%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM564+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:57:51 PM UTC 2026
% Result : Theorem 1.17s 1.62s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 53 ( 22 unt; 0 def)
% Number of atoms : 182 ( 44 equ)
% Maximal formula atoms : 39 ( 3 avg)
% Number of connectives : 227 ( 98 ~; 89 |; 25 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 61 ( 0 sgn 32 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mCountNFin,axiom,
! [X1] :
( ( aSet0(X1)
& isCountable0(X1) )
=> ~ isFinite0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(mDefSel,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElementOf0(X2,szNzAzT0) )
=> ! [X3] :
( X3 = slbdtsldtrb0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aSubsetOf0(X4,X1)
& sbrdtbr0(X4) = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(mSelNSet,axiom,
! [X1] :
( ( aSet0(X1)
& ~ isFinite0(X1) )
=> ! [X2] :
( aElementOf0(X2,szNzAzT0)
=> slbdtsldtrb0(X1,X2) != slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelNSet) ).
fof(m__3435,hypothesis,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(mNATSet,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(m__3453,hypothesis,
( aFunction0(xc)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
fof(m__3462,hypothesis,
xK = sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,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__,conjecture,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_12,plain,
! [X1] :
( ( aSet0(X1)
& isCountable0(X1) )
=> ~ isFinite0(X1) ),
inference(fof_simplification,[status(thm)],[mCountNFin]) ).
fof(c_0_13,plain,
! [X158] :
( ~ aSet0(X158)
| ~ isCountable0(X158)
| ~ isFinite0(X158) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
fof(c_0_14,plain,
! [X160,X161,X162,X163] :
( ( aSet0(X161)
| ~ aSubsetOf0(X161,X160)
| ~ aSet0(X160) )
& ( ~ aElementOf0(X162,X161)
| aElementOf0(X162,X160)
| ~ aSubsetOf0(X161,X160)
| ~ aSet0(X160) )
& ( aElementOf0(esk2_2(X160,X163),X163)
| ~ aSet0(X163)
| aSubsetOf0(X163,X160)
| ~ aSet0(X160) )
& ( ~ aElementOf0(esk2_2(X160,X163),X160)
| ~ aSet0(X163)
| aSubsetOf0(X163,X160)
| ~ aSet0(X160) ) ),
inference(distribute,[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_15,plain,
! [X257,X258,X259,X260,X261,X262] :
( ( aSet0(X259)
| X259 != slbdtsldtrb0(X257,X258)
| ~ aSet0(X257)
| ~ aElementOf0(X258,szNzAzT0) )
& ( aSubsetOf0(X260,X257)
| ~ aElementOf0(X260,X259)
| X259 != slbdtsldtrb0(X257,X258)
| ~ aSet0(X257)
| ~ aElementOf0(X258,szNzAzT0) )
& ( sbrdtbr0(X260) = X258
| ~ aElementOf0(X260,X259)
| X259 != slbdtsldtrb0(X257,X258)
| ~ aSet0(X257)
| ~ aElementOf0(X258,szNzAzT0) )
& ( ~ aSubsetOf0(X261,X257)
| sbrdtbr0(X261) != X258
| aElementOf0(X261,X259)
| X259 != slbdtsldtrb0(X257,X258)
| ~ aSet0(X257)
| ~ aElementOf0(X258,szNzAzT0) )
& ( ~ aElementOf0(esk11_3(X257,X258,X262),X262)
| ~ aSubsetOf0(esk11_3(X257,X258,X262),X257)
| sbrdtbr0(esk11_3(X257,X258,X262)) != X258
| ~ aSet0(X262)
| X262 = slbdtsldtrb0(X257,X258)
| ~ aSet0(X257)
| ~ aElementOf0(X258,szNzAzT0) )
& ( aSubsetOf0(esk11_3(X257,X258,X262),X257)
| aElementOf0(esk11_3(X257,X258,X262),X262)
| ~ aSet0(X262)
| X262 = slbdtsldtrb0(X257,X258)
| ~ aSet0(X257)
| ~ aElementOf0(X258,szNzAzT0) )
& ( sbrdtbr0(esk11_3(X257,X258,X262)) = X258
| aElementOf0(esk11_3(X257,X258,X262),X262)
| ~ aSet0(X262)
| X262 = slbdtsldtrb0(X257,X258)
| ~ aSet0(X257)
| ~ aElementOf0(X258,szNzAzT0) ) ),
inference(distribute,[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_16,plain,
! [X1] :
( ( aSet0(X1)
& ~ isFinite0(X1) )
=> ! [X2] :
( aElementOf0(X2,szNzAzT0)
=> slbdtsldtrb0(X1,X2) != slcrc0 ) ),
inference(fof_simplification,[status(thm)],[mSelNSet]) ).
cnf(c_0_17,plain,
( ~ aSet0(X1)
| ~ isCountable0(X1)
| ~ isFinite0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,hypothesis,
isCountable0(xS),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_19,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_21,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_22,plain,
( aSubsetOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != slbdtsldtrb0(X2,X4)
| ~ aSet0(X2)
| ~ aElementOf0(X4,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,hypothesis,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_24,hypothesis,
xK = sz00,
inference(split_conjunct,[status(thm)],[m__3462]) ).
cnf(c_0_25,plain,
( aSet0(X1)
| X1 != slbdtsldtrb0(X2,X3)
| ~ aSet0(X2)
| ~ aElementOf0(X3,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_26,plain,
! [X266,X267] :
( ~ aSet0(X266)
| isFinite0(X266)
| ~ aElementOf0(X267,szNzAzT0)
| slbdtsldtrb0(X266,X267) != slcrc0 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
cnf(c_0_27,hypothesis,
( ~ isFinite0(xS)
| ~ aSet0(xS) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_28,hypothesis,
aSet0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_29,plain,
( sbrdtbr0(X1) = X2
| ~ aElementOf0(X1,X3)
| X3 != slbdtsldtrb0(X4,X2)
| ~ aSet0(X4)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_30,plain,
( aSubsetOf0(X1,X2)
| ~ aElementOf0(X1,slbdtsldtrb0(X2,X3))
| ~ aElementOf0(X3,szNzAzT0)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_31,hypothesis,
slbdtsldtrb0(xS,sz00) = szDzozmdt0(xc),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
fof(c_0_33,plain,
! [X154,X155,X156] :
( ( aSet0(X154)
| X154 != slcrc0 )
& ( ~ aElementOf0(X155,X154)
| X154 != slcrc0 )
& ( ~ aSet0(X156)
| aElementOf0(esk1_1(X156),X156)
| X156 = slcrc0 ) ),
inference(distribute,[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_34,plain,
( aSet0(slbdtsldtrb0(X1,X2))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
( isFinite0(X1)
| ~ aSet0(X1)
| ~ aElementOf0(X2,szNzAzT0)
| slbdtsldtrb0(X1,X2) != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,hypothesis,
~ isFinite0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_37,plain,
( sbrdtbr0(X1) = X2
| ~ aElementOf0(X1,slbdtsldtrb0(X3,X2))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_38,hypothesis,
( aSubsetOf0(X1,xS)
| ~ aElementOf0(X1,szDzozmdt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_28])]) ).
cnf(c_0_39,plain,
( aElementOf0(esk1_1(X1),X1)
| X1 = slcrc0
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,hypothesis,
aSet0(szDzozmdt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_31]),c_0_32]),c_0_28])]) ).
cnf(c_0_41,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_35,c_0_31]),c_0_32]),c_0_28])]),c_0_36]) ).
fof(c_0_42,plain,
! [X221] :
( ( sbrdtbr0(X221) != sz00
| X221 = slcrc0
| ~ aSet0(X221) )
& ( X221 != slcrc0
| sbrdtbr0(X221) = sz00
| ~ aSet0(X221) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardEmpty])])]) ).
cnf(c_0_43,hypothesis,
( sbrdtbr0(X1) = sz00
| ~ aElementOf0(X1,szDzozmdt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_31]),c_0_32]),c_0_28])]) ).
cnf(c_0_44,hypothesis,
aSubsetOf0(esk1_1(szDzozmdt0(xc)),xS),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]),c_0_41]) ).
fof(c_0_45,negated_conjecture,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_46,plain,
( X1 = slcrc0
| sbrdtbr0(X1) != sz00
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_47,hypothesis,
sbrdtbr0(esk1_1(szDzozmdt0(xc))) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_39]),c_0_40])]),c_0_41]) ).
cnf(c_0_48,hypothesis,
aSet0(esk1_1(szDzozmdt0(xc))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_44]),c_0_28])]) ).
cnf(c_0_49,negated_conjecture,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_50,hypothesis,
esk1_1(szDzozmdt0(xc)) = slcrc0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48])]) ).
cnf(c_0_51,negated_conjecture,
~ aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(rw,[status(thm)],[c_0_49,c_0_31]) ).
cnf(c_0_52,hypothesis,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_50]),c_0_40])]),c_0_41]),c_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : NUM564+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 19:45:11 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.17/1.62 % Version : CSE_E---1.7
% 1.17/1.62 % Problem : theBenchmark.p
% 1.17/1.62 % SZS status Theorem for theBenchmark.p
% 1.17/1.62 % SZS output start CNFRefutation
% See solution above
% 1.17/1.62 % Total time : 1.363s
%------------------------------------------------------------------------------