TSTP Solution File: SET577+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET577+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n016.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 00:52:05 EDT 2022
% Result : Theorem 0.24s 1.41s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 10 unt; 0 def)
% Number of atoms : 133 ( 27 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 134 ( 48 ~; 67 |; 10 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 97 ( 11 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th18,conjecture,
! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X2)
| member(X4,X3) ) )
=> X1 = union(X2,X3) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_th18) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',subset_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',union_defn) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_of_union) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',equal_member_defn) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X2)
| member(X4,X3) ) )
=> X1 = union(X2,X3) ),
inference(assume_negation,[status(cth)],[prove_th18]) ).
fof(c_0_6,plain,
! [X4,X5,X6,X4,X5] :
( ( ~ subset(X4,X5)
| ~ member(X6,X4)
| member(X6,X5) )
& ( member(esk4_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk4_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_defn])])])])])])]) ).
fof(c_0_7,plain,
! [X4,X5,X6,X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X4)
| member(X6,union(X4,X5)) )
& ( ~ member(X6,X5)
| member(X6,union(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])])])]) ).
fof(c_0_8,negated_conjecture,
! [X8,X8] :
( ( ~ member(X8,esk1_0)
| member(X8,esk2_0)
| member(X8,esk3_0) )
& ( ~ member(X8,esk2_0)
| member(X8,esk1_0) )
& ( ~ member(X8,esk3_0)
| member(X8,esk1_0) )
& esk1_0 != union(esk2_0,esk3_0) ),
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)],[c_0_5])])])])])])]) ).
cnf(c_0_9,plain,
( subset(X1,X2)
| ~ member(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( member(X1,esk3_0)
| member(X1,esk2_0)
| ~ member(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( subset(X1,union(X2,X3))
| ~ member(esk4_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( subset(esk1_0,X1)
| member(esk4_2(esk1_0,X1),esk2_0)
| member(esk4_2(esk1_0,X1),esk3_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_16,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(c_0_17,plain,
! [X4,X5,X6,X6,X4,X5] :
( ( ~ member(X6,X4)
| member(X6,X5)
| X4 != X5 )
& ( ~ member(X6,X5)
| member(X6,X4)
| X4 != X5 )
& ( ~ member(esk5_2(X4,X5),X4)
| ~ member(esk5_2(X4,X5),X5)
| X4 = X5 )
& ( member(esk5_2(X4,X5),X4)
| member(esk5_2(X4,X5),X5)
| 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)],[equal_member_defn])])])])])])]) ).
cnf(c_0_18,plain,
( subset(X1,union(X2,X3))
| ~ member(esk4_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( subset(esk1_0,union(esk3_0,X1))
| member(esk4_2(esk1_0,union(esk3_0,X1)),esk2_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,plain,
( X1 = X2
| member(esk5_2(X1,X2),X2)
| member(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ member(esk5_2(X1,X2),X2)
| ~ member(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_25,negated_conjecture,
subset(esk1_0,union(esk2_0,esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_26,plain,
( X1 = union(X2,X3)
| member(esk5_2(X1,union(X2,X3)),X1)
| member(esk5_2(X1,union(X2,X3)),X2)
| member(esk5_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( X1 = union(X2,X3)
| ~ member(esk5_2(X1,union(X2,X3)),X1)
| ~ member(esk5_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_10]) ).
cnf(c_0_28,negated_conjecture,
( member(X1,union(esk2_0,esk3_0))
| ~ member(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
( union(X1,X2) = X1
| member(esk5_2(X1,union(X1,X2)),X2)
| member(esk5_2(X1,union(X1,X2)),X1) ),
inference(ef,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
( X1 = union(X2,X3)
| ~ member(esk5_2(X1,union(X2,X3)),X1)
| ~ member(esk5_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_13]) ).
cnf(c_0_31,negated_conjecture,
( union(esk2_0,esk3_0) = union(X1,X2)
| ~ member(esk5_2(union(esk2_0,esk3_0),union(X1,X2)),esk1_0)
| ~ member(esk5_2(union(esk2_0,esk3_0),union(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( union(X1,X2) = X1
| member(esk5_2(X1,union(X1,X2)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_29]),c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( union(esk2_0,esk3_0) = union(X1,X2)
| ~ member(esk5_2(union(esk2_0,esk3_0),union(X1,X2)),esk1_0)
| ~ member(esk5_2(union(esk2_0,esk3_0),union(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
( union(esk1_0,union(esk2_0,esk3_0)) = union(esk2_0,esk3_0)
| ~ member(esk5_2(union(esk2_0,esk3_0),union(esk1_0,union(esk2_0,esk3_0))),union(esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_20]),c_0_20]) ).
cnf(c_0_35,plain,
( union(X1,X2) = X2
| member(esk5_2(X2,union(X1,X2)),X2)
| member(esk5_2(X2,union(X1,X2)),X1) ),
inference(ef,[status(thm)],[c_0_26]) ).
cnf(c_0_36,negated_conjecture,
( union(esk1_0,union(esk2_0,esk3_0)) = union(esk2_0,esk3_0)
| ~ member(esk5_2(union(esk2_0,esk3_0),union(esk1_0,union(esk2_0,esk3_0))),esk1_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_32]),c_0_20]),c_0_20]) ).
cnf(c_0_37,negated_conjecture,
( member(X1,esk1_0)
| ~ member(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_38,negated_conjecture,
( member(X1,esk1_0)
| ~ member(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_39,negated_conjecture,
union(esk1_0,union(esk2_0,esk3_0)) = union(esk2_0,esk3_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_40,negated_conjecture,
esk1_0 != union(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_41,negated_conjecture,
( union(X1,X2) = esk1_0
| ~ member(esk5_2(esk1_0,union(X1,X2)),esk3_0)
| ~ member(esk5_2(esk1_0,union(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
( union(X1,X2) = esk1_0
| ~ member(esk5_2(esk1_0,union(X1,X2)),esk2_0)
| ~ member(esk5_2(esk1_0,union(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
member(esk5_2(esk1_0,union(esk2_0,esk3_0)),union(esk2_0,esk3_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_39]),c_0_40]) ).
cnf(c_0_44,negated_conjecture,
~ member(esk5_2(esk1_0,union(esk2_0,esk3_0)),esk3_0),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_39]),c_0_40]),c_0_13]) ).
cnf(c_0_45,negated_conjecture,
~ member(esk5_2(esk1_0,union(esk2_0,esk3_0)),esk2_0),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_39]),c_0_40]),c_0_10]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_43]),c_0_44]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET577+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : run_ET %s %d
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 02:18:55 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.24/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.41 # Preprocessing time : 0.015 s
% 0.24/1.41
% 0.24/1.41 # Proof found!
% 0.24/1.41 # SZS status Theorem
% 0.24/1.41 # SZS output start CNFRefutation
% See solution above
% 0.24/1.41 # Proof object total steps : 47
% 0.24/1.41 # Proof object clause steps : 36
% 0.24/1.41 # Proof object formula steps : 11
% 0.24/1.41 # Proof object conjectures : 22
% 0.24/1.41 # Proof object clause conjectures : 19
% 0.24/1.41 # Proof object formula conjectures : 3
% 0.24/1.41 # Proof object initial clauses used : 13
% 0.24/1.41 # Proof object initial formulas used : 5
% 0.24/1.41 # Proof object generating inferences : 23
% 0.24/1.41 # Proof object simplifying inferences : 14
% 0.24/1.41 # Training examples: 0 positive, 0 negative
% 0.24/1.41 # Parsed axioms : 7
% 0.24/1.41 # Removed by relevancy pruning/SinE : 0
% 0.24/1.41 # Initial clauses : 19
% 0.24/1.41 # Removed in clause preprocessing : 2
% 0.24/1.41 # Initial clauses in saturation : 17
% 0.24/1.41 # Processed clauses : 737
% 0.24/1.41 # ...of these trivial : 51
% 0.24/1.41 # ...subsumed : 488
% 0.24/1.41 # ...remaining for further processing : 198
% 0.24/1.41 # Other redundant clauses eliminated : 2
% 0.24/1.41 # Clauses deleted for lack of memory : 0
% 0.24/1.41 # Backward-subsumed : 1
% 0.24/1.41 # Backward-rewritten : 11
% 0.24/1.41 # Generated clauses : 1624
% 0.24/1.41 # ...of the previous two non-trivial : 1392
% 0.24/1.41 # Contextual simplify-reflections : 41
% 0.24/1.41 # Paramodulations : 1610
% 0.24/1.41 # Factorizations : 12
% 0.24/1.41 # Equation resolutions : 2
% 0.24/1.41 # Current number of processed clauses : 184
% 0.24/1.41 # Positive orientable unit clauses : 41
% 0.24/1.41 # Positive unorientable unit clauses: 1
% 0.24/1.41 # Negative unit clauses : 7
% 0.24/1.41 # Non-unit-clauses : 135
% 0.24/1.41 # Current number of unprocessed clauses: 645
% 0.24/1.41 # ...number of literals in the above : 1610
% 0.24/1.41 # Current number of archived formulas : 0
% 0.24/1.41 # Current number of archived clauses : 12
% 0.24/1.41 # Clause-clause subsumption calls (NU) : 5971
% 0.24/1.41 # Rec. Clause-clause subsumption calls : 5928
% 0.24/1.41 # Non-unit clause-clause subsumptions : 515
% 0.24/1.41 # Unit Clause-clause subsumption calls : 207
% 0.24/1.41 # Rewrite failures with RHS unbound : 0
% 0.24/1.41 # BW rewrite match attempts : 131
% 0.24/1.41 # BW rewrite match successes : 6
% 0.24/1.41 # Condensation attempts : 0
% 0.24/1.41 # Condensation successes : 0
% 0.24/1.41 # Termbank termtop insertions : 20669
% 0.24/1.41
% 0.24/1.41 # -------------------------------------------------
% 0.24/1.41 # User time : 0.057 s
% 0.24/1.41 # System time : 0.004 s
% 0.24/1.41 # Total time : 0.061 s
% 0.24/1.41 # Maximum resident set size: 3824 pages
%------------------------------------------------------------------------------