%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM545+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.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 04:57:46 PM UTC 2026
% Result : Theorem 1.37s 1.75s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 44 ( 16 unt; 0 def)
% Number of atoms : 133 ( 28 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 151 ( 62 ~; 61 |; 19 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 1 sgn 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(m__1986,hypothesis,
( aSubsetOf0(xS,szNzAzT0)
& isFinite0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1986) ).
fof(mNATSet,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(m__,conjecture,
? [X1] :
( aElementOf0(X1,szNzAzT0)
& aSubsetOf0(xS,slbdtrb0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(mSegZero,axiom,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegZero) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(m__2035,hypothesis,
( xS != slcrc0
=> aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2035) ).
fof(mDefMax,axiom,
! [X1] :
( ( aSubsetOf0(X1,szNzAzT0)
& isFinite0(X1)
& X1 != slcrc0 )
=> ! [X2] :
( X2 = szmzazxdt0(X1)
<=> ( aElementOf0(X2,X1)
& ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X3,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMax) ).
fof(mSuccNum,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
& szszuzczcdt0(X1) != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
fof(c_0_10,plain,
! [X107,X108,X109,X110] :
( ( aSet0(X108)
| ~ aSubsetOf0(X108,X107)
| ~ aSet0(X107) )
& ( ~ aElementOf0(X109,X108)
| aElementOf0(X109,X107)
| ~ aSubsetOf0(X108,X107)
| ~ aSet0(X107) )
& ( aElementOf0(esk2_2(X107,X110),X110)
| ~ aSet0(X110)
| aSubsetOf0(X110,X107)
| ~ aSet0(X107) )
& ( ~ aElementOf0(esk2_2(X107,X110),X107)
| ~ aSet0(X110)
| aSubsetOf0(X110,X107)
| ~ aSet0(X107) ) ),
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,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_12,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__1986]) ).
cnf(c_0_13,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
fof(c_0_14,negated_conjecture,
~ ? [X1] :
( aElementOf0(X1,szNzAzT0)
& aSubsetOf0(xS,slbdtrb0(X1)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_15,plain,
( aElementOf0(esk2_2(X1,X2),X2)
| aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,hypothesis,
aSet0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
fof(c_0_17,plain,
! [X101,X102,X103] :
( ( aSet0(X101)
| X101 != slcrc0 )
& ( ~ aElementOf0(X102,X101)
| X101 != slcrc0 )
& ( ~ aSet0(X103)
| aElementOf0(esk1_1(X103),X103)
| X103 = 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])])])])])]) ).
fof(c_0_18,negated_conjecture,
! [X201] :
( ~ aElementOf0(X201,szNzAzT0)
| ~ aSubsetOf0(xS,slbdtrb0(X201)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])]) ).
cnf(c_0_19,hypothesis,
( aSubsetOf0(xS,X1)
| aElementOf0(esk2_2(X1,xS),xS)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( aSet0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSubsetOf0(xS,slbdtrb0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
slbdtrb0(sz00) = slcrc0,
inference(split_conjunct,[status(thm)],[mSegZero]) ).
cnf(c_0_23,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_24,hypothesis,
( aSubsetOf0(xS,X1)
| aElementOf0(esk2_2(X1,xS),xS)
| X1 != slcrc0 ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
~ aSubsetOf0(xS,slcrc0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
fof(c_0_26,hypothesis,
( xS = slcrc0
| aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
inference(fof_nnf,[status(thm)],[m__2035]) ).
cnf(c_0_27,plain,
( ~ aElementOf0(X1,X2)
| X2 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,hypothesis,
aElementOf0(esk2_2(slcrc0,xS),xS),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_24]),c_0_25]) ).
fof(c_0_29,plain,
! [X183,X184,X185,X186] :
( ( aElementOf0(X184,X183)
| X184 != szmzazxdt0(X183)
| ~ aSubsetOf0(X183,szNzAzT0)
| ~ isFinite0(X183)
| X183 = slcrc0 )
& ( ~ aElementOf0(X185,X183)
| sdtlseqdt0(X185,X184)
| X184 != szmzazxdt0(X183)
| ~ aSubsetOf0(X183,szNzAzT0)
| ~ isFinite0(X183)
| X183 = slcrc0 )
& ( aElementOf0(esk8_2(X183,X186),X183)
| ~ aElementOf0(X186,X183)
| X186 = szmzazxdt0(X183)
| ~ aSubsetOf0(X183,szNzAzT0)
| ~ isFinite0(X183)
| X183 = slcrc0 )
& ( ~ sdtlseqdt0(esk8_2(X183,X186),X186)
| ~ aElementOf0(X186,X183)
| X186 = szmzazxdt0(X183)
| ~ aSubsetOf0(X183,szNzAzT0)
| ~ isFinite0(X183)
| X183 = 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)],[mDefMax])])])])])]) ).
cnf(c_0_30,hypothesis,
( xS = slcrc0
| aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,hypothesis,
xS != slcrc0,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( aElementOf0(X1,X2)
| X2 = slcrc0
| X1 != szmzazxdt0(X2)
| ~ aSubsetOf0(X2,szNzAzT0)
| ~ isFinite0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,hypothesis,
isFinite0(xS),
inference(split_conjunct,[status(thm)],[m__1986]) ).
cnf(c_0_34,hypothesis,
aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))),
inference(sr,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_35,plain,
! [X146] :
( ( aElementOf0(szszuzczcdt0(X146),szNzAzT0)
| ~ aElementOf0(X146,szNzAzT0) )
& ( szszuzczcdt0(X146) != sz00
| ~ aElementOf0(X146,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccNum])])]) ).
cnf(c_0_36,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_37,hypothesis,
( aElementOf0(X1,xS)
| X1 != szmzazxdt0(xS) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_12]),c_0_33])]),c_0_31]) ).
cnf(c_0_38,negated_conjecture,
~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0),
inference(spm,[status(thm)],[c_0_21,c_0_34]) ).
cnf(c_0_39,plain,
( aElementOf0(szszuzczcdt0(X1),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,hypothesis,
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_12]),c_0_13])]) ).
cnf(c_0_41,hypothesis,
aElementOf0(szmzazxdt0(xS),xS),
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_42,negated_conjecture,
~ aElementOf0(szmzazxdt0(xS),szNzAzT0),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM545+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.34 % Computer : n001.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 00:44:48 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.37/1.75 % Version : CSE_E---1.7
% 1.37/1.75 % Problem : theBenchmark.p
% 1.37/1.75 % SZS status Theorem for theBenchmark.p
% 1.37/1.75 % SZS output start CNFRefutation
% See solution above
% 1.37/1.75 % Total time : 1.371s
%------------------------------------------------------------------------------