%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM580+3 : 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 : n008.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 04:57:54 PM UTC 2026
% Result : Theorem 14.96s 9.42s
% Output : CNFRefutation 14.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 14 unt; 0 def)
% Number of atoms : 216 ( 38 equ)
% Maximal formula atoms : 52 ( 5 avg)
% Number of connectives : 271 ( 94 ~; 95 |; 56 &)
% ( 6 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 54 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__3671,hypothesis,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(m__,conjecture,
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) ) )
=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| X1 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
=> sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mCardCons,axiom,
! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardCons) ).
fof(mCardNum,axiom,
! [X1] :
( aSet0(X1)
=> ( aElementOf0(sbrdtbr0(X1),szNzAzT0)
<=> isFinite0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
fof(m__3989_02,hypothesis,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& X1 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
& aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989_02) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__3989,hypothesis,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElement0(X2) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElement0(X4)
& aElementOf0(X4,X1)
& X4 != X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(m__3533,hypothesis,
( aElementOf0(xk,szNzAzT0)
& szszuzczcdt0(xk) = xK ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3533) ).
fof(c_0_9,hypothesis,
! [X383,X384] :
( ( aSet0(sdtlpdtrp0(xN,X383))
| ~ aElementOf0(X383,szNzAzT0) )
& ( ~ aElementOf0(X384,sdtlpdtrp0(xN,X383))
| aElementOf0(X384,szNzAzT0)
| ~ aElementOf0(X383,szNzAzT0) )
& ( aSubsetOf0(sdtlpdtrp0(xN,X383),szNzAzT0)
| ~ aElementOf0(X383,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,X383))
| ~ aElementOf0(X383,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3671])])])]) ).
fof(c_0_10,negated_conjecture,
~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) ) )
=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| X1 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
=> sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_11,plain,
! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[mCardCons]) ).
fof(c_0_12,plain,
! [X256] :
( ( ~ aElementOf0(sbrdtbr0(X256),szNzAzT0)
| isFinite0(X256)
| ~ aSet0(X256) )
& ( ~ isFinite0(X256)
| aElementOf0(sbrdtbr0(X256),szNzAzT0)
| ~ aSet0(X256) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardNum])])]) ).
fof(c_0_13,hypothesis,
! [X392,X393,X394] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ( ~ aElementOf0(X392,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X392) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElement0(X393)
| ~ aElementOf0(X393,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( aElementOf0(X393,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X393,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( X393 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X393,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ~ aElement0(X393)
| ~ aElementOf0(X393,sdtlpdtrp0(xN,xi))
| X393 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X393,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(xQ)
& ( ~ aElementOf0(X394,xQ)
| aElementOf0(X394,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3989_02])])])]) ).
fof(c_0_14,plain,
! [X188,X189] :
( ~ aSet0(X188)
| ~ aElementOf0(X189,X188)
| aElement0(X189) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
cnf(c_0_15,hypothesis,
( aSet0(sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,hypothesis,
aElementOf0(xi,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3989]) ).
fof(c_0_17,plain,
! [X216,X217,X218,X219,X220,X221] :
( ( aSet0(X218)
| X218 != sdtmndt0(X216,X217)
| ~ aSet0(X216)
| ~ aElement0(X217) )
& ( aElement0(X219)
| ~ aElementOf0(X219,X218)
| X218 != sdtmndt0(X216,X217)
| ~ aSet0(X216)
| ~ aElement0(X217) )
& ( aElementOf0(X219,X216)
| ~ aElementOf0(X219,X218)
| X218 != sdtmndt0(X216,X217)
| ~ aSet0(X216)
| ~ aElement0(X217) )
& ( X219 != X217
| ~ aElementOf0(X219,X218)
| X218 != sdtmndt0(X216,X217)
| ~ aSet0(X216)
| ~ aElement0(X217) )
& ( ~ aElement0(X220)
| ~ aElementOf0(X220,X216)
| X220 = X217
| aElementOf0(X220,X218)
| X218 != sdtmndt0(X216,X217)
| ~ aSet0(X216)
| ~ aElement0(X217) )
& ( ~ aElementOf0(esk4_3(X216,X217,X221),X221)
| ~ aElement0(esk4_3(X216,X217,X221))
| ~ aElementOf0(esk4_3(X216,X217,X221),X216)
| esk4_3(X216,X217,X221) = X217
| ~ aSet0(X221)
| X221 = sdtmndt0(X216,X217)
| ~ aSet0(X216)
| ~ aElement0(X217) )
& ( aElement0(esk4_3(X216,X217,X221))
| aElementOf0(esk4_3(X216,X217,X221),X221)
| ~ aSet0(X221)
| X221 = sdtmndt0(X216,X217)
| ~ aSet0(X216)
| ~ aElement0(X217) )
& ( aElementOf0(esk4_3(X216,X217,X221),X216)
| aElementOf0(esk4_3(X216,X217,X221),X221)
| ~ aSet0(X221)
| X221 = sdtmndt0(X216,X217)
| ~ aSet0(X216)
| ~ aElement0(X217) )
& ( esk4_3(X216,X217,X221) != X217
| aElementOf0(esk4_3(X216,X217,X221),X221)
| ~ aSet0(X221)
| X221 = sdtmndt0(X216,X217)
| ~ aSet0(X216)
| ~ aElement0(X217) ) ),
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)],[mDefDiff])])])])])]) ).
fof(c_0_18,negated_conjecture,
! [X395,X396] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ( ~ aElementOf0(X395,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X395) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElement0(X396)
| ~ aElementOf0(X396,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( aElementOf0(X396,xQ)
| X396 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X396,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ~ aElementOf0(X396,xQ)
| ~ aElement0(X396)
| aElementOf0(X396,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( X396 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElement0(X396)
| aElementOf0(X396,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_19,plain,
! [X258,X259] :
( ~ aSet0(X258)
| ~ isFinite0(X258)
| ~ aElement0(X259)
| aElementOf0(X259,X258)
| sbrdtbr0(sdtpldt0(X258,X259)) = szszuzczcdt0(sbrdtbr0(X258)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
cnf(c_0_20,plain,
( isFinite0(X1)
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,hypothesis,
sbrdtbr0(xQ) = xk,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,hypothesis,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3533]) ).
cnf(c_0_23,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,hypothesis,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_26,hypothesis,
aSet0(sdtlpdtrp0(xN,xi)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_27,plain,
( X1 != X2
| ~ aElementOf0(X1,X3)
| X3 != sdtmndt0(X4,X2)
| ~ aSet0(X4)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,negated_conjecture,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
( aElementOf0(X2,X1)
| sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1))
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,hypothesis,
szszuzczcdt0(xk) = xK,
inference(split_conjunct,[status(thm)],[m__3533]) ).
cnf(c_0_31,hypothesis,
isFinite0(xQ),
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_32,hypothesis,
aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_33,plain,
( X1 != sdtmndt0(X2,X3)
| ~ aElementOf0(X3,X1)
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_34,hypothesis,
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X1,xQ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_35,negated_conjecture,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_21]),c_0_30]),c_0_31]),c_0_32]),c_0_23])]) ).
cnf(c_0_36,plain,
( ~ aElementOf0(X1,sdtmndt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_37,hypothesis,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,hypothesis,
$false,
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_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM580+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n008.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 00:47:58 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 14.96/9.42 % Version : CSE_E---1.7
% 14.96/9.42 % Problem : theBenchmark.p
% 14.96/9.42 % SZS status Theorem for theBenchmark.p
% 14.96/9.42 % SZS output start CNFRefutation
% See solution above
% 14.96/9.45 % Total time : 7.781s
%------------------------------------------------------------------------------