%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM538+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n011.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 : 600s
% DateTime : Mon Jul 18 09:33:33 EDT 2022
% Result : Theorem 0.25s 1.42s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 8 unt; 0 def)
% Number of atoms : 165 ( 34 equ)
% Maximal formula atoms : 52 ( 5 avg)
% Number of connectives : 223 ( 91 ~; 90 |; 26 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 54 ( 3 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElement0(X2) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElement0(X4)
& aElementOf0(X4,X1)
& X4 != X2 ) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDefDiff) ).
fof(m__,conjecture,
( ( aSet0(sdtmndt0(xS,xx))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(xS,xx))
<=> ( aElement0(X1)
& aElementOf0(X1,xS)
& X1 != xx ) ) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__) ).
fof(mCardCons,axiom,
! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1)) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mCardCons) ).
fof(mConsDiff,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> sdtpldt0(sdtmndt0(X1,X2),X2) = X1 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mConsDiff) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mEOfElem) ).
fof(m__1522_02,hypothesis,
( isFinite0(xS)
& aElementOf0(xx,xS) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__1522_02) ).
fof(m__1522,hypothesis,
aSet0(xS),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__1522) ).
fof(mFDiffSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( aSet0(X2)
& isFinite0(X2) )
=> isFinite0(sdtmndt0(X2,X1)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mFDiffSet) ).
fof(c_0_8,plain,
! [X5,X6,X7,X8,X8,X7] :
( ( aSet0(X7)
| X7 != sdtmndt0(X5,X6)
| ~ aSet0(X5)
| ~ aElement0(X6) )
& ( aElement0(X8)
| ~ aElementOf0(X8,X7)
| X7 != sdtmndt0(X5,X6)
| ~ aSet0(X5)
| ~ aElement0(X6) )
& ( aElementOf0(X8,X5)
| ~ aElementOf0(X8,X7)
| X7 != sdtmndt0(X5,X6)
| ~ aSet0(X5)
| ~ aElement0(X6) )
& ( X8 != X6
| ~ aElementOf0(X8,X7)
| X7 != sdtmndt0(X5,X6)
| ~ aSet0(X5)
| ~ aElement0(X6) )
& ( ~ aElement0(X8)
| ~ aElementOf0(X8,X5)
| X8 = X6
| aElementOf0(X8,X7)
| X7 != sdtmndt0(X5,X6)
| ~ aSet0(X5)
| ~ aElement0(X6) )
& ( ~ aElementOf0(esk1_3(X5,X6,X7),X7)
| ~ aElement0(esk1_3(X5,X6,X7))
| ~ aElementOf0(esk1_3(X5,X6,X7),X5)
| esk1_3(X5,X6,X7) = X6
| ~ aSet0(X7)
| X7 = sdtmndt0(X5,X6)
| ~ aSet0(X5)
| ~ aElement0(X6) )
& ( aElement0(esk1_3(X5,X6,X7))
| aElementOf0(esk1_3(X5,X6,X7),X7)
| ~ aSet0(X7)
| X7 = sdtmndt0(X5,X6)
| ~ aSet0(X5)
| ~ aElement0(X6) )
& ( aElementOf0(esk1_3(X5,X6,X7),X5)
| aElementOf0(esk1_3(X5,X6,X7),X7)
| ~ aSet0(X7)
| X7 = sdtmndt0(X5,X6)
| ~ aSet0(X5)
| ~ aElement0(X6) )
& ( esk1_3(X5,X6,X7) != X6
| aElementOf0(esk1_3(X5,X6,X7),X7)
| ~ aSet0(X7)
| X7 = sdtmndt0(X5,X6)
| ~ aSet0(X5)
| ~ aElement0(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])])])])]) ).
fof(c_0_9,negated_conjecture,
~ ( ( aSet0(sdtmndt0(xS,xx))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(xS,xx))
<=> ( aElement0(X1)
& aElementOf0(X1,xS)
& X1 != xx ) ) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_10,plain,
! [X3,X4] :
( ~ aSet0(X3)
| ~ isFinite0(X3)
| ~ aElement0(X4)
| aElementOf0(X4,X3)
| sbrdtbr0(sdtpldt0(X3,X4)) = szszuzczcdt0(sbrdtbr0(X3)) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[mCardCons])])])])])]) ).
fof(c_0_11,plain,
! [X3,X4] :
( ~ aSet0(X3)
| ~ aElementOf0(X4,X3)
| sdtpldt0(sdtmndt0(X3,X4),X4) = X3 ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mConsDiff])])])])]) ).
cnf(c_0_12,plain,
( aSet0(X3)
| ~ aElement0(X1)
| ~ aSet0(X2)
| X3 != sdtmndt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X3,X4] :
( ~ aSet0(X3)
| ~ aElementOf0(X4,X3)
| aElement0(X4) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])])]) ).
fof(c_0_14,negated_conjecture,
! [X2,X2] :
( aSet0(sdtmndt0(xS,xx))
& ( aElement0(X2)
| ~ aElementOf0(X2,sdtmndt0(xS,xx)) )
& ( aElementOf0(X2,xS)
| ~ aElementOf0(X2,sdtmndt0(xS,xx)) )
& ( X2 != xx
| ~ aElementOf0(X2,sdtmndt0(xS,xx)) )
& ( ~ aElement0(X2)
| ~ aElementOf0(X2,xS)
| X2 = xx
| aElementOf0(X2,sdtmndt0(xS,xx)) )
& szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])])]) ).
cnf(c_0_15,plain,
( sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1))
| aElementOf0(X2,X1)
| ~ aElement0(X2)
| ~ isFinite0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( sdtpldt0(sdtmndt0(X1,X2),X2) = X1
| ~ aElementOf0(X2,X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( aSet0(sdtmndt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( aElement0(X1)
| ~ aElementOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( ~ aElement0(X1)
| ~ aSet0(X2)
| X3 != sdtmndt0(X2,X1)
| ~ aElementOf0(X4,X3)
| X4 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1)
| aElementOf0(X2,sdtmndt0(X1,X2))
| ~ isFinite0(sdtmndt0(X1,X2))
| ~ aElementOf0(X2,X1)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]) ).
cnf(c_0_22,hypothesis,
aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[m__1522_02]) ).
cnf(c_0_23,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__1522]) ).
fof(c_0_24,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aSet0(X4)
| ~ isFinite0(X4)
| isFinite0(sdtmndt0(X4,X3)) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFDiffSet])])])])]) ).
cnf(c_0_25,plain,
( X1 != sdtmndt0(X2,X3)
| ~ aElementOf0(X3,X1)
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
( aElementOf0(xx,sdtmndt0(xS,xx))
| ~ isFinite0(sdtmndt0(xS,xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_27,plain,
( isFinite0(sdtmndt0(X1,X2))
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,hypothesis,
isFinite0(xS),
inference(split_conjunct,[status(thm)],[m__1522_02]) ).
cnf(c_0_29,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_22]),c_0_23])]) ).
cnf(c_0_30,plain,
( ~ aElementOf0(X1,sdtmndt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_31,negated_conjecture,
aElementOf0(xx,sdtmndt0(xS,xx)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29]),c_0_23])]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_29]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM538+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jul 7 01:39:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.25/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.25/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.25/1.42 # Preprocessing time : 0.020 s
% 0.25/1.42
% 0.25/1.42 # Proof found!
% 0.25/1.42 # SZS status Theorem
% 0.25/1.42 # SZS output start CNFRefutation
% See solution above
% 0.25/1.42 # Proof object total steps : 33
% 0.25/1.42 # Proof object clause steps : 18
% 0.25/1.42 # Proof object formula steps : 15
% 0.25/1.42 # Proof object conjectures : 7
% 0.25/1.42 # Proof object clause conjectures : 4
% 0.25/1.42 # Proof object formula conjectures : 3
% 0.25/1.42 # Proof object initial clauses used : 10
% 0.25/1.42 # Proof object initial formulas used : 8
% 0.25/1.42 # Proof object generating inferences : 7
% 0.25/1.42 # Proof object simplifying inferences : 15
% 0.25/1.42 # Training examples: 0 positive, 0 negative
% 0.25/1.42 # Parsed axioms : 46
% 0.25/1.42 # Removed by relevancy pruning/SinE : 7
% 0.25/1.42 # Initial clauses : 69
% 0.25/1.42 # Removed in clause preprocessing : 5
% 0.25/1.42 # Initial clauses in saturation : 64
% 0.25/1.42 # Processed clauses : 218
% 0.25/1.42 # ...of these trivial : 1
% 0.25/1.42 # ...subsumed : 66
% 0.25/1.42 # ...remaining for further processing : 151
% 0.25/1.42 # Other redundant clauses eliminated : 13
% 0.25/1.42 # Clauses deleted for lack of memory : 0
% 0.25/1.42 # Backward-subsumed : 13
% 0.25/1.42 # Backward-rewritten : 2
% 0.25/1.42 # Generated clauses : 417
% 0.25/1.42 # ...of the previous two non-trivial : 341
% 0.25/1.42 # Contextual simplify-reflections : 140
% 0.25/1.42 # Paramodulations : 391
% 0.25/1.42 # Factorizations : 0
% 0.25/1.42 # Equation resolutions : 26
% 0.25/1.42 # Current number of processed clauses : 134
% 0.25/1.42 # Positive orientable unit clauses : 12
% 0.25/1.42 # Positive unorientable unit clauses: 0
% 0.25/1.42 # Negative unit clauses : 4
% 0.25/1.42 # Non-unit-clauses : 118
% 0.25/1.42 # Current number of unprocessed clauses: 169
% 0.25/1.42 # ...number of literals in the above : 1094
% 0.25/1.42 # Current number of archived formulas : 0
% 0.25/1.42 # Current number of archived clauses : 15
% 0.25/1.42 # Clause-clause subsumption calls (NU) : 5917
% 0.25/1.42 # Rec. Clause-clause subsumption calls : 1383
% 0.25/1.42 # Non-unit clause-clause subsumptions : 212
% 0.25/1.42 # Unit Clause-clause subsumption calls : 90
% 0.25/1.42 # Rewrite failures with RHS unbound : 0
% 0.25/1.42 # BW rewrite match attempts : 2
% 0.25/1.42 # BW rewrite match successes : 2
% 0.25/1.42 # Condensation attempts : 0
% 0.25/1.42 # Condensation successes : 0
% 0.25/1.42 # Termbank termtop insertions : 11615
% 0.25/1.42
% 0.25/1.42 # -------------------------------------------------
% 0.25/1.42 # User time : 0.041 s
% 0.25/1.42 # System time : 0.004 s
% 0.25/1.42 # Total time : 0.045 s
% 0.25/1.42 # Maximum resident set size: 3364 pages
%------------------------------------------------------------------------------