TSTP Solution File: SET159+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET159+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n022.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 00:49:42 EDT 2022
% Result : Theorem 0.23s 1.41s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 22 unt; 0 def)
% Number of atoms : 96 ( 22 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 79 ( 31 ~; 37 |; 7 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 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 : 129 ( 13 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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',subset_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',union_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',equal_defn) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',commutativity_of_union) ).
fof(prove_associativity_of_union,conjecture,
! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',prove_associativity_of_union) ).
fof(c_0_5,plain,
! [X4,X5,X6,X4,X5] :
( ( ~ subset(X4,X5)
| ~ member(X6,X4)
| member(X6,X5) )
& ( member(esk1_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk1_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_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,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
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]) ).
cnf(c_0_9,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
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,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_9]) ).
cnf(c_0_14,plain,
( subset(union(X1,X2),X3)
| member(esk1_2(union(X1,X2),X3),X1)
| member(esk1_2(union(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_16,plain,
( subset(union(X1,X2),union(X2,X3))
| member(esk1_2(union(X1,X2),union(X2,X3)),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,plain,
subset(union(X1,X2),union(X2,union(X1,X3))),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_19,plain,
! [X3,X4,X3,X4] :
( ( subset(X3,X4)
| X3 != X4 )
& ( subset(X4,X3)
| X3 != X4 )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| 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_defn])])])])]) ).
cnf(c_0_20,plain,
( subset(union(X1,X2),X2)
| member(esk1_2(union(X1,X2),X2),X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_14]) ).
cnf(c_0_21,plain,
( member(X1,union(X2,union(X3,X4)))
| ~ member(X1,union(X3,X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),X4) ),
inference(spm,[status(thm)],[c_0_12,c_0_8]) ).
cnf(c_0_23,plain,
( subset(X1,union(union(X2,X3),X4))
| ~ member(esk1_2(X1,union(union(X2,X3),X4)),X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_8]) ).
cnf(c_0_24,plain,
( subset(union(X1,X2),union(X3,X2))
| member(esk1_2(union(X1,X2),union(X3,X2)),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_25,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
subset(union(X1,union(X1,X2)),union(X1,X2)),
inference(spm,[status(thm)],[c_0_13,c_0_20]) ).
cnf(c_0_27,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
fof(c_0_28,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(c_0_29,negated_conjecture,
~ ! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
inference(assume_negation,[status(cth)],[prove_associativity_of_union]) ).
cnf(c_0_30,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),union(X3,X2)) ),
inference(spm,[status(thm)],[c_0_7,c_0_21]) ).
cnf(c_0_31,plain,
( subset(union(X1,X2),union(X3,union(X4,X1)))
| member(esk1_2(union(X1,X2),union(X3,union(X4,X1))),X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_14]) ).
cnf(c_0_32,plain,
subset(union(X1,X2),union(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_33,plain,
union(X1,union(X1,X2)) = union(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_34,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_35,negated_conjecture,
union(union(esk3_0,esk4_0),esk5_0) != union(esk3_0,union(esk4_0,esk5_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
cnf(c_0_36,plain,
subset(union(X1,union(X2,X3)),union(X3,union(X2,X1))),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
( union(union(X1,X2),X3) = union(X2,X3)
| ~ subset(union(union(X1,X2),X3),union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
cnf(c_0_38,plain,
union(X1,union(X2,X1)) = union(X2,X1),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
union(union(esk3_0,esk4_0),esk5_0) != union(esk3_0,union(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,plain,
union(X1,union(X2,X3)) = union(X3,union(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_36]),c_0_36])]) ).
cnf(c_0_41,plain,
union(X1,union(X2,union(X3,X1))) = union(X2,union(X3,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_27])]) ).
cnf(c_0_42,negated_conjecture,
union(esk5_0,union(esk3_0,esk4_0)) != union(esk3_0,union(esk4_0,esk5_0)),
inference(rw,[status(thm)],[c_0_39,c_0_34]) ).
cnf(c_0_43,plain,
union(union(X1,X2),X3) = union(X2,union(X1,X3)),
inference(spm,[status(thm)],[c_0_34,c_0_40]) ).
cnf(c_0_44,plain,
union(X1,union(X2,union(X1,X3))) = union(X2,union(X1,X3)),
inference(spm,[status(thm)],[c_0_41,c_0_34]) ).
cnf(c_0_45,negated_conjecture,
union(esk4_0,union(esk3_0,esk5_0)) != union(esk3_0,union(esk4_0,esk5_0)),
inference(rw,[status(thm)],[c_0_42,c_0_40]) ).
cnf(c_0_46,plain,
union(X1,union(X2,X3)) = union(X3,union(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_38]),c_0_43]),c_0_44]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET159+3 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 02:12:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.23/1.41 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.23/1.41 # Preprocessing time : 0.015 s
% 0.23/1.41
% 0.23/1.41 # Proof found!
% 0.23/1.41 # SZS status Theorem
% 0.23/1.41 # SZS output start CNFRefutation
% See solution above
% 0.23/1.41 # Proof object total steps : 48
% 0.23/1.41 # Proof object clause steps : 37
% 0.23/1.41 # Proof object formula steps : 11
% 0.23/1.41 # Proof object conjectures : 7
% 0.23/1.41 # Proof object clause conjectures : 4
% 0.23/1.41 # Proof object formula conjectures : 3
% 0.23/1.41 # Proof object initial clauses used : 9
% 0.23/1.41 # Proof object initial formulas used : 5
% 0.23/1.41 # Proof object generating inferences : 25
% 0.23/1.41 # Proof object simplifying inferences : 13
% 0.23/1.41 # Training examples: 0 positive, 0 negative
% 0.23/1.41 # Parsed axioms : 7
% 0.23/1.41 # Removed by relevancy pruning/SinE : 0
% 0.23/1.41 # Initial clauses : 16
% 0.23/1.41 # Removed in clause preprocessing : 2
% 0.23/1.41 # Initial clauses in saturation : 14
% 0.23/1.41 # Processed clauses : 2424
% 0.23/1.41 # ...of these trivial : 197
% 0.23/1.41 # ...subsumed : 1808
% 0.23/1.41 # ...remaining for further processing : 419
% 0.23/1.41 # Other redundant clauses eliminated : 2
% 0.23/1.41 # Clauses deleted for lack of memory : 0
% 0.23/1.41 # Backward-subsumed : 1
% 0.23/1.41 # Backward-rewritten : 236
% 0.23/1.41 # Generated clauses : 37550
% 0.23/1.41 # ...of the previous two non-trivial : 33817
% 0.23/1.41 # Contextual simplify-reflections : 89
% 0.23/1.41 # Paramodulations : 37204
% 0.23/1.41 # Factorizations : 344
% 0.23/1.41 # Equation resolutions : 2
% 0.23/1.41 # Current number of processed clauses : 180
% 0.23/1.41 # Positive orientable unit clauses : 33
% 0.23/1.41 # Positive unorientable unit clauses: 3
% 0.23/1.41 # Negative unit clauses : 0
% 0.23/1.41 # Non-unit-clauses : 144
% 0.23/1.41 # Current number of unprocessed clauses: 7196
% 0.23/1.41 # ...number of literals in the above : 20195
% 0.23/1.41 # Current number of archived formulas : 0
% 0.23/1.41 # Current number of archived clauses : 237
% 0.23/1.41 # Clause-clause subsumption calls (NU) : 68070
% 0.23/1.41 # Rec. Clause-clause subsumption calls : 48288
% 0.23/1.41 # Non-unit clause-clause subsumptions : 1874
% 0.23/1.41 # Unit Clause-clause subsumption calls : 4123
% 0.23/1.41 # Rewrite failures with RHS unbound : 0
% 0.23/1.41 # BW rewrite match attempts : 2371
% 0.23/1.41 # BW rewrite match successes : 438
% 0.23/1.41 # Condensation attempts : 0
% 0.23/1.41 # Condensation successes : 0
% 0.23/1.41 # Termbank termtop insertions : 745830
% 0.23/1.41
% 0.23/1.41 # -------------------------------------------------
% 0.23/1.41 # User time : 0.430 s
% 0.23/1.41 # System time : 0.016 s
% 0.23/1.41 # Total time : 0.446 s
% 0.23/1.41 # Maximum resident set size: 30224 pages
% 0.23/23.41 eprover: CPU time limit exceeded, terminating
% 0.23/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.43 eprover: No such file or directory
% 0.23/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.43 eprover: No such file or directory
% 0.23/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.44 eprover: No such file or directory
% 0.23/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.44 eprover: No such file or directory
% 0.23/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.47 eprover: No such file or directory
% 0.23/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.47 eprover: No such file or directory
% 0.23/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.48 eprover: No such file or directory
% 0.23/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.48 eprover: No such file or directory
%------------------------------------------------------------------------------