%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM604+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 : n002.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 04:58:00 PM UTC 2026
% Result : Theorem 4.60s 3.34s
% Output : CNFRefutation 4.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 14 unt; 0 def)
% Number of atoms : 126 ( 30 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 139 ( 53 ~; 54 |; 22 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 24 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(mDefMin,axiom,
! [X1] :
( ( aSubsetOf0(X1,szNzAzT0)
& X1 != slcrc0 )
=> ! [X2] :
( X2 = szmzizndt0(X1)
<=> ( aElementOf0(X2,X1)
& ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMin) ).
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(m__4660,hypothesis,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).
fof(m__3671,hypothesis,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(m__5045,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5045) ).
fof(m__,conjecture,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mCountNFin_01,axiom,
! [X1] :
( ( aSet0(X1)
& isCountable0(X1) )
=> X1 != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(m__5034,hypothesis,
( aElementOf0(xi,szNzAzT0)
& sdtlpdtrp0(xe,xi) = xx ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5034) ).
fof(c_0_11,plain,
! [X186,X187,X188,X189] :
( ( aSet0(X187)
| ~ aSubsetOf0(X187,X186)
| ~ aSet0(X186) )
& ( ~ aElementOf0(X188,X187)
| aElementOf0(X188,X186)
| ~ aSubsetOf0(X187,X186)
| ~ aSet0(X186) )
& ( aElementOf0(esk2_2(X186,X189),X189)
| ~ aSet0(X189)
| aSubsetOf0(X189,X186)
| ~ aSet0(X186) )
& ( ~ aElementOf0(esk2_2(X186,X189),X186)
| ~ aSet0(X189)
| aSubsetOf0(X189,X186)
| ~ aSet0(X186) ) ),
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_12,plain,
! [X257,X258,X259,X260] :
( ( aElementOf0(X258,X257)
| X258 != szmzizndt0(X257)
| ~ aSubsetOf0(X257,szNzAzT0)
| X257 = slcrc0 )
& ( ~ aElementOf0(X259,X257)
| sdtlseqdt0(X258,X259)
| X258 != szmzizndt0(X257)
| ~ aSubsetOf0(X257,szNzAzT0)
| X257 = slcrc0 )
& ( aElementOf0(esk7_2(X257,X260),X257)
| ~ aElementOf0(X260,X257)
| X260 = szmzizndt0(X257)
| ~ aSubsetOf0(X257,szNzAzT0)
| X257 = slcrc0 )
& ( ~ sdtlseqdt0(X260,esk7_2(X257,X260))
| ~ aElementOf0(X260,X257)
| X260 = szmzizndt0(X257)
| ~ aSubsetOf0(X257,szNzAzT0)
| X257 = 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)],[mDefMin])])])])])]) ).
cnf(c_0_13,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_15,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_16,plain,
( aElementOf0(X1,X2)
| X2 = slcrc0
| X1 != szmzizndt0(X2)
| ~ aSubsetOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,hypothesis,
! [X366] :
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ( ~ aElementOf0(X366,szNzAzT0)
| sdtlpdtrp0(xe,X366) = szmzizndt0(sdtlpdtrp0(xN,X366)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4660])])]) ).
fof(c_0_18,hypothesis,
! [X346] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X346),szNzAzT0)
| ~ aElementOf0(X346,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,X346))
| ~ aElementOf0(X346,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3671])])]) ).
fof(c_0_19,plain,
! [X180,X181,X182] :
( ( aSet0(X180)
| X180 != slcrc0 )
& ( ~ aElementOf0(X181,X180)
| X180 != slcrc0 )
& ( ~ aSet0(X182)
| aElementOf0(esk1_1(X182),X182)
| X182 = 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_20,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(split_conjunct,[status(thm)],[m__5045]) ).
cnf(c_0_22,hypothesis,
aSet0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_23,plain,
( X1 = slcrc0
| aElementOf0(szmzizndt0(X1),X1)
| ~ aSubsetOf0(X1,szNzAzT0) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_24,hypothesis,
( sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,hypothesis,
( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_26,negated_conjecture,
~ aElementOf0(xx,xS),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_27,plain,
! [X185] :
( ~ aSet0(X185)
| ~ isCountable0(X185)
| X185 != slcrc0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCountNFin_01])]) ).
cnf(c_0_28,plain,
( aSet0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,hypothesis,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_30,hypothesis,
( sdtlpdtrp0(xN,X1) = slcrc0
| aElementOf0(sdtlpdtrp0(xe,X1),sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_31,hypothesis,
sdtlpdtrp0(xe,xi) = xx,
inference(split_conjunct,[status(thm)],[m__5034]) ).
cnf(c_0_32,hypothesis,
aElementOf0(xi,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__5034]) ).
cnf(c_0_33,negated_conjecture,
~ aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
( ~ aSet0(X1)
| ~ isCountable0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,plain,
aSet0(slcrc0),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_36,hypothesis,
( isCountable0(sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_37,hypothesis,
sdtlpdtrp0(xN,xi) = slcrc0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]),c_0_33]) ).
cnf(c_0_38,plain,
~ isCountable0(slcrc0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_34]),c_0_35])]) ).
cnf(c_0_39,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_32])]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM604+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 : n002.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 00:50:01 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 4.60/3.34 % Version : CSE_E---1.7
% 4.60/3.34 % Problem : theBenchmark.p
% 4.60/3.34 % SZS status Theorem for theBenchmark.p
% 4.60/3.34 % SZS output start CNFRefutation
% See solution above
% 4.60/3.35 % Total time : 2.370s
%------------------------------------------------------------------------------