%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM566+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 01:49:35 PM UTC 2026
% Result : Theorem 1.02s 0.73s
% Output : CNFRefutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 53 ( 14 unt; 0 def)
% Number of atoms : 327 ( 53 equ)
% Maximal formula atoms : 87 ( 6 avg)
% Number of connectives : 440 ( 166 ~; 160 |; 88 &)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-2 aty)
% Number of variables : 74 ( 1 sgn 48 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
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__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/sandbox/benchmark/theBenchmark.p',m__3453) ).
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(m__3507,hypothesis,
! [X1] :
( ( aElementOf0(X1,slbdtsldtrb0(xS,sz00))
| ( sbrdtbr0(X1) = sz00
& ( aSubsetOf0(X1,xS)
| ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) )
& aSet0(X1) ) ) ) )
=> ( sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0)
& ~ ? [X2] : aElementOf0(X2,slcrc0)
& aSet0(slcrc0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3507) ).
fof(mCountNFin,axiom,
! [X1] :
( ( isCountable0(X1)
& aSet0(X1) )
=> ~ isFinite0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(m__3462,hypothesis,
xK = sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3462) ).
fof(m__3435,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
fof(mDomSet,axiom,
! [X1] :
( aFunction0(X1)
=> aSet0(szDzozmdt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDomSet) ).
fof(m__,conjecture,
? [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/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( ~ ? [X2] : aElementOf0(X2,X1)
& aSet0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(mSubRefl,axiom,
! [X1] :
( aSet0(X1)
=> aSubsetOf0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
fof(c_0_12,plain,
! [X1] :
( ( ~ isFinite0(X1)
& aSet0(X1) )
=> ! [X2] :
( aElementOf0(X2,szNzAzT0)
=> slbdtsldtrb0(X1,X2) != slcrc0 ) ),
inference(fof_simplification,[status(thm)],[mSelNSet]) ).
fof(c_0_13,hypothesis,
! [X179,X180,X181,X183,X185,X186,X187] :
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& ( aElementOf0(X187,xT)
| ~ aElementOf0(X187,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ( aElementOf0(X185,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| sdtlpdtrp0(xc,X186) != X185
| ~ aElementOf0(X186,szDzozmdt0(xc)) )
& ( ~ aElementOf0(X183,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| sdtlpdtrp0(xc,esk21_1(X183)) = X183 )
& ( ~ aElementOf0(X183,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(esk21_1(X183),szDzozmdt0(xc)) )
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& ( aElementOf0(X181,szDzozmdt0(xc))
| sbrdtbr0(X181) != xK
| ~ aSubsetOf0(X181,xS) )
& ( aElementOf0(X181,szDzozmdt0(xc))
| sbrdtbr0(X181) != xK
| ~ aSet0(X181)
| ~ aElementOf0(esk20_1(X181),xS) )
& ( aElementOf0(X181,szDzozmdt0(xc))
| sbrdtbr0(X181) != xK
| ~ aSet0(X181)
| aElementOf0(esk20_1(X181),X181) )
& ( ~ aElementOf0(X179,szDzozmdt0(xc))
| sbrdtbr0(X179) = xK )
& ( ~ aElementOf0(X179,szDzozmdt0(xc))
| aSubsetOf0(X179,xS) )
& ( ~ aElementOf0(X179,szDzozmdt0(xc))
| aElementOf0(X180,xS)
| ~ aElementOf0(X180,X179) )
& ( ~ aElementOf0(X179,szDzozmdt0(xc))
| aSet0(X179) )
& 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])])])])])])]) ).
fof(c_0_14,plain,
! [X165,X166] :
( aElementOf0(sdtlpdtrp0(X165,X166),sdtlcdtrc0(X165,szDzozmdt0(X165)))
| ~ aElementOf0(X166,szDzozmdt0(X165))
| ~ aFunction0(X165) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mImgRng])])])]) ).
fof(c_0_15,hypothesis,
! [X208,X210] :
( ( ~ aElementOf0(X208,slbdtsldtrb0(xS,sz00))
| sdtlpdtrp0(xc,X208) = sdtlpdtrp0(xc,slcrc0) )
& ( ~ aElementOf0(X208,slbdtsldtrb0(xS,sz00))
| ~ aElementOf0(X210,slcrc0) )
& ( ~ aElementOf0(X208,slbdtsldtrb0(xS,sz00))
| aSet0(slcrc0) )
& ( sbrdtbr0(X208) != sz00
| ~ aSubsetOf0(X208,xS)
| sdtlpdtrp0(xc,X208) = sdtlpdtrp0(xc,slcrc0) )
& ( sbrdtbr0(X208) != sz00
| ~ aSubsetOf0(X208,xS)
| ~ aElementOf0(X210,slcrc0) )
& ( sbrdtbr0(X208) != sz00
| ~ aSubsetOf0(X208,xS)
| aSet0(slcrc0) )
& ( sbrdtbr0(X208) != sz00
| ~ aSet0(X208)
| ~ aElementOf0(esk31_1(X208),xS)
| sdtlpdtrp0(xc,X208) = sdtlpdtrp0(xc,slcrc0) )
& ( sbrdtbr0(X208) != sz00
| ~ aSet0(X208)
| ~ aElementOf0(esk31_1(X208),xS)
| ~ aElementOf0(X210,slcrc0) )
& ( sbrdtbr0(X208) != sz00
| ~ aSet0(X208)
| ~ aElementOf0(esk31_1(X208),xS)
| aSet0(slcrc0) )
& ( sbrdtbr0(X208) != sz00
| ~ aSet0(X208)
| aElementOf0(esk31_1(X208),X208)
| sdtlpdtrp0(xc,X208) = sdtlpdtrp0(xc,slcrc0) )
& ( sbrdtbr0(X208) != sz00
| ~ aSet0(X208)
| aElementOf0(esk31_1(X208),X208)
| ~ aElementOf0(X210,slcrc0) )
& ( sbrdtbr0(X208) != sz00
| ~ aSet0(X208)
| aElementOf0(esk31_1(X208),X208)
| aSet0(slcrc0) ) ),
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)],[m__3507])])])])])]) ).
fof(c_0_16,plain,
! [X1] :
( ( isCountable0(X1)
& aSet0(X1) )
=> ~ isFinite0(X1) ),
inference(fof_simplification,[status(thm)],[mCountNFin]) ).
fof(c_0_17,plain,
! [X130,X131] :
( slbdtsldtrb0(X130,X131) != slcrc0
| ~ aElementOf0(X131,szNzAzT0)
| isFinite0(X130)
| ~ aSet0(X130) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
cnf(c_0_18,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_19,hypothesis,
xK = sz00,
inference(split_conjunct,[status(thm)],[m__3462]) ).
fof(c_0_20,hypothesis,
! [X178] :
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ( aElementOf0(X178,szNzAzT0)
| ~ aElementOf0(X178,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_21,hypothesis,
( ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(X1,xT) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
( ~ aElementOf0(X2,szDzozmdt0(X1))
| ~ aFunction0(X1)
| aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,hypothesis,
aFunction0(xc),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,hypothesis,
( ~ aElementOf0(X1,slbdtsldtrb0(xS,sz00))
| sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,hypothesis,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_26,plain,
! [X142] :
( aSet0(szDzozmdt0(X142))
| ~ aFunction0(X142) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDomSet])])]) ).
fof(c_0_27,plain,
! [X18] :
( ~ isFinite0(X18)
| ~ isCountable0(X18)
| ~ aSet0(X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
cnf(c_0_28,plain,
( slbdtsldtrb0(X1,X2) != slcrc0
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X1)
| isFinite0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_29,plain,
aElementOf0(xK,szNzAzT0),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_30,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_31,negated_conjecture,
~ ? [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__]) ).
cnf(c_0_32,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,X1),xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_33,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xc))
| sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_19]),c_0_25]) ).
fof(c_0_34,plain,
! [X13,X14,X15] :
( ( X15 = slcrc0
| aElementOf0(esk1_1(X15),X15)
| ~ aSet0(X15) )
& ( X13 != slcrc0
| ~ aElementOf0(X14,X13) )
& ( X13 != slcrc0
| aSet0(X13) ) ),
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_35,plain,
( ~ aFunction0(X1)
| aSet0(szDzozmdt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,plain,
( ~ isFinite0(X1)
| ~ isCountable0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,hypothesis,
( szDzozmdt0(xc) != slcrc0
| isFinite0(xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_25]),c_0_29]),c_0_30])]) ).
cnf(c_0_38,hypothesis,
isCountable0(xS),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_39,negated_conjecture,
! [X211,X212,X215] :
( ( ~ aElementOf0(X211,xT)
| ~ isCountable0(X212)
| ~ aSubsetOf0(X212,xS)
| sdtlpdtrp0(xc,esk33_2(X211,X212)) != X211 )
& ( ~ aElementOf0(X211,xT)
| ~ isCountable0(X212)
| ~ aSubsetOf0(X212,xS)
| aElementOf0(esk33_2(X211,X212),slbdtsldtrb0(X212,xK)) )
& ( ~ aElementOf0(X211,xT)
| ~ isCountable0(X212)
| ~ aSubsetOf0(X212,xS)
| sbrdtbr0(esk33_2(X211,X212)) = xK )
& ( ~ aElementOf0(X211,xT)
| ~ isCountable0(X212)
| ~ aSubsetOf0(X212,xS)
| aSubsetOf0(esk33_2(X211,X212),X212) )
& ( ~ aElementOf0(X211,xT)
| ~ isCountable0(X212)
| ~ aSubsetOf0(X212,xS)
| aElementOf0(X215,X212)
| ~ aElementOf0(X215,esk33_2(X211,X212)) )
& ( ~ aElementOf0(X211,xT)
| ~ isCountable0(X212)
| ~ aSubsetOf0(X212,xS)
| aSet0(esk33_2(X211,X212)) )
& ( ~ aElementOf0(X211,xT)
| ~ isCountable0(X212)
| ~ aSet0(X212)
| ~ aElementOf0(esk32_2(X211,X212),xS)
| sdtlpdtrp0(xc,esk33_2(X211,X212)) != X211 )
& ( ~ aElementOf0(X211,xT)
| ~ isCountable0(X212)
| ~ aSet0(X212)
| ~ aElementOf0(esk32_2(X211,X212),xS)
| aElementOf0(esk33_2(X211,X212),slbdtsldtrb0(X212,xK)) )
& ( ~ aElementOf0(X211,xT)
| ~ isCountable0(X212)
| ~ aSet0(X212)
| ~ aElementOf0(esk32_2(X211,X212),xS)
| sbrdtbr0(esk33_2(X211,X212)) = xK )
& ( ~ aElementOf0(X211,xT)
| ~ isCountable0(X212)
| ~ aSet0(X212)
| ~ aElementOf0(esk32_2(X211,X212),xS)
| aSubsetOf0(esk33_2(X211,X212),X212) )
& ( ~ aElementOf0(X211,xT)
| ~ isCountable0(X212)
| ~ aSet0(X212)
| ~ aElementOf0(esk32_2(X211,X212),xS)
| aElementOf0(X215,X212)
| ~ aElementOf0(X215,esk33_2(X211,X212)) )
& ( ~ aElementOf0(X211,xT)
| ~ isCountable0(X212)
| ~ aSet0(X212)
| ~ aElementOf0(esk32_2(X211,X212),xS)
| aSet0(esk33_2(X211,X212)) )
& ( ~ aElementOf0(X211,xT)
| ~ isCountable0(X212)
| ~ aSet0(X212)
| aElementOf0(esk32_2(X211,X212),X212)
| sdtlpdtrp0(xc,esk33_2(X211,X212)) != X211 )
& ( ~ aElementOf0(X211,xT)
| ~ isCountable0(X212)
| ~ aSet0(X212)
| aElementOf0(esk32_2(X211,X212),X212)
| aElementOf0(esk33_2(X211,X212),slbdtsldtrb0(X212,xK)) )
& ( ~ aElementOf0(X211,xT)
| ~ isCountable0(X212)
| ~ aSet0(X212)
| aElementOf0(esk32_2(X211,X212),X212)
| sbrdtbr0(esk33_2(X211,X212)) = xK )
& ( ~ aElementOf0(X211,xT)
| ~ isCountable0(X212)
| ~ aSet0(X212)
| aElementOf0(esk32_2(X211,X212),X212)
| aSubsetOf0(esk33_2(X211,X212),X212) )
& ( ~ aElementOf0(X211,xT)
| ~ isCountable0(X212)
| ~ aSet0(X212)
| aElementOf0(esk32_2(X211,X212),X212)
| aElementOf0(X215,X212)
| ~ aElementOf0(X215,esk33_2(X211,X212)) )
& ( ~ aElementOf0(X211,xT)
| ~ isCountable0(X212)
| ~ aSet0(X212)
| aElementOf0(esk32_2(X211,X212),X212)
| aSet0(esk33_2(X211,X212)) ) ),
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_31])])])])])]) ).
cnf(c_0_40,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,plain,
( ~ aSet0(X1)
| X1 = slcrc0
| aElementOf0(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,hypothesis,
aSet0(szDzozmdt0(xc)),
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
cnf(c_0_43,hypothesis,
szDzozmdt0(xc) != slcrc0,
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_30])]) ).
cnf(c_0_44,negated_conjecture,
( ~ aElementOf0(X1,xT)
| ~ isCountable0(X2)
| ~ aSubsetOf0(X2,xS)
| sdtlpdtrp0(xc,esk33_2(X1,X2)) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,hypothesis,
aElementOf0(sdtlpdtrp0(xc,slcrc0),xT),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]),c_0_43]) ).
cnf(c_0_46,negated_conjecture,
( ~ aElementOf0(X1,xT)
| ~ isCountable0(X2)
| ~ aSubsetOf0(X2,xS)
| aElementOf0(esk33_2(X1,X2),slbdtsldtrb0(X2,xK)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,hypothesis,
( ~ aElementOf0(esk33_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_44,c_0_33])]),c_0_45])]) ).
cnf(c_0_48,hypothesis,
( ~ aElementOf0(X1,xT)
| ~ aSubsetOf0(xS,xS)
| aElementOf0(esk33_2(X1,xS),szDzozmdt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_25]),c_0_38])]) ).
fof(c_0_49,plain,
! [X27] :
( aSubsetOf0(X27,X27)
| ~ aSet0(X27) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])])]) ).
cnf(c_0_50,hypothesis,
~ aSubsetOf0(xS,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_38]),c_0_45])]) ).
cnf(c_0_51,plain,
( ~ aSet0(X1)
| aSubsetOf0(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_52,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM566+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n008.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 02:41:23 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 1.02/0.73 % Version: 3.5.1
% 1.02/0.73 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.02/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.02/0.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.02/0.73 % Starting new_bool_3 with 300s (1) cores
% 1.02/0.73 % Starting new_bool_1 with 300s (1) cores
% 1.02/0.73 % Starting sh5l with 300s (1) cores
% 1.02/0.73 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 4166858 completed with status 0
% 1.02/0.73 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.02/0.73 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.02/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.02/0.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.02/0.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.02/0.73 % No SInE strategy applied
% 1.02/0.73 % Search class: FGHSF-SMLM32-MFFFFFNN
% 1.02/0.73 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.02/0.73 % Starting SubtermCWHack with 136s (1) cores
% 1.02/0.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.02/0.73 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 1.02/0.73 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 1.02/0.73 % Starting new_bool_3 with 136s (1) cores
% 1.02/0.73 % SubtermCWHack with pid 4166862 completed with status 0
% 1.02/0.73 % Result found by SubtermCWHack
% 1.02/0.73 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.02/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.02/0.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.02/0.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.02/0.73 % No SInE strategy applied
% 1.02/0.73 % Search class: FGHSF-SMLM32-MFFFFFNN
% 1.02/0.73 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.02/0.73 % Starting SubtermCWHack with 136s (1) cores
% 1.02/0.73 % Preprocessing time : 0.100 s
% 1.02/0.73
% 1.02/0.73 % Proof found!
% 1.02/0.73 % SZS status Theorem
% 1.02/0.73 % SZS output start CNFRefutation
% See solution above
% 1.02/0.73 % Parsed axioms : 81
% 1.02/0.73 % Removed by relevancy pruning/SinE : 0
% 1.02/0.73 % Initial clauses : 4171
% 1.02/0.73 % Removed in clause preprocessing : 7
% 1.02/0.73 % Initial clauses in saturation : 4164
% 1.02/0.73 % Processed clauses : 552
% 1.02/0.73 % ...of these trivial : 8
% 1.02/0.73 % ...subsumed : 211
% 1.02/0.73 % ...remaining for further processing : 333
% 1.02/0.73 % Other redundant clauses eliminated : 45
% 1.02/0.73 % Clauses deleted for lack of memory : 0
% 1.02/0.73 % Backward-subsumed : 8
% 1.02/0.73 % Backward-rewritten : 8
% 1.02/0.73 % Generated clauses : 1116
% 1.02/0.73 % ...of the previous two non-redundant : 930
% 1.02/0.73 % ...aggressively subsumed : 0
% 1.02/0.73 % Contextual simplify-reflections : 25
% 1.02/0.73 % Paramodulations : 1072
% 1.02/0.73 % Factorizations : 0
% 1.02/0.73 % NegExts : 0
% 1.02/0.73 % Equation resolutions : 46
% 1.02/0.73 % Disequality decompositions : 0
% 1.02/0.73 % Total rewrite steps : 683
% 1.02/0.73 % ...of those cached : 652
% 1.02/0.73 % Propositional unsat checks : 0
% 1.02/0.73 % Propositional check models : 0
% 1.02/0.73 % Propositional check unsatisfiable : 0
% 1.02/0.73 % Propositional clauses : 0
% 1.02/0.73 % Propositional clauses after purity: 0
% 1.02/0.73 % Propositional unsat core size : 0
% 1.02/0.73 % Propositional preprocessing time : 0.000
% 1.02/0.73 % Propositional encoding time : 0.000
% 1.02/0.73 % Propositional solver time : 0.000
% 1.02/0.73 % Success case prop preproc time : 0.000
% 1.02/0.73 % Success case prop encoding time : 0.000
% 1.02/0.73 % Success case prop solver time : 0.000
% 1.02/0.73 % Current number of processed clauses : 280
% 1.02/0.73 % Positive orientable unit clauses : 35
% 1.02/0.73 % Positive unorientable unit clauses: 0
% 1.02/0.73 % Negative unit clauses : 9
% 1.02/0.73 % Non-unit-clauses : 236
% 1.02/0.73 % Current number of unprocessed clauses: 4522
% 1.02/0.73 % ...number of literals in the above : 53174
% 1.02/0.73 % Current number of archived formulas : 0
% 1.02/0.73 % Current number of archived clauses : 18
% 1.02/0.73 % Clause-clause subsumption calls (NU) : 8534
% 1.02/0.73 % Rec. Clause-clause subsumption calls : 5021
% 1.02/0.73 % Non-unit clause-clause subsumptions : 190
% 1.02/0.73 % Unit Clause-clause subsumption calls : 209
% 1.02/0.73 % Rewrite failures with RHS unbound : 0
% 1.02/0.73 % BW rewrite match attempts : 6
% 1.02/0.73 % BW rewrite match successes : 6
% 1.02/0.73 % Condensation attempts : 0
% 1.02/0.73 % Condensation successes : 0
% 1.02/0.73 % Termbank termtop insertions : 348013
% 1.02/0.73 % Search garbage collected termcells : 26750
% 1.02/0.73
% 1.02/0.73 % -------------------------------------------------
% 1.02/0.73 % User time : 0.246 s
% 1.02/0.73 % System time : 0.029 s
% 1.02/0.73 % Total time : 0.275 s
% 1.02/0.73 % Maximum resident set size: 15020 pages
% 1.02/0.73
% 1.02/0.73 % -------------------------------------------------
% 1.02/0.73 % User time : 0.759 s
% 1.02/0.73 % System time : 0.086 s
% 1.02/0.73 % Total time : 0.846 s
% 1.02/0.73 % Maximum resident set size: 4864 pages
% 1.02/0.73 % E exiting
%------------------------------------------------------------------------------