%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM623+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 : n021.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 04:58:04 PM UTC 2026
% Result : Theorem 2.15s 1.92s
% Output : CNFRefutation 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 16
% Syntax : Number of formulae : 51 ( 21 unt; 0 def)
% Number of atoms : 138 ( 29 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 149 ( 62 ~; 55 |; 21 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 24 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mCountNFin,axiom,
! [X1] :
( ( aSet0(X1)
& isCountable0(X1) )
=> ~ isFinite0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin) ).
fof(mMinMin,axiom,
! [X1,X2] :
( ( aSubsetOf0(X1,szNzAzT0)
& aSubsetOf0(X2,szNzAzT0)
& X1 != slcrc0
& X2 != slcrc0 )
=> ( ( aElementOf0(szmzizndt0(X1),X2)
& aElementOf0(szmzizndt0(X2),X1) )
=> szmzizndt0(X1) = szmzizndt0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMinMin) ).
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(mSubFSet,axiom,
! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> ! [X2] :
( aSubsetOf0(X2,X1)
=> isFinite0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubFSet) ).
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__5147,hypothesis,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
fof(m__5106,hypothesis,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5106) ).
fof(m__5093,hypothesis,
( aSubsetOf0(xQ,xO)
& xQ != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
fof(m__,conjecture,
xp = xx,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__5461,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5461) ).
fof(m__5401,hypothesis,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5401) ).
fof(m__5481,hypothesis,
( aElementOf0(xp,sdtlpdtrp0(xN,xm))
& aElementOf0(xx,xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5481) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(m__5309,hypothesis,
( aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& sdtlpdtrp0(xe,xn) = xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5309) ).
fof(m__5389,hypothesis,
( aElementOf0(xm,szNzAzT0)
& xx = sdtlpdtrp0(xe,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5389) ).
fof(mEmpFin,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEmpFin) ).
fof(c_0_16,plain,
! [X1] :
( ( aSet0(X1)
& isCountable0(X1) )
=> ~ isFinite0(X1) ),
inference(fof_simplification,[status(thm)],[mCountNFin]) ).
fof(c_0_17,plain,
! [X267,X268] :
( ~ aSubsetOf0(X267,szNzAzT0)
| ~ aSubsetOf0(X268,szNzAzT0)
| X267 = slcrc0
| X268 = slcrc0
| ~ aElementOf0(szmzizndt0(X267),X268)
| ~ aElementOf0(szmzizndt0(X268),X267)
| szmzizndt0(X267) = szmzizndt0(X268) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMinMin])]) ).
fof(c_0_18,plain,
! [X184] :
( ~ aSet0(X184)
| ~ isCountable0(X184)
| ~ isFinite0(X184) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])]) ).
fof(c_0_19,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_20,plain,
! [X191,X192] :
( ~ aSet0(X191)
| ~ isFinite0(X191)
| ~ aSubsetOf0(X192,X191)
| isFinite0(X192) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubFSet])])]) ).
fof(c_0_21,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])])])])])]) ).
cnf(c_0_22,plain,
( X1 = slcrc0
| X2 = slcrc0
| szmzizndt0(X1) = szmzizndt0(X2)
| ~ aSubsetOf0(X1,szNzAzT0)
| ~ aSubsetOf0(X2,szNzAzT0)
| ~ aElementOf0(szmzizndt0(X1),X2)
| ~ aElementOf0(szmzizndt0(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,hypothesis,
xp = szmzizndt0(xQ),
inference(split_conjunct,[status(thm)],[m__5147]) ).
cnf(c_0_24,hypothesis,
aSubsetOf0(xQ,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__5106]) ).
cnf(c_0_25,hypothesis,
xQ != slcrc0,
inference(split_conjunct,[status(thm)],[m__5093]) ).
fof(c_0_26,negated_conjecture,
xp != xx,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_27,plain,
( ~ aSet0(X1)
| ~ isCountable0(X1)
| ~ isFinite0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,hypothesis,
( isCountable0(sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
( isFinite0(X2)
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
inference(split_conjunct,[status(thm)],[m__5461]) ).
cnf(c_0_31,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,hypothesis,
( szmzizndt0(X1) = xp
| X1 = slcrc0
| ~ aSubsetOf0(X1,szNzAzT0)
| ~ aElementOf0(szmzizndt0(X1),xQ)
| ~ aElementOf0(xp,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_33,hypothesis,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(split_conjunct,[status(thm)],[m__5401]) ).
cnf(c_0_34,hypothesis,
aElementOf0(xx,xQ),
inference(split_conjunct,[status(thm)],[m__5481]) ).
cnf(c_0_35,hypothesis,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(split_conjunct,[status(thm)],[m__5481]) ).
cnf(c_0_36,negated_conjecture,
xp != xx,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_37,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_38,hypothesis,
( ~ isFinite0(sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_39,hypothesis,
( isFinite0(sdtlpdtrp0(xN,xn))
| ~ isFinite0(sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,xm)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_40,hypothesis,
aElementOf0(xn,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__5309]) ).
cnf(c_0_41,hypothesis,
( aSet0(sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtlpdtrp0(xN,xm)) ),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_42,hypothesis,
( sdtlpdtrp0(xN,xm) = slcrc0
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35])]),c_0_36]) ).
cnf(c_0_43,hypothesis,
( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_44,hypothesis,
aElementOf0(xm,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__5389]) ).
cnf(c_0_45,plain,
( aSet0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,hypothesis,
( ~ isFinite0(sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,xm)) ),
inference(csr,[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]) ).
cnf(c_0_47,hypothesis,
sdtlpdtrp0(xN,xm) = slcrc0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_48,plain,
isFinite0(slcrc0),
inference(split_conjunct,[status(thm)],[mEmpFin]) ).
cnf(c_0_49,plain,
aSet0(slcrc0),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_50,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_47]),c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM623+1 : 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 : n021.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 00:52:10 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 2.15/1.92 % Version : CSE_E---1.7
% 2.15/1.92 % Problem : theBenchmark.p
% 2.15/1.92 % SZS status Theorem for theBenchmark.p
% 2.15/1.92 % SZS output start CNFRefutation
% See solution above
% 2.15/1.93 % Total time : 1.372s
%------------------------------------------------------------------------------