TSTP Solution File: SET635+3 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET635+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n021.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 00:52:46 EDT 2022
% Result : Theorem 0.22s 1.41s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 37 unt; 0 def)
% Number of atoms : 72 ( 36 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 47 ( 22 ~; 15 |; 6 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 10 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th117,conjecture,
! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),intersection(X1,X3)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_th117) ).
fof(difference_and_intersection,axiom,
! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),X3),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',difference_and_intersection) ).
fof(difference_and_intersection_and_union,axiom,
! [X1,X2,X3] : difference(X1,intersection(X2,X3)) = union(difference(X1,X2),difference(X1,X3)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',difference_and_intersection_and_union) ).
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(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',empty_set_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(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',equal_defn) ).
fof(difference_empty_set,axiom,
! [X1,X2] :
( difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',difference_empty_set) ).
fof(reflexivity_of_subset,axiom,
! [X1] : subset(X1,X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',reflexivity_of_subset) ).
fof(intersection_is_subset,axiom,
! [X1,X2] : subset(intersection(X1,X2),X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',intersection_is_subset) ).
fof(union_empty_set,axiom,
! [X1] : union(X1,empty_set) = X1,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',union_empty_set) ).
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_12,negated_conjecture,
~ ! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),intersection(X1,X3)),
inference(assume_negation,[status(cth)],[prove_th117]) ).
fof(c_0_13,negated_conjecture,
intersection(esk4_0,difference(esk5_0,esk6_0)) != difference(intersection(esk4_0,esk5_0),intersection(esk4_0,esk6_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_14,plain,
! [X4,X5,X6] : intersection(X4,difference(X5,X6)) = difference(intersection(X4,X5),X6),
inference(variable_rename,[status(thm)],[difference_and_intersection]) ).
fof(c_0_15,plain,
! [X4,X5,X6] : difference(X4,intersection(X5,X6)) = union(difference(X4,X5),difference(X4,X6)),
inference(variable_rename,[status(thm)],[difference_and_intersection_and_union]) ).
fof(c_0_16,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_17,plain,
! [X2] : ~ member(X2,empty_set),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[empty_set_defn])]) ).
fof(c_0_18,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])])])])])])]) ).
cnf(c_0_19,negated_conjecture,
intersection(esk4_0,difference(esk5_0,esk6_0)) != difference(intersection(esk4_0,esk5_0),intersection(esk4_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
difference(X1,intersection(X2,X3)) = union(difference(X1,X2),difference(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_23,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_24,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
intersection(esk4_0,union(difference(esk5_0,esk4_0),difference(esk5_0,esk6_0))) != intersection(esk4_0,difference(esk5_0,esk6_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_27,plain,
intersection(X1,union(difference(X2,X3),difference(X2,X4))) = union(intersection(X1,difference(X2,X3)),intersection(X1,difference(X2,X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_20]),c_0_20]),c_0_21]) ).
cnf(c_0_28,plain,
intersection(X1,difference(X2,X3)) = intersection(X2,difference(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_22]),c_0_20]) ).
fof(c_0_29,plain,
! [X3,X4,X3,X4] :
( ( difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| difference(X3,X4) = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[difference_empty_set])])])]) ).
fof(c_0_30,plain,
! [X2] : subset(X2,X2),
inference(variable_rename,[status(thm)],[reflexivity_of_subset]) ).
cnf(c_0_31,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_33,plain,
! [X3,X4] : subset(intersection(X3,X4),X3),
inference(variable_rename,[status(thm)],[intersection_is_subset]) ).
fof(c_0_34,plain,
! [X2] : union(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[union_empty_set]) ).
fof(c_0_35,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_36,negated_conjecture,
union(intersection(esk5_0,difference(esk4_0,esk4_0)),intersection(esk5_0,difference(esk4_0,esk6_0))) != intersection(esk5_0,difference(esk4_0,esk6_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_28]),c_0_28]) ).
cnf(c_0_37,plain,
( difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,plain,
subset(intersection(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
union(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,negated_conjecture,
union(intersection(empty_set,esk5_0),intersection(esk5_0,difference(esk4_0,esk6_0))) != intersection(esk5_0,difference(esk4_0,esk6_0)),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]),c_0_22]) ).
cnf(c_0_44,plain,
intersection(empty_set,X1) = empty_set,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,plain,
union(empty_set,X1) = X1,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET635+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n021.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 : Sun Jul 10 13:28:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.22/1.41 # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.22/1.41 # Preprocessing time : 0.016 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 : 47
% 0.22/1.41 # Proof object clause steps : 22
% 0.22/1.41 # Proof object formula steps : 25
% 0.22/1.41 # Proof object conjectures : 8
% 0.22/1.41 # Proof object clause conjectures : 5
% 0.22/1.41 # Proof object formula conjectures : 3
% 0.22/1.41 # Proof object initial clauses used : 12
% 0.22/1.41 # Proof object initial formulas used : 12
% 0.22/1.41 # Proof object generating inferences : 7
% 0.22/1.41 # Proof object simplifying inferences : 16
% 0.22/1.41 # Training examples: 0 positive, 0 negative
% 0.22/1.41 # Parsed axioms : 16
% 0.22/1.41 # Removed by relevancy pruning/SinE : 0
% 0.22/1.41 # Initial clauses : 29
% 0.22/1.41 # Removed in clause preprocessing : 2
% 0.22/1.41 # Initial clauses in saturation : 27
% 0.22/1.41 # Processed clauses : 48
% 0.22/1.41 # ...of these trivial : 3
% 0.22/1.41 # ...subsumed : 2
% 0.22/1.41 # ...remaining for further processing : 43
% 0.22/1.41 # Other redundant clauses eliminated : 2
% 0.22/1.41 # Clauses deleted for lack of memory : 0
% 0.22/1.41 # Backward-subsumed : 0
% 0.22/1.41 # Backward-rewritten : 6
% 0.22/1.41 # Generated clauses : 176
% 0.22/1.41 # ...of the previous two non-trivial : 151
% 0.22/1.41 # Contextual simplify-reflections : 0
% 0.22/1.41 # Paramodulations : 172
% 0.22/1.41 # Factorizations : 2
% 0.22/1.41 # Equation resolutions : 2
% 0.22/1.41 # Current number of processed clauses : 35
% 0.22/1.41 # Positive orientable unit clauses : 11
% 0.22/1.41 # Positive unorientable unit clauses: 4
% 0.22/1.41 # Negative unit clauses : 3
% 0.22/1.41 # Non-unit-clauses : 17
% 0.22/1.41 # Current number of unprocessed clauses: 128
% 0.22/1.41 # ...number of literals in the above : 232
% 0.22/1.41 # Current number of archived formulas : 0
% 0.22/1.41 # Current number of archived clauses : 6
% 0.22/1.41 # Clause-clause subsumption calls (NU) : 47
% 0.22/1.41 # Rec. Clause-clause subsumption calls : 41
% 0.22/1.41 # Non-unit clause-clause subsumptions : 1
% 0.22/1.41 # Unit Clause-clause subsumption calls : 8
% 0.22/1.41 # Rewrite failures with RHS unbound : 0
% 0.22/1.41 # BW rewrite match attempts : 31
% 0.22/1.41 # BW rewrite match successes : 30
% 0.22/1.41 # Condensation attempts : 0
% 0.22/1.41 # Condensation successes : 0
% 0.22/1.41 # Termbank termtop insertions : 2933
% 0.22/1.41
% 0.22/1.41 # -------------------------------------------------
% 0.22/1.41 # User time : 0.016 s
% 0.22/1.41 # System time : 0.003 s
% 0.22/1.41 # Total time : 0.019 s
% 0.22/1.41 # Maximum resident set size: 2780 pages
% 0.22/23.40 eprover: CPU time limit exceeded, terminating
% 0.22/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.43 eprover: No such file or directory
% 0.22/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.43 eprover: No such file or directory
% 0.22/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.44 eprover: No such file or directory
% 0.22/23.44 eprover: CPU time limit exceeded, terminating
% 0.22/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.44 eprover: No such file or directory
% 0.22/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.45 eprover: No such file or directory
% 0.22/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.45 eprover: No such file or directory
% 0.22/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.45 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.47 eprover: No such file or directory
% 0.22/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47 eprover: No such file or directory
% 0.22/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.47 eprover: No such file or directory
% 0.22/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47 eprover: No such file or directory
% 0.22/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.48 eprover: No such file or directory
% 0.22/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.48 eprover: No such file or directory
% 0.22/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.48 eprover: No such file or directory
% 0.22/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.48 eprover: No such file or directory
% 0.22/23.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.49 eprover: No such file or directory
% 0.22/23.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.50 eprover: No such file or directory
% 0.22/23.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.50 eprover: No such file or directory
%------------------------------------------------------------------------------