%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM595+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 : n007.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 04:57:58 PM UTC 2026
% Result : Theorem 6.04s 4.45s
% Output : CNFRefutation 6.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 53 ( 13 unt; 0 def)
% Number of atoms : 198 ( 42 equ)
% Maximal formula atoms : 39 ( 3 avg)
% Number of connectives : 246 ( 101 ~; 100 |; 32 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 12 con; 0-3 aty)
% Number of variables : 65 ( 0 sgn 33 !; 2 ?)
% 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__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(m__4826,hypothesis,
( xX = slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xi)),xk)
& xX != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4826) ).
fof(m__3533,hypothesis,
( aElementOf0(xk,szNzAzT0)
& szszuzczcdt0(xk) = xK ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3533) ).
fof(m__4730,hypothesis,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( ( aSet0(X2)
& aElementOf0(X2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),xk)) )
=> sdtlpdtrp0(xd,X1) = sdtlpdtrp0(sdtlpdtrp0(xC,X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4730) ).
fof(m__4618,hypothesis,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ? [X2] :
( aElementOf0(X2,xT)
& ! [X3] :
( ( aSet0(X3)
& aElementOf0(X3,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),xk)) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,X1),X3) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4618) ).
fof(mNATSet,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(m__4806,hypothesis,
( aElementOf0(xi,szNzAzT0)
& sdtlpdtrp0(xd,xi) = xx ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4806) ).
fof(mSuccNum,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
& szszuzczcdt0(X1) != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(m__,conjecture,
aElementOf0(xx,xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_12,plain,
! [X281,X282,X283,X284,X285,X286] :
( ( aSet0(X283)
| X283 != slbdtsldtrb0(X281,X282)
| ~ aSet0(X281)
| ~ aElementOf0(X282,szNzAzT0) )
& ( aSubsetOf0(X284,X281)
| ~ aElementOf0(X284,X283)
| X283 != slbdtsldtrb0(X281,X282)
| ~ aSet0(X281)
| ~ aElementOf0(X282,szNzAzT0) )
& ( sbrdtbr0(X284) = X282
| ~ aElementOf0(X284,X283)
| X283 != slbdtsldtrb0(X281,X282)
| ~ aSet0(X281)
| ~ aElementOf0(X282,szNzAzT0) )
& ( ~ aSubsetOf0(X285,X281)
| sbrdtbr0(X285) != X282
| aElementOf0(X285,X283)
| X283 != slbdtsldtrb0(X281,X282)
| ~ aSet0(X281)
| ~ aElementOf0(X282,szNzAzT0) )
& ( ~ aElementOf0(esk11_3(X281,X282,X286),X286)
| ~ aSubsetOf0(esk11_3(X281,X282,X286),X281)
| sbrdtbr0(esk11_3(X281,X282,X286)) != X282
| ~ aSet0(X286)
| X286 = slbdtsldtrb0(X281,X282)
| ~ aSet0(X281)
| ~ aElementOf0(X282,szNzAzT0) )
& ( aSubsetOf0(esk11_3(X281,X282,X286),X281)
| aElementOf0(esk11_3(X281,X282,X286),X286)
| ~ aSet0(X286)
| X286 = slbdtsldtrb0(X281,X282)
| ~ aSet0(X281)
| ~ aElementOf0(X282,szNzAzT0) )
& ( sbrdtbr0(esk11_3(X281,X282,X286)) = X282
| aElementOf0(esk11_3(X281,X282,X286),X286)
| ~ aSet0(X286)
| X286 = slbdtsldtrb0(X281,X282)
| ~ aSet0(X281)
| ~ aElementOf0(X282,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])])])])])]) ).
cnf(c_0_13,plain,
( aSubsetOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != slbdtsldtrb0(X2,X4)
| ~ aSet0(X2)
| ~ aElementOf0(X4,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_14,plain,
( aSet0(X1)
| X1 != slbdtsldtrb0(X2,X3)
| ~ aSet0(X2)
| ~ aElementOf0(X3,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X184,X185,X186,X187] :
( ( aSet0(X185)
| ~ aSubsetOf0(X185,X184)
| ~ aSet0(X184) )
& ( ~ aElementOf0(X186,X185)
| aElementOf0(X186,X184)
| ~ aSubsetOf0(X185,X184)
| ~ aSet0(X184) )
& ( aElementOf0(esk2_2(X184,X187),X187)
| ~ aSet0(X187)
| aSubsetOf0(X187,X184)
| ~ aSet0(X184) )
& ( ~ aElementOf0(esk2_2(X184,X187),X184)
| ~ aSet0(X187)
| aSubsetOf0(X187,X184)
| ~ aSet0(X184) ) ),
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_16,hypothesis,
! [X344] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X344),szNzAzT0)
| ~ aElementOf0(X344,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,X344))
| ~ aElementOf0(X344,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3671])])]) ).
cnf(c_0_17,plain,
( aSubsetOf0(X1,X2)
| ~ aElementOf0(X1,slbdtsldtrb0(X2,X3))
| ~ aElementOf0(X3,szNzAzT0)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_18,hypothesis,
xX = slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xi)),xk),
inference(split_conjunct,[status(thm)],[m__4826]) ).
cnf(c_0_19,hypothesis,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3533]) ).
fof(c_0_20,hypothesis,
! [X365,X366] :
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ( ~ aElementOf0(X365,szNzAzT0)
| ~ aSet0(X366)
| ~ aElementOf0(X366,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X365)),xk))
| sdtlpdtrp0(xd,X365) = sdtlpdtrp0(sdtlpdtrp0(xC,X365),X366) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4730])])]) ).
fof(c_0_21,hypothesis,
! [X361,X363] :
( ( aElementOf0(esk24_1(X361),xT)
| ~ aElementOf0(X361,szNzAzT0) )
& ( ~ aSet0(X363)
| ~ aElementOf0(X363,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X361)),xk))
| sdtlpdtrp0(sdtlpdtrp0(xC,X361),X363) = esk24_1(X361)
| ~ aElementOf0(X361,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4618])])])])]) ).
cnf(c_0_22,plain,
( aSet0(slbdtsldtrb0(X1,X2))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,hypothesis,
( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_26,hypothesis,
( aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(xi)))
| ~ aElementOf0(X1,xX)
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xi))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_27,hypothesis,
( sdtlpdtrp0(xd,X1) = sdtlpdtrp0(sdtlpdtrp0(xC,X1),X2)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X2)
| ~ aElementOf0(X2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),xk)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,hypothesis,
sdtlpdtrp0(xd,xi) = xx,
inference(split_conjunct,[status(thm)],[m__4806]) ).
cnf(c_0_29,hypothesis,
aElementOf0(xi,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__4806]) ).
cnf(c_0_30,hypothesis,
( sdtlpdtrp0(sdtlpdtrp0(xC,X2),X1) = esk24_1(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X2)),xk))
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,hypothesis,
( aSet0(xX)
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xi))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_18]),c_0_19])]) ).
cnf(c_0_32,hypothesis,
( aSet0(sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
fof(c_0_33,plain,
! [X223] :
( ( aElementOf0(szszuzczcdt0(X223),szNzAzT0)
| ~ aElementOf0(X223,szNzAzT0) )
& ( szszuzczcdt0(X223) != sz00
| ~ aElementOf0(X223,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccNum])])]) ).
cnf(c_0_34,hypothesis,
( aSet0(X1)
| ~ aElementOf0(X1,xX)
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xi))) ),
inference(spm,[status(thm)],[c_0_23,c_0_26]) ).
cnf(c_0_35,hypothesis,
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X1) = xx
| ~ aElementOf0(X1,xX)
| ~ aSet0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_18]),c_0_28]),c_0_29])]) ).
cnf(c_0_36,hypothesis,
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X1) = esk24_1(xi)
| ~ aElementOf0(X1,xX)
| ~ aSet0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_18]),c_0_29])]) ).
fof(c_0_37,plain,
! [X178,X179,X180] :
( ( aSet0(X178)
| X178 != slcrc0 )
& ( ~ aElementOf0(X179,X178)
| X178 != slcrc0 )
& ( ~ aSet0(X180)
| aElementOf0(esk1_1(X180),X180)
| X180 = 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,
( aSet0(xX)
| ~ aElementOf0(szszuzczcdt0(xi),szNzAzT0) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,plain,
( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,hypothesis,
( aSet0(X1)
| ~ aElementOf0(szszuzczcdt0(xi),szNzAzT0)
| ~ aElementOf0(X1,xX) ),
inference(spm,[status(thm)],[c_0_34,c_0_32]) ).
cnf(c_0_41,hypothesis,
( esk24_1(xi) = xx
| ~ aElementOf0(X1,xX)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
( aElementOf0(esk1_1(X1),X1)
| X1 = slcrc0
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,hypothesis,
aSet0(xX),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_29])]) ).
cnf(c_0_44,hypothesis,
xX != slcrc0,
inference(split_conjunct,[status(thm)],[m__4826]) ).
cnf(c_0_45,hypothesis,
( aSet0(X1)
| ~ aElementOf0(X1,xX) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_39]),c_0_29])]) ).
cnf(c_0_46,hypothesis,
( esk24_1(xi) = xx
| ~ aSet0(esk1_1(xX)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]),c_0_44]) ).
cnf(c_0_47,hypothesis,
aSet0(esk1_1(xX)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_42]),c_0_43])]),c_0_44]) ).
fof(c_0_48,negated_conjecture,
~ aElementOf0(xx,xT),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_49,hypothesis,
( aElementOf0(esk24_1(X1),xT)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_50,hypothesis,
esk24_1(xi) = xx,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
cnf(c_0_51,negated_conjecture,
~ aElementOf0(xx,xT),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_52,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_29])]),c_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM595+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 : n007.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 00:48:08 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 6.04/4.45 % Version : CSE_E---1.7
% 6.04/4.45 % Problem : theBenchmark.p
% 6.04/4.45 % SZS status Theorem for theBenchmark.p
% 6.04/4.45 % SZS output start CNFRefutation
% See solution above
% 6.04/4.47 % Total time : 3.375s
%------------------------------------------------------------------------------