%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM565+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.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 1.33s 1.73s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 17 unt; 0 def)
% Number of atoms : 133 ( 37 equ)
% Maximal formula atoms : 39 ( 3 avg)
% Number of connectives : 161 ( 65 ~; 67 |; 19 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 40 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(m__,conjecture,
! [X1] :
( aElementOf0(X1,slbdtsldtrb0(xS,sz00))
=> sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__3453,hypothesis,
( aFunction0(xc)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3453) ).
fof(m__3462,hypothesis,
xK = sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3462) ).
fof(m__3435,hypothesis,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
fof(mNATSet,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(mCardEmpty,axiom,
! [X1] :
( aSet0(X1)
=> ( sbrdtbr0(X1) = sz00
<=> X1 = slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
fof(c_0_9,plain,
! [X258,X259,X260,X261,X262,X263] :
( ( aSet0(X260)
| X260 != slbdtsldtrb0(X258,X259)
| ~ aSet0(X258)
| ~ aElementOf0(X259,szNzAzT0) )
& ( aSubsetOf0(X261,X258)
| ~ aElementOf0(X261,X260)
| X260 != slbdtsldtrb0(X258,X259)
| ~ aSet0(X258)
| ~ aElementOf0(X259,szNzAzT0) )
& ( sbrdtbr0(X261) = X259
| ~ aElementOf0(X261,X260)
| X260 != slbdtsldtrb0(X258,X259)
| ~ aSet0(X258)
| ~ aElementOf0(X259,szNzAzT0) )
& ( ~ aSubsetOf0(X262,X258)
| sbrdtbr0(X262) != X259
| aElementOf0(X262,X260)
| X260 != slbdtsldtrb0(X258,X259)
| ~ aSet0(X258)
| ~ aElementOf0(X259,szNzAzT0) )
& ( ~ aElementOf0(esk11_3(X258,X259,X263),X263)
| ~ aSubsetOf0(esk11_3(X258,X259,X263),X258)
| sbrdtbr0(esk11_3(X258,X259,X263)) != X259
| ~ aSet0(X263)
| X263 = slbdtsldtrb0(X258,X259)
| ~ aSet0(X258)
| ~ aElementOf0(X259,szNzAzT0) )
& ( aSubsetOf0(esk11_3(X258,X259,X263),X258)
| aElementOf0(esk11_3(X258,X259,X263),X263)
| ~ aSet0(X263)
| X263 = slbdtsldtrb0(X258,X259)
| ~ aSet0(X258)
| ~ aElementOf0(X259,szNzAzT0) )
& ( sbrdtbr0(esk11_3(X258,X259,X263)) = X259
| aElementOf0(esk11_3(X258,X259,X263),X263)
| ~ aSet0(X263)
| X263 = slbdtsldtrb0(X258,X259)
| ~ aSet0(X258)
| ~ aElementOf0(X259,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_10,plain,
! [X161,X162,X163,X164] :
( ( aSet0(X162)
| ~ aSubsetOf0(X162,X161)
| ~ aSet0(X161) )
& ( ~ aElementOf0(X163,X162)
| aElementOf0(X163,X161)
| ~ aSubsetOf0(X162,X161)
| ~ aSet0(X161) )
& ( aElementOf0(esk2_2(X161,X164),X164)
| ~ aSet0(X164)
| aSubsetOf0(X164,X161)
| ~ aSet0(X161) )
& ( ~ aElementOf0(esk2_2(X161,X164),X161)
| ~ aSet0(X164)
| aSubsetOf0(X164,X161)
| ~ aSet0(X161) ) ),
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_11,negated_conjecture,
~ ! [X1] :
( aElementOf0(X1,slbdtsldtrb0(xS,sz00))
=> sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_12,plain,
( aSubsetOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != slbdtsldtrb0(X2,X4)
| ~ aSet0(X2)
| ~ aElementOf0(X4,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,hypothesis,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_14,hypothesis,
xK = sz00,
inference(split_conjunct,[status(thm)],[m__3462]) ).
cnf(c_0_15,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_17,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
fof(c_0_18,negated_conjecture,
( aElementOf0(esk22_0,slbdtsldtrb0(xS,sz00))
& sdtlpdtrp0(xc,esk22_0) != sdtlpdtrp0(xc,slcrc0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
cnf(c_0_19,plain,
( sbrdtbr0(X1) = X2
| ~ aElementOf0(X1,X3)
| X3 != slbdtsldtrb0(X4,X2)
| ~ aSet0(X4)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,plain,
( aSubsetOf0(X1,X2)
| ~ aElementOf0(X1,slbdtsldtrb0(X2,X3))
| ~ aElementOf0(X3,szNzAzT0)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_21,hypothesis,
slbdtsldtrb0(xS,sz00) = szDzozmdt0(xc),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_22,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_23,hypothesis,
aSet0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_24,negated_conjecture,
aElementOf0(esk22_0,slbdtsldtrb0(xS,sz00)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( sbrdtbr0(X1) = X2
| ~ aElementOf0(X1,slbdtsldtrb0(X3,X2))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_26,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_20,c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_27,negated_conjecture,
aElementOf0(esk22_0,szDzozmdt0(xc)),
inference(rw,[status(thm)],[c_0_24,c_0_21]) ).
fof(c_0_28,plain,
! [X222] :
( ( sbrdtbr0(X222) != sz00
| X222 = slcrc0
| ~ aSet0(X222) )
& ( X222 != slcrc0
| sbrdtbr0(X222) = sz00
| ~ aSet0(X222) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardEmpty])])]) ).
cnf(c_0_29,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_25,c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_30,negated_conjecture,
aSubsetOf0(esk22_0,xS),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
( X1 = slcrc0
| sbrdtbr0(X1) != sz00
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,negated_conjecture,
sbrdtbr0(esk22_0) = sz00,
inference(spm,[status(thm)],[c_0_29,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
aSet0(esk22_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_30]),c_0_23])]) ).
cnf(c_0_34,negated_conjecture,
sdtlpdtrp0(xc,esk22_0) != sdtlpdtrp0(xc,slcrc0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_35,negated_conjecture,
esk22_0 = slcrc0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM565+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n022.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 00:45:21 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.33/1.73 % Version : CSE_E---1.7
% 1.33/1.73 % Problem : theBenchmark.p
% 1.33/1.73 % SZS status Theorem for theBenchmark.p
% 1.33/1.73 % SZS output start CNFRefutation
% See solution above
% 1.33/1.73 % Total time : 1.369s
%------------------------------------------------------------------------------