%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET018+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n023.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 : Tue Jul 19 00:47:49 EDT 2022
% Result : Theorem 0.22s 1.40s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 14 unt; 0 def)
% Number of atoms : 123 ( 57 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 104 ( 36 ~; 52 |; 9 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 13 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI50b,conjecture,
! [X1,X2,X6,X7] :
( equal_set(unordered_pair(singleton(X1),unordered_pair(X1,X2)),unordered_pair(singleton(X6),unordered_pair(X6,X7)))
=> X2 = X7 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thI50b) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(unordered_pair,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( X3 = X1
| X3 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',unordered_pair) ).
fof(singleton,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X6,X7] :
( equal_set(unordered_pair(singleton(X1),unordered_pair(X1,X2)),unordered_pair(singleton(X6),unordered_pair(X6,X7)))
=> X2 = X7 ),
inference(assume_negation,[status(cth)],[thI50b]) ).
fof(c_0_6,plain,
! [X3,X4,X3,X4] :
( ( subset(X3,X4)
| ~ equal_set(X3,X4) )
& ( subset(X4,X3)
| ~ equal_set(X3,X4) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])])]) ).
fof(c_0_7,negated_conjecture,
( equal_set(unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0)),unordered_pair(singleton(esk3_0),unordered_pair(esk3_0,esk4_0)))
& esk2_0 != esk4_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X4,X5,X6,X4,X5] :
( ( ~ subset(X4,X5)
| ~ member(X6,X4)
| member(X6,X5) )
& ( member(esk5_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk5_2(X4,X5),X5)
| subset(X4,X5) ) ),
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)],[subset])])])])])])]) ).
cnf(c_0_9,plain,
( subset(X2,X1)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
equal_set(unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0)),unordered_pair(singleton(esk3_0),unordered_pair(esk3_0,esk4_0))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X4,X5,X6,X4,X5,X6] :
( ( ~ member(X4,unordered_pair(X5,X6))
| X4 = X5
| X4 = X6 )
& ( X4 != X5
| member(X4,unordered_pair(X5,X6)) )
& ( X4 != X6
| member(X4,unordered_pair(X5,X6)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair])])])])]) ).
cnf(c_0_12,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
subset(unordered_pair(singleton(esk3_0),unordered_pair(esk3_0,esk4_0)),unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X4,X5,X4,X5] :
( ( ~ member(X4,singleton(X5))
| X4 = X5 )
& ( X4 != X5
| member(X4,singleton(X5)) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])])])]) ).
cnf(c_0_16,negated_conjecture,
( member(X1,unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0)))
| ~ member(X1,unordered_pair(singleton(esk3_0),unordered_pair(esk3_0,esk4_0))) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
member(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( member(X1,singleton(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
member(singleton(esk3_0),unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
member(X1,singleton(X1)),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( singleton(esk3_0) = unordered_pair(esk1_0,esk2_0)
| singleton(esk3_0) = singleton(esk1_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
( subset(X1,X2)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,negated_conjecture,
( singleton(esk3_0) = unordered_pair(esk1_0,esk2_0)
| member(esk3_0,singleton(esk1_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
subset(unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0)),unordered_pair(singleton(esk3_0),unordered_pair(esk3_0,esk4_0))),
inference(spm,[status(thm)],[c_0_23,c_0_10]) ).
cnf(c_0_26,plain,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_27,negated_conjecture,
( member(esk3_0,unordered_pair(esk1_0,esk2_0))
| member(esk3_0,singleton(esk1_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_24]) ).
cnf(c_0_28,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,negated_conjecture,
( member(X1,unordered_pair(singleton(esk3_0),unordered_pair(esk3_0,esk4_0)))
| ~ member(X1,unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0))) ),
inference(spm,[status(thm)],[c_0_12,c_0_25]) ).
cnf(c_0_30,negated_conjecture,
( esk3_0 = esk1_0
| member(esk3_0,unordered_pair(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
member(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( X1 = unordered_pair(esk3_0,esk4_0)
| X1 = singleton(esk3_0)
| ~ member(X1,unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0))) ),
inference(spm,[status(thm)],[c_0_19,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( esk3_0 = esk1_0
| esk3_0 = esk2_0 ),
inference(spm,[status(thm)],[c_0_19,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
member(unordered_pair(esk3_0,esk4_0),unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_16,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( unordered_pair(esk3_0,esk4_0) = unordered_pair(esk1_0,esk2_0)
| singleton(esk3_0) = unordered_pair(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( esk3_0 = esk1_0
| esk2_0 != esk1_0 ),
inference(ef,[status(thm)],[c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( unordered_pair(esk3_0,esk4_0) = unordered_pair(esk1_0,esk2_0)
| singleton(esk1_0) = unordered_pair(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( unordered_pair(esk1_0,esk4_0) = unordered_pair(esk1_0,esk2_0)
| singleton(esk1_0) = unordered_pair(esk1_0,esk2_0)
| esk2_0 != esk1_0 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( unordered_pair(esk3_0,esk4_0) = unordered_pair(esk1_0,esk2_0)
| X1 = esk3_0
| ~ member(X1,unordered_pair(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_26,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( unordered_pair(esk1_0,esk4_0) = unordered_pair(esk1_0,esk2_0)
| unordered_pair(esk3_0,esk4_0) = unordered_pair(esk1_0,esk2_0)
| esk2_0 != esk1_0 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
( unordered_pair(esk3_0,esk4_0) = unordered_pair(esk1_0,esk2_0)
| esk3_0 = esk2_0 ),
inference(spm,[status(thm)],[c_0_39,c_0_31]) ).
cnf(c_0_42,negated_conjecture,
( unordered_pair(esk1_0,esk4_0) = unordered_pair(esk1_0,esk2_0)
| esk2_0 != esk1_0 ),
inference(spm,[status(thm)],[c_0_40,c_0_36]) ).
cnf(c_0_43,negated_conjecture,
( esk3_0 = esk2_0
| member(esk4_0,unordered_pair(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_31,c_0_41]) ).
cnf(c_0_44,negated_conjecture,
esk2_0 != esk4_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_45,negated_conjecture,
( member(esk4_0,unordered_pair(esk1_0,esk2_0))
| esk2_0 != esk1_0 ),
inference(spm,[status(thm)],[c_0_31,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
( esk3_0 = esk2_0
| esk4_0 = esk1_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_43]),c_0_44]) ).
cnf(c_0_47,negated_conjecture,
( X1 = esk3_0
| member(esk3_0,singleton(esk1_0))
| ~ member(X1,unordered_pair(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_48,negated_conjecture,
( esk4_0 = esk1_0
| esk2_0 != esk1_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_45]),c_0_44]) ).
cnf(c_0_49,negated_conjecture,
( unordered_pair(esk3_0,esk1_0) = unordered_pair(esk1_0,esk2_0)
| esk3_0 = esk2_0 ),
inference(spm,[status(thm)],[c_0_41,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
esk3_0 = esk1_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_17]),c_0_26]) ).
cnf(c_0_51,negated_conjecture,
esk2_0 != esk1_0,
inference(spm,[status(thm)],[c_0_44,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
unordered_pair(esk1_0,esk2_0) = unordered_pair(esk1_0,esk1_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_50]),c_0_51]) ).
cnf(c_0_53,negated_conjecture,
member(esk2_0,unordered_pair(esk1_0,esk1_0)),
inference(spm,[status(thm)],[c_0_31,c_0_52]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_53]),c_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET018+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 01:30:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.22/1.40 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.40 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.40 # Preprocessing time : 0.015 s
% 0.22/1.40
% 0.22/1.40 # Proof found!
% 0.22/1.40 # SZS status Theorem
% 0.22/1.40 # SZS output start CNFRefutation
% See solution above
% 0.22/1.40 # Proof object total steps : 55
% 0.22/1.40 # Proof object clause steps : 44
% 0.22/1.40 # Proof object formula steps : 11
% 0.22/1.40 # Proof object conjectures : 36
% 0.22/1.40 # Proof object clause conjectures : 33
% 0.22/1.40 # Proof object formula conjectures : 3
% 0.22/1.40 # Proof object initial clauses used : 10
% 0.22/1.40 # Proof object initial formulas used : 5
% 0.22/1.40 # Proof object generating inferences : 30
% 0.22/1.40 # Proof object simplifying inferences : 10
% 0.22/1.40 # Training examples: 0 positive, 0 negative
% 0.22/1.40 # Parsed axioms : 12
% 0.22/1.40 # Removed by relevancy pruning/SinE : 7
% 0.22/1.40 # Initial clauses : 13
% 0.22/1.40 # Removed in clause preprocessing : 0
% 0.22/1.40 # Initial clauses in saturation : 13
% 0.22/1.40 # Processed clauses : 201
% 0.22/1.40 # ...of these trivial : 15
% 0.22/1.40 # ...subsumed : 43
% 0.22/1.40 # ...remaining for further processing : 143
% 0.22/1.40 # Other redundant clauses eliminated : 5
% 0.22/1.40 # Clauses deleted for lack of memory : 0
% 0.22/1.40 # Backward-subsumed : 18
% 0.22/1.40 # Backward-rewritten : 90
% 0.22/1.40 # Generated clauses : 1263
% 0.22/1.40 # ...of the previous two non-trivial : 1157
% 0.22/1.40 # Contextual simplify-reflections : 22
% 0.22/1.40 # Paramodulations : 1252
% 0.22/1.40 # Factorizations : 6
% 0.22/1.40 # Equation resolutions : 5
% 0.22/1.40 # Current number of processed clauses : 32
% 0.22/1.40 # Positive orientable unit clauses : 9
% 0.22/1.40 # Positive unorientable unit clauses: 0
% 0.22/1.40 # Negative unit clauses : 1
% 0.22/1.40 # Non-unit-clauses : 22
% 0.22/1.40 # Current number of unprocessed clauses: 63
% 0.22/1.40 # ...number of literals in the above : 169
% 0.22/1.40 # Current number of archived formulas : 0
% 0.22/1.40 # Current number of archived clauses : 108
% 0.22/1.40 # Clause-clause subsumption calls (NU) : 1024
% 0.22/1.40 # Rec. Clause-clause subsumption calls : 877
% 0.22/1.40 # Non-unit clause-clause subsumptions : 69
% 0.22/1.40 # Unit Clause-clause subsumption calls : 65
% 0.22/1.40 # Rewrite failures with RHS unbound : 0
% 0.22/1.40 # BW rewrite match attempts : 23
% 0.22/1.40 # BW rewrite match successes : 6
% 0.22/1.40 # Condensation attempts : 0
% 0.22/1.40 # Condensation successes : 0
% 0.22/1.40 # Termbank termtop insertions : 20600
% 0.22/1.40
% 0.22/1.40 # -------------------------------------------------
% 0.22/1.40 # User time : 0.042 s
% 0.22/1.40 # System time : 0.002 s
% 0.22/1.40 # Total time : 0.044 s
% 0.22/1.40 # Maximum resident set size: 3460 pages
%------------------------------------------------------------------------------