%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM548+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 : n003.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 04:57:47 PM UTC 2026
% Result : Theorem 1.32s 1.72s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 12 unt; 0 def)
% Number of atoms : 114 ( 19 equ)
% Maximal formula atoms : 39 ( 4 avg)
% Number of connectives : 152 ( 63 ~; 65 |; 16 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 36 ( 0 sgn 19 !; 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__2270,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2270) ).
fof(m__2202,hypothesis,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202) ).
fof(m__2202_02,hypothesis,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(mCardNum,axiom,
! [X1] :
( aSet0(X1)
=> ( aElementOf0(sbrdtbr0(X1),szNzAzT0)
<=> isFinite0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
fof(m__,conjecture,
isFinite0(xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_7,plain,
! [X216,X217,X218,X219,X220,X221] :
( ( aSet0(X218)
| X218 != slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) )
& ( aSubsetOf0(X219,X216)
| ~ aElementOf0(X219,X218)
| X218 != slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) )
& ( sbrdtbr0(X219) = X217
| ~ aElementOf0(X219,X218)
| X218 != slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) )
& ( ~ aSubsetOf0(X220,X216)
| sbrdtbr0(X220) != X217
| aElementOf0(X220,X218)
| X218 != slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) )
& ( ~ aElementOf0(esk11_3(X216,X217,X221),X221)
| ~ aSubsetOf0(esk11_3(X216,X217,X221),X216)
| sbrdtbr0(esk11_3(X216,X217,X221)) != X217
| ~ aSet0(X221)
| X221 = slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) )
& ( aSubsetOf0(esk11_3(X216,X217,X221),X216)
| aElementOf0(esk11_3(X216,X217,X221),X221)
| ~ aSet0(X221)
| X221 = slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) )
& ( sbrdtbr0(esk11_3(X216,X217,X221)) = X217
| aElementOf0(esk11_3(X216,X217,X221),X221)
| ~ aSet0(X221)
| X221 = slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,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_8,plain,
( aSubsetOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != slbdtsldtrb0(X2,X4)
| ~ aSet0(X2)
| ~ aElementOf0(X4,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_9,plain,
( sbrdtbr0(X1) = X2
| ~ aElementOf0(X1,X3)
| X3 != slbdtsldtrb0(X4,X2)
| ~ aSet0(X4)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X119,X120,X121,X122] :
( ( aSet0(X120)
| ~ aSubsetOf0(X120,X119)
| ~ aSet0(X119) )
& ( ~ aElementOf0(X121,X120)
| aElementOf0(X121,X119)
| ~ aSubsetOf0(X120,X119)
| ~ aSet0(X119) )
& ( aElementOf0(esk2_2(X119,X122),X122)
| ~ aSet0(X122)
| aSubsetOf0(X122,X119)
| ~ aSet0(X119) )
& ( ~ aElementOf0(esk2_2(X119,X122),X119)
| ~ aSet0(X122)
| aSubsetOf0(X122,X119)
| ~ aSet0(X119) ) ),
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_11,plain,
( aSubsetOf0(X1,X2)
| ~ aElementOf0(X1,slbdtsldtrb0(X2,X3))
| ~ aElementOf0(X3,szNzAzT0)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_12,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(split_conjunct,[status(thm)],[m__2270]) ).
cnf(c_0_13,hypothesis,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__2202]) ).
cnf(c_0_14,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__2202_02]) ).
fof(c_0_15,plain,
! [X179] :
( ( ~ aElementOf0(sbrdtbr0(X179),szNzAzT0)
| isFinite0(X179)
| ~ aSet0(X179) )
& ( ~ isFinite0(X179)
| aElementOf0(sbrdtbr0(X179),szNzAzT0)
| ~ aSet0(X179) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardNum])])]) ).
cnf(c_0_16,plain,
( sbrdtbr0(X1) = X2
| ~ aElementOf0(X1,slbdtsldtrb0(X3,X2))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,hypothesis,
aSubsetOf0(xQ,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]) ).
fof(c_0_19,negated_conjecture,
~ isFinite0(xQ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_20,plain,
( isFinite0(X1)
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,hypothesis,
sbrdtbr0(xQ) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_12]),c_0_13]),c_0_14])]) ).
cnf(c_0_22,hypothesis,
aSet0(xQ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_14])]) ).
cnf(c_0_23,negated_conjecture,
~ isFinite0(xQ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_13]),c_0_22])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM548+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
% 0.14/0.32 % Computer : n003.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 00:44:26 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.32/1.72 % Version : CSE_E---1.7
% 1.32/1.72 % Problem : theBenchmark.p
% 1.32/1.72 % SZS status Theorem for theBenchmark.p
% 1.32/1.72 % SZS output start CNFRefutation
% See solution above
% 1.32/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------