TSTP Solution File: LCL109-5 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : LCL109-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n012.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 : Sun Jul 17 14:20:16 EDT 2022

% Result   : Unsatisfiable 0.18s 0.55s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   32 (  29 unt;   0 nHn;   6 RR)
%            Number of literals    :   35 (  25 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   47 (  12 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
    implies(truth,X) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).

cnf(wajsberg_2,axiom,
    implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).

cnf(wajsberg_3,axiom,
    implies(implies(X,Y),Y) = implies(implies(Y,X),X),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).

cnf(wajsberg_4,axiom,
    implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
    file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_4) ).

cnf(big_V_definition,axiom,
    big_V(X,Y) = implies(implies(X,Y),Y),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL001-1.ax',big_V_definition) ).

cnf(big_hat_definition,axiom,
    big_hat(X,Y) = not(big_V(not(X),not(Y))),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL001-1.ax',big_hat_definition) ).

cnf(partial_order_definition1,axiom,
    ( ~ ordered(X,Y)
    | implies(X,Y) = truth ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL001-1.ax',partial_order_definition1) ).

cnf(partial_order_definition2,axiom,
    ( implies(X,Y) != truth
    | ordered(X,Y) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL001-1.ax',partial_order_definition2) ).

cnf(lemma_1,axiom,
    ( ~ ordered(X,Y)
    | ordered(implies(X,Z),implies(Y,Z)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1) ).

cnf(lemma_6,axiom,
    implies(big_V(X,Y),Z) = big_hat(implies(X,Z),implies(Y,Z)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_6) ).

cnf(17,plain,
    implies(big_V(X,Y),Z) = not(big_V(not(implies(X,Z)),not(implies(Y,Z)))),
    inference('REWRITE',[status(thm)],[lemma_6,big_hat_definition,theory(equality)]) ).

cnf(prove_mv_4,negated_conjecture,
    big_V(implies(x,y),implies(y,x)) != truth,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_mv_4) ).

cnf(21,plain,
    big_V(X,Y) = big_V(Y,X),
    inference('REWRITE',[status(thm)],[wajsberg_3,big_V_definition,theory(equality)]) ).

cnf(22,plain,
    ordered(truth,truth),
    inference('HYPERRESOLVE',[status(thm)],[partial_order_definition2,wajsberg_1]) ).

cnf(24,plain,
    big_V(truth,X) = implies(X,X),
    inference('PARAMODULATE',[status(thm)],[big_V_definition,wajsberg_1,theory(equality)]) ).

cnf(38,plain,
    implies(X,big_V(X,Y)) = truth,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[wajsberg_2,wajsberg_1,theory(equality)]),big_V_definition,wajsberg_1,theory(equality)]) ).

cnf(86,plain,
    ordered(X,X),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[lemma_1,22]),wajsberg_1,theory(equality)]) ).

cnf(87,plain,
    big_V(truth,X) = truth,
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[partial_order_definition1,86]),24,theory(equality)]) ).

cnf(89,plain,
    truth = implies(X,X),
    inference('REWRITE',[status(thm)],[24,87,theory(equality)]) ).

cnf(92,plain,
    big_V(X,X) = X,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[big_V_definition,89,theory(equality)]),wajsberg_1,theory(equality)]) ).

cnf(95,plain,
    truth = not(big_V(not(truth),not(implies(X,big_V(Y,X))))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[17,89,theory(equality)]),38,theory(equality)]) ).

cnf(100,plain,
    truth = big_V(X,truth),
    inference('PARAMODULATE',[status(thm)],[21,87,theory(equality)]) ).

cnf(105,plain,
    implies(X,big_V(Y,X)) = truth,
    inference('PARAMODULATE',[status(thm)],[38,21,theory(equality)]) ).

cnf(106,plain,
    truth = not(not(truth)),
    inference('REWRITE',[status(thm)],[95,92,105,theory(equality)]) ).

cnf(115,plain,
    implies(implies(not(X),truth),implies(not(truth),X)) = truth,
    inference('PARAMODULATE',[status(thm)],[wajsberg_4,106,theory(equality)]) ).

cnf(123,plain,
    implies(X,truth) = truth,
    inference('PARAMODULATE',[status(thm)],[38,100,theory(equality)]) ).

cnf(124,plain,
    implies(not(truth),X) = truth,
    inference('REWRITE',[status(thm)],[115,wajsberg_1,123,theory(equality)]) ).

cnf(153,plain,
    ordered(not(truth),X),
    inference('HYPERRESOLVE',[status(thm)],[partial_order_definition2,124]) ).

cnf(158,plain,
    ordered(truth,implies(X,Y)),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[lemma_1,153]),124,theory(equality)]) ).

cnf(166,plain,
    ordered(truth,X),
    inference('PARAMODULATE',[status(thm)],[158,wajsberg_1,theory(equality)]) ).

cnf(167,plain,
    X = truth,
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[partial_order_definition1,166]),wajsberg_1,theory(equality)]) ).

cnf(168,plain,
    $false,
    inference('REWRITE',[status(thm)],[prove_mv_4,167,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : LCL109-5 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : run-snark %s %d
% 0.12/0.33  % Computer : n012.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 : Sat Jul  2 09:47:17 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.44  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45  * 
% 0.18/0.45  * 
% 0.18/0.46  #<PACKAGE "SNARK-USER">
% 0.18/0.46  * 
% 0.18/0.46  SNARK-TPTP-OPTIONS
% 0.18/0.46  * 
% 0.18/0.46  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.46   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.46   (USE-FACTORING :POS)
% 0.18/0.46   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.46   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.46   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.46   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.46   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.46   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.46   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.46   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.46   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.46   (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.46  * 
% 0.18/0.46  "."
% 0.18/0.46  * 
% 0.18/0.46  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-02T09:47:17
% 0.18/0.46  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n012.cluster.edu at 2022-07-02T09:47:17
% 0.18/0.47  
% 0.18/0.55  WARNING: Cannot use equality or equivalence (= ?X truth) as rewrite.
% 0.18/0.55  ; Recognized left identity assertion (= (|implies| |truth| ?X) ?X).
% 0.18/0.55  
% 0.18/0.55  #||
% 0.18/0.55  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.55  % SZS output start Refutation
% See solution above
% 0.18/0.55  ||#
% 0.18/0.55  
% 0.18/0.55  ; Summary of computation:
% 0.18/0.55  ;       481 formulas have been input or derived (from 41 formulas).
% 0.18/0.55  ;       168 (35%) were retained.  Of these,
% 0.18/0.55  ;           93 (55%) were simplified or subsumed later,
% 0.18/0.55  ;           75 (45%) are still being kept.
% 0.18/0.55  ; 
% 0.18/0.55  ; Run time in seconds excluding printing time:
% 0.18/0.55  ;     0.004   4%   Read assertion file          (1 call)
% 0.18/0.55  ;     0.000   0%   Assert                       (17 calls)
% 0.18/0.55  ;     0.023  26%   Process new row              (398 calls)
% 0.18/0.55  ;     0.004   4%   Resolution                   (80 calls)
% 0.18/0.55  ;     0.006   7%   Paramodulation               (40 calls)
% 0.18/0.55  ;     0.000   0%   Condensing                   (18 calls)
% 0.18/0.55  ;     0.000   0%   Forward subsumption          (18 calls)
% 0.18/0.55  ;     0.000   0%   Backward subsumption         (17 calls)
% 0.18/0.55  ;     0.001   1%   Clause clause subsumption    (12 calls)
% 0.18/0.55  ;     0.014  16%   Forward simplification       (380 calls)
% 0.18/0.55  ;     0.010  11%   Backward simplification      (164 calls)
% 0.18/0.55  ;     0.003   3%   Ordering                     (517 calls)
% 0.18/0.55  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.18/0.55  ;     0.000   0%   Purity testing               (1 call)
% 0.18/0.55  ;     0.025  28%   Other
% 0.18/0.55  ;     0.090        Total
% 0.18/0.55  ;     0.094        Real time
% 0.18/0.55  ; 
% 0.18/0.55  ; Term-hash-array has 572 terms in all.
% 0.18/0.55  ; Feature-vector-row-index has 6 entries (17 at peak, 17 added, 11 deleted).
% 0.18/0.55  ; Feature-vector-row-index has 36 nodes (85 at peak, 85 added, 49 deleted).
% 0.18/0.55  ;  Retrieved 9 possibly forward subsuming rows in 18 calls.
% 0.18/0.55  ;  Retrieved 3 possibly backward subsumed rows in 17 calls.
% 0.18/0.55  ; Path-index has 254 entries (458 at peak, 588 added, 334 deleted).
% 0.18/0.55  ; Path-index has 1,509 nodes (1,867 at peak, 2,080 added, 571 deleted).
% 0.18/0.55  ; Trie-index has 254 entries (458 at peak, 588 added, 334 deleted).
% 0.18/0.55  ; Trie-index has 934 nodes (2,313 at peak, 3,007 added, 2,073 deleted).
% 0.18/0.55  ; Retrieved 1,470 generalization terms in 2,131 calls.
% 0.18/0.55  ; Retrieved 674 instance terms in 149 calls.
% 0.18/0.55  ; Retrieved 1,309 unifiable terms in 273 calls.
% 0.18/0.55  ; 
% 0.18/0.55  ; The agenda of backward simplifiable rows to process has 3 entries:
% 0.18/0.55  ;     3 with value 0
% 0.18/0.55  ; The agenda of rows to process has 7 entries:
% 0.18/0.55  ;     3 with value 14              4 with value 16
% 0.18/0.55  ; The agenda of rows to give has 54 entries:
% 0.18/0.55  ;     1 with value (4 11)          1 with value (4 19)           1 with value (4 27)
% 0.18/0.55  ;     7 with value (4 13)          3 with value (4 20)           1 with value (4 30)
% 0.18/0.55  ;     3 with value (4 14)          2 with value (4 22)           2 with value (4 34)
% 0.18/0.55  ;     5 with value (4 15)          1 with value (4 23)           1 with value (4 35)
% 0.18/0.55  ;     4 with value (4 16)          2 with value (4 24)           1 with value (4 47)
% 0.18/0.55  ;     2 with value (4 17)          7 with value (4 25)           1 with value (4 48)
% 0.18/0.55  ;     7 with value (4 18)          2 with value (4 26)
% 0.18/0.55  Evaluation took:
% 0.18/0.55    0.094 seconds of real time
% 0.18/0.55    0.084617 seconds of user run time
% 0.18/0.55    0.009848 seconds of system run time
% 0.18/0.55    0 calls to %EVAL
% 0.18/0.55    0 page faults and
% 0.18/0.55    6,559,296 bytes consed.
% 0.18/0.55  :PROOF-FOUND
% 0.18/0.55  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-02T09:47:17
% 0.18/0.55  :PROOF-FOUND
% 0.18/0.55  * 
%------------------------------------------------------------------------------