.71 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.56/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.56/0.71 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.56/0.71 % Starting new_bool_3 with 300s (1) cores
% 0.56/0.71 % Starting new_bool_1 with 300s (1) cores
% 0.56/0.71 % Starting sh5l with 300s (1) cores
% 0.56/0.71 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 667561 completed with status 0
% 0.56/0.71 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.56/0.71 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.56/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.56/0.71 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.56/0.71 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.56/0.71 % No SInE strategy applied
% 0.56/0.71 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.56/0.71 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.56/0.71 % Starting SubtermCWHack with 136s (1) cores
% 0.56/0.71 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.56/0.71 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.56/0.71 % Starting G-E--_302_C18_F1_URBAN_S0Y with 136s (1) cores
% 0.56/0.71 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0U with 136s (1) cores
% 0.56/0.71 % G-E--_208_C18_F1_SE_CS_SP_PS_S0U with pid 667570 completed with status 0
% 0.56/0.71 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S0U
% 0.56/0.71 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.56/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.56/0.71 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.56/0.71 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.56/0.71 % No SInE strategy applied
% 0.56/0.71 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.56/0.71 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.56/0.71 % Starting SubtermCWHack with 136s (1) cores
% 0.56/0.71 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.56/0.71 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.56/0.71 % Starting G-E--_302_C18_F1_URBAN_S0Y with 136s (1) cores
% 0.56/0.71 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0U with 136s (1) cores
% 0.56/0.71 % Preprocessing time : 0.006 s
% 0.56/0.71 % Presaturation interreduction done
% 0.56/0.71
% 0.56/0.71 % Proof found!
% 0.56/0.71 % SZS status Theorem
% 0.56/0.71 % SZS output start CNFRefutation
% See solution above
% 0.56/0.71 % Parsed axioms : 78
% 0.56/0.71 % Removed by relevancy pruning/SinE : 0
% 0.56/0.71 % Initial clauses : 159
% 0.56/0.71 % Removed in clause preprocessing : 7
% 0.56/0.71 % Initial clauses in saturation : 152
% 0.56/0.71 % Processed clauses : 634
% 0.56/0.71 % ...of these trivial : 2
% 0.56/0.71 % ...subsumed : 121
% 0.56/0.71 % ...remaining for further processing : 511
% 0.56/0.71 % Other redundant clauses eliminated : 47
% 0.56/0.71 % Clauses deleted for lack of memory : 0
% 0.56/0.71 % Backward-subsumed : 5
% 0.56/0.71 % Backward-rewritten : 21
% 0.56/0.71 % Generated clauses : 983
% 0.56/0.71 % ...of the previous two non-redundant : 924
% 0.56/0.71 % ...aggressively subsumed : 0
% 0.56/0.71 % Contextual simplify-reflections : 18
% 0.56/0.71 % Paramodulations : 938
% 0.56/0.71 % Factorizations : 0
% 0.56/0.71 % NegExts : 0
% 0.56/0.71 % Equation resolutions : 48
% 0.56/0.71 % Disequality decompositions : 0
% 0.56/0.71 % Total rewrite steps : 382
% 0.56/0.71 % ...of those cached : 351
% 0.56/0.71 % Propositional unsat checks : 0
% 0.56/0.71 % Propositional check models : 0
% 0.56/0.71 % Propositional check unsatisfiable : 0
% 0.56/0.71 % Propositional clauses : 0
% 0.56/0.71 % Propositional clauses after purity: 0
% 0.56/0.71 % Propositional unsat core size : 0
% 0.56/0.71 % Propositional preprocessing time : 0.000
% 0.56/0.71 % Propositional encoding time : 0.000
% 0.56/0.71 % Propositional solver time : 0.000
% 0.56/0.71 % Success case prop preproc time : 0.000
% 0.56/0.71 % Success case prop encoding time : 0.000
% 0.56/0.71 % Success case prop solver time : 0.000
% 0.56/0.71 % Current number of processed clauses : 292
% 0.56/0.71 % Positive orientable unit clauses : 31
% 0.56/0.71 % Positive unorientable unit clauses: 0
% 0.56/0.71 % Negative unit clauses : 32
% 0.56/0.71 % Non-unit-clauses : 229
% 0.56/0.71 % Current number of unprocessed clauses: 586
% 0.56/0.71 % ...number of literals in the above : 2089
% 0.56/0.71 % Current number of archived formulas : 0
% 0.56/0.71 % Current number of archived clauses : 179
% 0.56/0.71 % Clause-clause subsumption calls (NU) : 17554
% 0.56/0.71 % Rec. Clause-clause subsumption calls : 7894
% 0.56/0.71 % Non-unit clause-clause subsumptions : 83
% 0.56/0.71 % Unit Clause-clause subsumption calls : 994
% 0.56/0.71 % Rewrite failures with RHS unbound : 0
% 0.56/0.71 % BW rewrite match attempts : 4
% 0.56/0.71 % BW rewrite match successes : 4
% 0.56/0.71 % Condensation attempts : 0
% 0.56/0.71 % Condensation successes : 0
% 0.56/0.71 % Termbank termtop insertions : 31133
% 0.56/0.71 % Search garbage collected termcells : 3454
% 0.56/0.71
% 0.56/0.71 % -------------------------------------------------
% 0.56/0.71 % User time : 0.096 s
% 0.56/0.71 % System time : 0.012 s
% 0.56/0.71 % Total time : 0.108 s
% 0.56/0.71 % Maximum resident set size: 3992 pages
% 0.56/0.71
% 0.56/0.71 % -------------------------------------------------
% 0.56/0.71 % User time : 0.228 s
% 0.56/0.71 % System time : 0.033 s
% 0.56/0.71 % Total time : 0.261 s
% 0.56/0.71 % Maximum resident set size: 4864 pages
% 0.56/0.71 % E exiting
%------------------------------------------------------------------------------