TSTP Solution File: SET624+3 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET624+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 00:52:38 EDT 2022
% Result : Theorem 0.22s 1.41s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 8 unt; 0 def)
% Number of atoms : 90 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 89 ( 35 ~; 42 |; 7 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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; 3 con; 0-2 aty)
% Number of variables : 68 ( 10 sgn 30 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersect_defn,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',intersect_defn) ).
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(prove_intersect_with_union,conjecture,
! [X1,X2,X3] :
( intersect(X1,union(X2,X3))
<=> ( intersect(X1,X2)
| intersect(X1,X3) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_intersect_with_union) ).
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(symmetry_of_intersect,axiom,
! [X1,X2] :
( intersect(X1,X2)
=> intersect(X2,X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',symmetry_of_intersect) ).
fof(c_0_5,plain,
! [X4,X5,X4,X5,X7] :
( ( member(esk4_2(X4,X5),X4)
| ~ intersect(X4,X5) )
& ( member(esk4_2(X4,X5),X5)
| ~ intersect(X4,X5) )
& ( ~ member(X7,X4)
| ~ member(X7,X5)
| intersect(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)],[intersect_defn])])])])])])]) ).
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])])])])]) ).
cnf(c_0_7,plain,
( intersect(X1,X2)
| ~ member(X3,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2,X3] :
( intersect(X1,union(X2,X3))
<=> ( intersect(X1,X2)
| intersect(X1,X3) ) ),
inference(assume_negation,[status(cth)],[prove_intersect_with_union]) ).
cnf(c_0_10,plain,
( intersect(X1,union(X2,X3))
| ~ member(X4,X1)
| ~ member(X4,X3) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( member(esk4_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_12,negated_conjecture,
( ( ~ intersect(esk1_0,esk2_0)
| ~ intersect(esk1_0,union(esk2_0,esk3_0)) )
& ( ~ intersect(esk1_0,esk3_0)
| ~ intersect(esk1_0,union(esk2_0,esk3_0)) )
& ( intersect(esk1_0,union(esk2_0,esk3_0))
| intersect(esk1_0,esk2_0)
| intersect(esk1_0,esk3_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
cnf(c_0_13,plain,
( intersect(X1,union(X2,X3))
| ~ intersect(X1,X4)
| ~ member(esk4_2(X1,X4),X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( member(esk4_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_15,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_16,negated_conjecture,
( ~ intersect(esk1_0,union(esk2_0,esk3_0))
| ~ intersect(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( intersect(X1,union(X2,X3))
| ~ intersect(X1,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( intersect(esk1_0,esk3_0)
| intersect(esk1_0,esk2_0)
| intersect(esk1_0,union(esk2_0,esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,negated_conjecture,
~ intersect(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( ~ intersect(esk1_0,union(esk2_0,esk3_0))
| ~ intersect(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,plain,
( intersect(X1,union(X2,X3))
| ~ intersect(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,negated_conjecture,
( intersect(esk1_0,union(esk2_0,esk3_0))
| intersect(esk1_0,esk2_0) ),
inference(sr,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
~ intersect(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( member(esk4_2(X1,union(X2,X3)),X2)
| member(esk4_2(X1,union(X2,X3)),X3)
| ~ intersect(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_23,c_0_14]) ).
cnf(c_0_27,negated_conjecture,
intersect(esk1_0,union(esk2_0,esk3_0)),
inference(sr,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
( intersect(X1,X2)
| ~ intersect(X2,X3)
| ~ member(esk4_2(X2,X3),X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_29,negated_conjecture,
( member(esk4_2(esk1_0,union(esk2_0,esk3_0)),esk3_0)
| member(esk4_2(esk1_0,union(esk2_0,esk3_0)),esk2_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_30,plain,
! [X3,X4] :
( ~ intersect(X3,X4)
| intersect(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_of_intersect])]) ).
cnf(c_0_31,negated_conjecture,
( intersect(esk3_0,esk1_0)
| member(esk4_2(esk1_0,union(esk2_0,esk3_0)),esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_27])]) ).
cnf(c_0_32,plain,
( intersect(X1,X2)
| ~ intersect(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( intersect(esk3_0,esk1_0)
| intersect(esk2_0,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_31]),c_0_27])]) ).
cnf(c_0_34,negated_conjecture,
intersect(esk2_0,esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_20]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_34]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET624+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % 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 21:13:49 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.22/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.41 # Preprocessing time : 0.015 s
% 0.22/1.41
% 0.22/1.41 # Proof found!
% 0.22/1.41 # SZS status Theorem
% 0.22/1.41 # SZS output start CNFRefutation
% See solution above
% 0.22/1.41 # Proof object total steps : 36
% 0.22/1.41 # Proof object clause steps : 25
% 0.22/1.41 # Proof object formula steps : 11
% 0.22/1.41 # Proof object conjectures : 15
% 0.22/1.41 # Proof object clause conjectures : 12
% 0.22/1.41 # Proof object formula conjectures : 3
% 0.22/1.41 # Proof object initial clauses used : 10
% 0.22/1.41 # Proof object initial formulas used : 5
% 0.22/1.41 # Proof object generating inferences : 13
% 0.22/1.41 # Proof object simplifying inferences : 8
% 0.22/1.41 # Training examples: 0 positive, 0 negative
% 0.22/1.41 # Parsed axioms : 6
% 0.22/1.41 # Removed by relevancy pruning/SinE : 0
% 0.22/1.41 # Initial clauses : 15
% 0.22/1.41 # Removed in clause preprocessing : 2
% 0.22/1.41 # Initial clauses in saturation : 13
% 0.22/1.41 # Processed clauses : 119
% 0.22/1.41 # ...of these trivial : 11
% 0.22/1.41 # ...subsumed : 31
% 0.22/1.41 # ...remaining for further processing : 77
% 0.22/1.41 # Other redundant clauses eliminated : 0
% 0.22/1.41 # Clauses deleted for lack of memory : 0
% 0.22/1.41 # Backward-subsumed : 1
% 0.22/1.41 # Backward-rewritten : 5
% 0.22/1.41 # Generated clauses : 527
% 0.22/1.41 # ...of the previous two non-trivial : 437
% 0.22/1.41 # Contextual simplify-reflections : 3
% 0.22/1.41 # Paramodulations : 504
% 0.22/1.41 # Factorizations : 14
% 0.22/1.41 # Equation resolutions : 0
% 0.22/1.41 # Current number of processed clauses : 62
% 0.22/1.41 # Positive orientable unit clauses : 18
% 0.22/1.41 # Positive unorientable unit clauses: 1
% 0.22/1.41 # Negative unit clauses : 2
% 0.22/1.41 # Non-unit-clauses : 41
% 0.22/1.41 # Current number of unprocessed clauses: 278
% 0.22/1.41 # ...number of literals in the above : 789
% 0.22/1.41 # Current number of archived formulas : 0
% 0.22/1.41 # Current number of archived clauses : 15
% 0.22/1.41 # Clause-clause subsumption calls (NU) : 625
% 0.22/1.41 # Rec. Clause-clause subsumption calls : 566
% 0.22/1.41 # Non-unit clause-clause subsumptions : 30
% 0.22/1.41 # Unit Clause-clause subsumption calls : 30
% 0.22/1.41 # Rewrite failures with RHS unbound : 0
% 0.22/1.41 # BW rewrite match attempts : 7
% 0.22/1.41 # BW rewrite match successes : 7
% 0.22/1.41 # Condensation attempts : 0
% 0.22/1.41 # Condensation successes : 0
% 0.22/1.41 # Termbank termtop insertions : 6752
% 0.22/1.41
% 0.22/1.41 # -------------------------------------------------
% 0.22/1.41 # User time : 0.024 s
% 0.22/1.41 # System time : 0.003 s
% 0.22/1.41 # Total time : 0.027 s
% 0.22/1.41 # Maximum resident set size: 3024 pages
%------------------------------------------------------------------------------