TSTP Solution File: SET002-1 by SNARK---20120808r022

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%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : SET002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n006.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 05:05:30 EDT 2022

% Result   : Unsatisfiable 0.39s 0.60s
% Output   : Refutation 0.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   22 (   6 unt;  11 nHn;  19 RR)
%            Number of literals    :   45 (   0 equ;  10 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   21 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(subsets_axiom1,axiom,
    ( subset(X,Y)
    | member(member_of_1_not_of_2(X,Y),X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',subsets_axiom1) ).

cnf(subsets_axiom2,axiom,
    ( ~ member(member_of_1_not_of_2(X,Y),Y)
    | subset(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',subsets_axiom2) ).

cnf(set_equal_sets_are_subsets1,axiom,
    ( ~ equal_sets(X,Y)
    | subset(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',set_equal_sets_are_subsets1) ).

cnf(set_equal_sets_are_subsets2,axiom,
    ( ~ equal_sets(X,Y)
    | subset(Y,X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',set_equal_sets_are_subsets2) ).

cnf(subsets_are_set_equal_sets,axiom,
    ( ~ subset(X,Y)
    | ~ subset(Y,X)
    | equal_sets(Y,X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',subsets_are_set_equal_sets) ).

cnf(member_of_union_is_member_of_one_set,axiom,
    ( ~ union(X,Y,Z)
    | ~ member(U,Z)
    | member(U,X)
    | member(U,Y) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',member_of_union_is_member_of_one_set) ).

cnf(member_of_set1_is_member_of_union,axiom,
    ( ~ union(X,Y,Z)
    | ~ member(U,X)
    | member(U,Z) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',member_of_set1_is_member_of_union) ).

cnf(a_union_a_is_aUa,hypothesis,
    union(a,a,aUa),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_union_a_is_aUa) ).

cnf(prove_a_equals_aUa,negated_conjecture,
    ~ equal_sets(aUa,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_equals_aUa) ).

cnf(15,plain,
    ( member(member_of_1_not_of_2(X,Y),X)
    | member(member_of_1_not_of_2(Y,X),Y)
    | equal_sets(Y,X) ),
    inference('HYPERRESOLVE',[status(thm)],[subsets_are_set_equal_sets,subsets_axiom1,subsets_axiom1]) ).

cnf(22,plain,
    ( member(member_of_1_not_of_2(X,aUa),X)
    | equal_sets(X,aUa)
    | member(member_of_1_not_of_2(aUa,X),a) ),
    inference('HYPERRESOLVE',[status(thm)],[member_of_union_is_member_of_one_set,15,a_union_a_is_aUa]) ).

cnf(44,plain,
    ( member(member_of_1_not_of_2(a,aUa),a)
    | equal_sets(a,aUa)
    | subset(aUa,a) ),
    inference('HYPERRESOLVE',[status(thm)],[subsets_axiom2,22]) ).

cnf(62,plain,
    ( member(member_of_1_not_of_2(a,aUa),a)
    | equal_sets(a,aUa) ),
    inference('HYPERRESOLVE',[status(thm)],[subsets_are_set_equal_sets,44,subsets_axiom1]) ).

cnf(63,plain,
    ( equal_sets(a,aUa)
    | member(member_of_1_not_of_2(a,aUa),aUa) ),
    inference('HYPERRESOLVE',[status(thm)],[member_of_set1_is_member_of_union,62,a_union_a_is_aUa]) ).

cnf(72,plain,
    ( equal_sets(a,aUa)
    | subset(a,aUa) ),
    inference('HYPERRESOLVE',[status(thm)],[subsets_axiom2,63]) ).

cnf(81,plain,
    ( equal_sets(a,aUa)
    | member(member_of_1_not_of_2(aUa,a),aUa) ),
    inference('HYPERRESOLVE',[status(thm)],[subsets_are_set_equal_sets,72,subsets_axiom1]) ).

cnf(82,plain,
    ( equal_sets(a,aUa)
    | member(member_of_1_not_of_2(aUa,a),a) ),
    inference('HYPERRESOLVE',[status(thm)],[member_of_union_is_member_of_one_set,81,a_union_a_is_aUa]) ).

cnf(91,plain,
    ( equal_sets(a,aUa)
    | subset(aUa,a) ),
    inference('HYPERRESOLVE',[status(thm)],[subsets_axiom2,82]) ).

cnf(100,plain,
    equal_sets(a,aUa),
    inference('HYPERRESOLVE',[status(thm)],[subsets_are_set_equal_sets,91,72]) ).

cnf(101,plain,
    subset(aUa,a),
    inference('HYPERRESOLVE',[status(thm)],[set_equal_sets_are_subsets2,100]) ).

cnf(102,plain,
    subset(a,aUa),
    inference('HYPERRESOLVE',[status(thm)],[set_equal_sets_are_subsets1,100]) ).

cnf(103,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[subsets_are_set_equal_sets,101,prove_a_equals_aUa]),102]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : SET002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.14  % Command  : run-snark %s %d
% 0.14/0.36  % Computer : n006.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Mon Jul 11 10:03:35 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.22/0.49  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.50  * 
% 0.22/0.50  * 
% 0.22/0.51  #<PACKAGE "SNARK-USER">
% 0.22/0.51  * 
% 0.22/0.51  SNARK-TPTP-OPTIONS
% 0.22/0.51  * 
% 0.22/0.51  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.22/0.51   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.22/0.51   (USE-FACTORING :POS)
% 0.22/0.51   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.22/0.51   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.22/0.51   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.22/0.51   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.22/0.51   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.22/0.51   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.22/0.51   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.22/0.51   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.22/0.51   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.22/0.51   (DECLARE-TPTP-SYMBOLS2))
% 0.22/0.51  * 
% 0.22/0.51  "."
% 0.22/0.51  * 
% 0.22/0.51  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-11T10:03:35
% 0.22/0.51  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n006.cluster.edu at 2022-07-11T10:03:35
% 0.39/0.60  
% 0.39/0.60  
% 0.39/0.60  #||
% 0.39/0.60  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.60  % SZS output start Refutation
% See solution above
% 0.39/0.60  ||#
% 0.39/0.60  
% 0.39/0.60  ; Summary of computation:
% 0.39/0.60  ;       229 formulas have been input or derived (from 33 formulas).
% 0.39/0.60  ;       103 (45%) were retained.  Of these,
% 0.39/0.60  ;           42 (41%) were simplified or subsumed later,
% 0.39/0.60  ;           61 (59%) are still being kept.
% 0.39/0.60  ; 
% 0.39/0.60  ; Run time in seconds excluding printing time:
% 0.39/0.60  ;     0.004   5%   Read assertion file          (1 call)
% 0.39/0.60  ;     0.001   1%   Assert                       (14 calls)
% 0.39/0.60  ;     0.014  16%   Process new row              (192 calls)
% 0.39/0.60  ;     0.009  10%   Resolution                   (64 calls)
% 0.39/0.60  ;     0.000   0%   Paramodulation               (32 calls)
% 0.39/0.60  ;     0.001   1%   Factoring                    (16 calls)
% 0.39/0.60  ;     0.003   3%   Condensing                   (163 calls)
% 0.39/0.60  ;     0.018  21%   Forward subsumption          (163 calls)
% 0.39/0.60  ;     0.002   2%   Backward subsumption         (95 calls)
% 0.39/0.60  ;     0.006   7%   Clause clause subsumption    (1,144 calls)
% 0.39/0.60  ;     0.002   2%   Forward simplification       (177 calls)
% 0.39/0.60  ;     0.002   2%   Backward simplification      (103 calls)
% 0.39/0.60  ;     0.002   2%   Ordering                     (819 calls)
% 0.39/0.60  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.39/0.60  ;     0.000   0%   Purity testing               (1 call)
% 0.39/0.60  ;     0.022  26%   Other
% 0.39/0.60  ;     0.086        Total
% 0.39/0.60  ;     0.089        Real time
% 0.39/0.60  ; 
% 0.39/0.60  ; Term-hash-array has 188 terms in all.
% 0.39/0.60  ; Feature-vector-row-index has 53 entries (91 at peak, 95 added, 42 deleted).
% 0.39/0.60  ; Feature-vector-row-index has 144 nodes (263 at peak, 287 added, 143 deleted).
% 0.39/0.60  ;  Retrieved 1,357 possibly forward subsuming rows in 163 calls.
% 0.39/0.60  ;  Retrieved 161 possibly backward subsumed rows in 95 calls.
% 0.39/0.60  ; Path-index has 128 entries (188 at peak, 198 added, 70 deleted).
% 0.39/0.60  ; Path-index has 76 nodes (82 at peak, 88 added, 12 deleted).
% 0.39/0.60  ; Trie-index has 128 entries (188 at peak, 198 added, 70 deleted).
% 0.39/0.60  ; Trie-index has 89 nodes (124 at peak, 135 added, 46 deleted).
% 0.39/0.60  ; Retrieved 127 generalization terms in 170 calls.
% 0.39/0.60  ; Retrieved 17 instance terms in 7 calls.
% 0.39/0.60  ; Retrieved 1,393 unifiable terms in 230 calls.
% 0.39/0.60  ; 
% 0.39/0.60  ; The agenda of rows to process has 5 entries:
% 0.39/0.60  ;     3 with value 23              2 with value 30
% 0.39/0.60  ; The agenda of rows to give has 36 entries:
% 0.39/0.60  ;     1 with value (4 15)          8 with value (4 36)           4 with value (4 45)
% 0.39/0.60  ;     3 with value (4 20)          8 with value (4 37)           2 with value (4 51)
% 0.39/0.60  ;     2 with value (4 27)          4 with value (4 44)           2 with value (4 52)
% 0.39/0.60  ;     2 with value (4 28)
% 0.39/0.60  Evaluation took:
% 0.39/0.60    0.089 seconds of real time
% 0.39/0.60    0.071789 seconds of user run time
% 0.39/0.60    0.017816 seconds of system run time
% 0.39/0.60    0 calls to %EVAL
% 0.39/0.60    0 page faults and
% 0.39/0.60    5,892,240 bytes consed.
% 0.39/0.60  :PROOF-FOUND
% 0.39/0.60  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-11T10:03:36
% 0.39/0.60  :PROOF-FOUND
% 0.39/0.60  * 
%------------------------------------------------------------------------------