TSTP Solution File: SET578+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET578+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n014.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 00:52:06 EDT 2022
% Result : Theorem 0.21s 1.41s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 9 unt; 0 def)
% Number of atoms : 108 ( 17 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 112 ( 41 ~; 49 |; 13 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 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 : 77 ( 11 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th19,conjecture,
! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X2)
& member(X4,X3) ) )
=> X1 = intersection(X2,X3) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_th19) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',subset_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',intersection_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_of_intersection) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox/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 = intersection(X2,X3) ),
inference(assume_negation,[status(cth)],[prove_th19]) ).
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,negated_conjecture,
! [X8,X8] :
( ( member(X8,esk2_0)
| ~ member(X8,esk1_0) )
& ( member(X8,esk3_0)
| ~ member(X8,esk1_0) )
& ( ~ member(X8,esk2_0)
| ~ member(X8,esk3_0)
| member(X8,esk1_0) )
& esk1_0 != intersection(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])])])])])])]) ).
fof(c_0_8,plain,
! [X4,X5,X6,X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,intersection(X4,X5)) )
& ( member(X6,X5)
| ~ member(X6,intersection(X4,X5)) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(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)],[intersection_defn])])])])]) ).
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,negated_conjecture,
( member(X1,esk1_0)
| ~ member(X1,esk3_0)
| ~ member(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
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,negated_conjecture,
( subset(X1,esk1_0)
| ~ member(esk4_2(X1,esk1_0),esk2_0)
| ~ member(esk4_2(X1,esk1_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( subset(intersection(X1,X2),X3)
| member(esk4_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_16,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_17,negated_conjecture,
( subset(intersection(esk3_0,X1),esk1_0)
| ~ member(esk4_2(intersection(esk3_0,X1),esk1_0),esk2_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( subset(intersection(X1,X2),X3)
| member(esk4_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_19,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,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_21,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
subset(intersection(esk2_0,esk3_0),esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,plain,
( X1 = X2
| member(esk5_2(X1,X2),X2)
| member(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( member(X1,esk2_0)
| ~ member(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_26,plain,
( X1 = X2
| ~ member(esk5_2(X1,X2),X2)
| ~ member(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
( member(X1,esk1_0)
| ~ member(X1,intersection(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( X1 = esk1_0
| member(esk5_2(X1,esk1_0),esk3_0)
| member(esk5_2(X1,esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
esk1_0 != intersection(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_30,negated_conjecture,
( X1 = esk1_0
| member(esk5_2(X1,esk1_0),esk2_0)
| member(esk5_2(X1,esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
( X1 = esk1_0
| ~ member(esk5_2(X1,esk1_0),esk2_0)
| ~ member(esk5_2(X1,esk1_0),esk3_0)
| ~ member(esk5_2(X1,esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_10]) ).
cnf(c_0_32,negated_conjecture,
member(esk5_2(intersection(esk2_0,esk3_0),esk1_0),esk3_0),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_23]) ).
cnf(c_0_33,negated_conjecture,
member(esk5_2(intersection(esk2_0,esk3_0),esk1_0),esk2_0),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_30]),c_0_29]),c_0_25]) ).
cnf(c_0_34,negated_conjecture,
~ member(esk5_2(intersection(esk2_0,esk3_0),esk1_0),intersection(esk2_0,esk3_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]),c_0_29]) ).
cnf(c_0_35,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_32]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET578+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.13 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n014.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 : Sun Jul 10 05:11:20 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.21/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.21/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.21/1.41 # Preprocessing time : 0.015 s
% 0.21/1.41
% 0.21/1.41 # Proof found!
% 0.21/1.41 # SZS status Theorem
% 0.21/1.41 # SZS output start CNFRefutation
% See solution above
% 0.21/1.41 # Proof object total steps : 37
% 0.21/1.41 # Proof object clause steps : 26
% 0.21/1.41 # Proof object formula steps : 11
% 0.21/1.41 # Proof object conjectures : 18
% 0.21/1.41 # Proof object clause conjectures : 15
% 0.21/1.41 # Proof object formula conjectures : 3
% 0.21/1.41 # Proof object initial clauses used : 13
% 0.21/1.41 # Proof object initial formulas used : 5
% 0.21/1.41 # Proof object generating inferences : 13
% 0.21/1.41 # Proof object simplifying inferences : 11
% 0.21/1.41 # Training examples: 0 positive, 0 negative
% 0.21/1.41 # Parsed axioms : 7
% 0.21/1.41 # Removed by relevancy pruning/SinE : 0
% 0.21/1.41 # Initial clauses : 19
% 0.21/1.41 # Removed in clause preprocessing : 2
% 0.21/1.41 # Initial clauses in saturation : 17
% 0.21/1.41 # Processed clauses : 61
% 0.21/1.41 # ...of these trivial : 0
% 0.21/1.41 # ...subsumed : 14
% 0.21/1.41 # ...remaining for further processing : 47
% 0.21/1.41 # Other redundant clauses eliminated : 2
% 0.21/1.41 # Clauses deleted for lack of memory : 0
% 0.21/1.41 # Backward-subsumed : 0
% 0.21/1.41 # Backward-rewritten : 0
% 0.21/1.41 # Generated clauses : 133
% 0.21/1.41 # ...of the previous two non-trivial : 112
% 0.21/1.41 # Contextual simplify-reflections : 3
% 0.21/1.41 # Paramodulations : 121
% 0.21/1.41 # Factorizations : 10
% 0.21/1.41 # Equation resolutions : 2
% 0.21/1.41 # Current number of processed clauses : 45
% 0.21/1.41 # Positive orientable unit clauses : 8
% 0.21/1.41 # Positive unorientable unit clauses: 1
% 0.21/1.41 # Negative unit clauses : 3
% 0.21/1.41 # Non-unit-clauses : 33
% 0.21/1.41 # Current number of unprocessed clauses: 68
% 0.21/1.41 # ...number of literals in the above : 175
% 0.21/1.41 # Current number of archived formulas : 0
% 0.21/1.41 # Current number of archived clauses : 0
% 0.21/1.41 # Clause-clause subsumption calls (NU) : 115
% 0.21/1.41 # Rec. Clause-clause subsumption calls : 108
% 0.21/1.41 # Non-unit clause-clause subsumptions : 17
% 0.21/1.41 # Unit Clause-clause subsumption calls : 9
% 0.21/1.41 # Rewrite failures with RHS unbound : 0
% 0.21/1.41 # BW rewrite match attempts : 9
% 0.21/1.41 # BW rewrite match successes : 2
% 0.21/1.41 # Condensation attempts : 0
% 0.21/1.41 # Condensation successes : 0
% 0.21/1.41 # Termbank termtop insertions : 2553
% 0.21/1.41
% 0.21/1.41 # -------------------------------------------------
% 0.21/1.41 # User time : 0.019 s
% 0.21/1.41 # System time : 0.001 s
% 0.21/1.41 # Total time : 0.020 s
% 0.21/1.41 # Maximum resident set size: 2768 pages
%------------------------------------------------------------------------------