TSTP Solution File: SET185+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET185+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n028.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 00:49:57 EDT 2022
% Result : Theorem 0.24s 1.43s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 8 unt; 0 def)
% Number of atoms : 91 ( 22 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 92 ( 33 ~; 44 |; 8 &)
% ( 4 <=>; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 72 ( 10 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_subset_union,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> union(X1,X2) = X2 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_subset_union) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',union_defn) ).
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(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(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_of_union) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> union(X1,X2) = X2 ),
inference(assume_negation,[status(cth)],[prove_subset_union]) ).
fof(c_0_6,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_7,plain,
! [X4,X5,X6,X6,X4,X5] :
( ( ~ member(X6,X4)
| member(X6,X5)
| X4 != X5 )
& ( ~ member(X6,X5)
| member(X6,X4)
| X4 != X5 )
& ( ~ member(esk4_2(X4,X5),X4)
| ~ member(esk4_2(X4,X5),X5)
| X4 = X5 )
& ( member(esk4_2(X4,X5),X4)
| member(esk4_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])])])])])])]) ).
fof(c_0_8,plain,
! [X4,X5,X6,X4,X5] :
( ( ~ subset(X4,X5)
| ~ member(X6,X4)
| member(X6,X5) )
& ( member(esk3_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk3_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_9,negated_conjecture,
( subset(esk1_0,esk2_0)
& union(esk1_0,esk2_0) != esk2_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_10,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( X1 = X2
| member(esk4_2(X1,X2),X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( X1 = X2
| ~ member(esk4_2(X1,X2),X2)
| ~ member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( X1 = union(X2,X3)
| member(esk4_2(X1,union(X2,X3)),X1)
| member(esk4_2(X1,union(X2,X3)),X2)
| member(esk4_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,plain,
( X1 = union(X2,X3)
| ~ member(esk4_2(X1,union(X2,X3)),X1)
| ~ member(esk4_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( member(X1,esk2_0)
| ~ member(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( union(X1,X2) = X1
| member(esk4_2(X1,union(X1,X2)),X2)
| member(esk4_2(X1,union(X1,X2)),X1) ),
inference(ef,[status(thm)],[c_0_16]) ).
fof(c_0_21,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_22,plain,
( X1 = union(X2,X3)
| ~ member(esk4_2(X1,union(X2,X3)),X1)
| ~ member(esk4_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( union(X1,X2) = esk2_0
| ~ member(esk4_2(esk2_0,union(X1,X2)),esk1_0)
| ~ member(esk4_2(esk2_0,union(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( union(X1,X2) = X1
| member(esk4_2(X1,union(X1,X2)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_20]),c_0_20]) ).
cnf(c_0_25,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
union(esk1_0,esk2_0) != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,negated_conjecture,
( union(X1,X2) = esk2_0
| ~ member(esk4_2(esk2_0,union(X1,X2)),esk1_0)
| ~ member(esk4_2(esk2_0,union(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_28,negated_conjecture,
~ member(esk4_2(esk2_0,union(esk1_0,esk2_0)),esk2_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_25]),c_0_26]) ).
cnf(c_0_29,plain,
( union(X1,X2) = X2
| member(esk4_2(X2,union(X1,X2)),X2)
| member(esk4_2(X2,union(X1,X2)),X1) ),
inference(ef,[status(thm)],[c_0_16]) ).
cnf(c_0_30,negated_conjecture,
~ member(esk4_2(esk2_0,union(esk1_0,esk2_0)),esk1_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_24]),c_0_25]),c_0_25]),c_0_26]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_26]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET185+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : run_ET %s %d
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 10:48:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.24/1.43 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.43 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.43 # Preprocessing time : 0.015 s
% 0.24/1.43
% 0.24/1.43 # Proof found!
% 0.24/1.43 # SZS status Theorem
% 0.24/1.43 # SZS output start CNFRefutation
% See solution above
% 0.24/1.43 # Proof object total steps : 32
% 0.24/1.43 # Proof object clause steps : 21
% 0.24/1.43 # Proof object formula steps : 11
% 0.24/1.43 # Proof object conjectures : 11
% 0.24/1.43 # Proof object clause conjectures : 8
% 0.24/1.43 # Proof object formula conjectures : 3
% 0.24/1.43 # Proof object initial clauses used : 9
% 0.24/1.43 # Proof object initial formulas used : 5
% 0.24/1.43 # Proof object generating inferences : 12
% 0.24/1.43 # Proof object simplifying inferences : 9
% 0.24/1.43 # Training examples: 0 positive, 0 negative
% 0.24/1.43 # Parsed axioms : 7
% 0.24/1.43 # Removed by relevancy pruning/SinE : 0
% 0.24/1.43 # Initial clauses : 17
% 0.24/1.43 # Removed in clause preprocessing : 2
% 0.24/1.43 # Initial clauses in saturation : 15
% 0.24/1.43 # Processed clauses : 328
% 0.24/1.43 # ...of these trivial : 16
% 0.24/1.43 # ...subsumed : 227
% 0.24/1.43 # ...remaining for further processing : 85
% 0.24/1.43 # Other redundant clauses eliminated : 2
% 0.24/1.43 # Clauses deleted for lack of memory : 0
% 0.24/1.43 # Backward-subsumed : 1
% 0.24/1.43 # Backward-rewritten : 1
% 0.24/1.43 # Generated clauses : 558
% 0.24/1.43 # ...of the previous two non-trivial : 474
% 0.24/1.43 # Contextual simplify-reflections : 12
% 0.24/1.43 # Paramodulations : 544
% 0.24/1.43 # Factorizations : 12
% 0.24/1.43 # Equation resolutions : 2
% 0.24/1.43 # Current number of processed clauses : 81
% 0.24/1.43 # Positive orientable unit clauses : 18
% 0.24/1.43 # Positive unorientable unit clauses: 1
% 0.24/1.43 # Negative unit clauses : 3
% 0.24/1.43 # Non-unit-clauses : 59
% 0.24/1.43 # Current number of unprocessed clauses: 151
% 0.24/1.43 # ...number of literals in the above : 364
% 0.24/1.43 # Current number of archived formulas : 0
% 0.24/1.43 # Current number of archived clauses : 2
% 0.24/1.43 # Clause-clause subsumption calls (NU) : 2048
% 0.24/1.43 # Rec. Clause-clause subsumption calls : 2007
% 0.24/1.43 # Non-unit clause-clause subsumptions : 240
% 0.24/1.43 # Unit Clause-clause subsumption calls : 51
% 0.24/1.43 # Rewrite failures with RHS unbound : 0
% 0.24/1.43 # BW rewrite match attempts : 50
% 0.24/1.43 # BW rewrite match successes : 3
% 0.24/1.43 # Condensation attempts : 0
% 0.24/1.43 # Condensation successes : 0
% 0.24/1.43 # Termbank termtop insertions : 6670
% 0.24/1.43
% 0.24/1.43 # -------------------------------------------------
% 0.24/1.43 # User time : 0.028 s
% 0.24/1.43 # System time : 0.001 s
% 0.24/1.43 # Total time : 0.029 s
% 0.24/1.43 # Maximum resident set size: 3024 pages
%------------------------------------------------------------------------------