TSTP Solution File: LCL145-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : LCL145-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n028.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 14:20:33 EDT 2022

% Result   : Unsatisfiable 0.38s 0.62s
% Output   : Refutation 0.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   44 (  42 unt;   0 nHn;   8 RR)
%            Number of literals    :   46 (  34 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    5 (   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   :   66 (  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(prove_wajsberg_theorem,negated_conjecture,
    not(big_V(x,y)) != big_hat(not(x),not(y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_theorem) ).

cnf(10,plain,
    not(big_V(x,y)) != not(big_V(not(not(x)),not(not(y)))),
    inference('REWRITE',[status(thm)],[prove_wajsberg_theorem,big_hat_definition,theory(equality)]) ).

cnf(11,plain,
    big_V(X,Y) = big_V(Y,X),
    inference('REWRITE',[status(thm)],[wajsberg_3,big_V_definition,theory(equality)]) ).

cnf(16,plain,
    big_V(implies(X,Y),Y) = implies(big_V(X,Y),Y),
    inference('PARAMODULATE',[status(thm)],[big_V_definition,big_V_definition,theory(equality)]) ).

cnf(18,plain,
    implies(implies(not(X),not(truth)),X) = truth,
    inference('PARAMODULATE',[status(thm)],[wajsberg_4,wajsberg_1,theory(equality)]) ).

cnf(22,plain,
    ordered(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),
    inference('HYPERRESOLVE',[status(thm)],[partial_order_definition2,wajsberg_2]) ).

cnf(24,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(25,plain,
    implies(implies(X,truth),implies(Y,implies(X,Y))) = truth,
    inference('PARAMODULATE',[status(thm)],[wajsberg_2,wajsberg_1,theory(equality)]) ).

cnf(46,plain,
    ordered(X,big_V(X,Y)),
    inference('HYPERRESOLVE',[status(thm)],[partial_order_definition2,24]) ).

cnf(47,plain,
    big_V(truth,X) = truth,
    inference('PARAMODULATE',[status(thm)],[wajsberg_1,24,theory(equality)]) ).

cnf(53,plain,
    big_V(X,big_V(X,Y)) = big_V(X,Y),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[big_V_definition,24,theory(equality)]),wajsberg_1,theory(equality)]) ).

cnf(59,plain,
    ordered(X,big_V(Y,X)),
    inference('PARAMODULATE',[status(thm)],[46,11,theory(equality)]) ).

cnf(61,plain,
    ordered(X,truth),
    inference('PARAMODULATE',[status(thm)],[59,47,theory(equality)]) ).

cnf(62,plain,
    implies(X,truth) = truth,
    inference('HYPERRESOLVE',[status(thm)],[partial_order_definition1,61]) ).

cnf(63,plain,
    implies(X,implies(Y,X)) = truth,
    inference('REWRITE',[status(thm)],[25,wajsberg_1,62,theory(equality)]) ).

cnf(65,plain,
    big_V(X,implies(Y,X)) = implies(Y,X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[big_V_definition,63,theory(equality)]),wajsberg_1,theory(equality)]) ).

cnf(73,plain,
    big_V(not(not(truth)),not(truth)) = truth,
    inference('PARAMODULATE',[status(thm)],[big_V_definition,18,theory(equality)]) ).

cnf(74,plain,
    big_V(implies(not(X),not(truth)),X) = X,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[big_V_definition,18,theory(equality)]),wajsberg_1,theory(equality)]) ).

cnf(77,plain,
    big_V(X,Y) = big_V(big_V(X,Y),X),
    inference('PARAMODULATE',[status(thm)],[11,53,theory(equality)]) ).

cnf(78,plain,
    implies(X,Y) = big_V(implies(X,Y),Y),
    inference('PARAMODULATE',[status(thm)],[11,65,theory(equality)]) ).

cnf(79,plain,
    implies(X,Y) = implies(big_V(X,Y),Y),
    inference('REWRITE',[status(thm)],[16,78,theory(equality)]) ).

cnf(80,plain,
    implies(X,Y) = implies(big_V(Y,X),Y),
    inference('PARAMODULATE',[status(thm)],[79,11,theory(equality)]) ).

cnf(92,plain,
    implies(not(truth),not(not(truth))) = not(not(truth)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[80,73,theory(equality)]),wajsberg_1,theory(equality)]) ).

cnf(98,plain,
    ordered(implies(X,Y),implies(X,big_V(Y,Z))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[22,24,theory(equality)]),wajsberg_1,theory(equality)]) ).

cnf(107,plain,
    ordered(implies(X,implies(not(Y),not(truth))),implies(X,Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[22,18,theory(equality)]),wajsberg_1,theory(equality)]) ).

cnf(115,plain,
    ordered(truth,implies(X,big_V(implies(Y,X),Z))),
    inference('PARAMODULATE',[status(thm)],[98,63,theory(equality)]) ).

cnf(163,plain,
    ordered(truth,implies(not(truth),X)),
    inference('PARAMODULATE',[status(thm)],[115,74,theory(equality)]) ).

cnf(165,plain,
    implies(not(truth),X) = truth,
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[partial_order_definition1,163]),wajsberg_1,theory(equality)]) ).

cnf(167,plain,
    truth = not(not(truth)),
    inference('REWRITE',[status(thm)],[92,165,theory(equality)]) ).

cnf(310,plain,
    ordered(truth,implies(not(not(X)),X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[107,wajsberg_4,theory(equality)]),wajsberg_1,167,theory(equality)]) ).

cnf(320,plain,
    implies(not(not(X)),X) = truth,
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[partial_order_definition1,310]),wajsberg_1,theory(equality)]) ).

cnf(328,plain,
    big_V(not(not(X)),X) = X,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[big_V_definition,320,theory(equality)]),wajsberg_1,theory(equality)]) ).

cnf(329,plain,
    implies(X,not(not(X))) = truth,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[wajsberg_4,320,theory(equality)]),wajsberg_1,theory(equality)]) ).

cnf(340,plain,
    X = big_V(X,not(not(X))),
    inference('PARAMODULATE',[status(thm)],[77,328,theory(equality)]) ).

cnf(351,plain,
    X = not(not(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[big_V_definition,329,theory(equality)]),wajsberg_1,340,theory(equality)]) ).

cnf(352,plain,
    $false,
    inference('REWRITE',[status(thm)],[10,351,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL145-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run-snark %s %d
% 0.13/0.33  % Computer : n028.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jul  3 06:41:48 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.45  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46  * 
% 0.19/0.46  * 
% 0.19/0.46  #<PACKAGE "SNARK-USER">
% 0.19/0.46  * 
% 0.19/0.46  SNARK-TPTP-OPTIONS
% 0.19/0.46  * 
% 0.19/0.46  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.46   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.46   (USE-FACTORING :POS)
% 0.19/0.46   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.46   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.46   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.46   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.46   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.46   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.46   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.46   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.46   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.46   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.46  * 
% 0.19/0.46  "."
% 0.19/0.46  * 
% 0.19/0.46  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-03T06:41:48
% 0.19/0.46  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n028.cluster.edu at 2022-07-03T06:41:48
% 0.19/0.48  
% 0.38/0.62  ; Recognized left identity assertion (= (|implies| |truth| ?X) ?X).
% 0.38/0.62  
% 0.38/0.62  #||
% 0.38/0.62  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.38/0.62  % SZS output start Refutation
% See solution above
% 0.38/0.62  ||#
% 0.38/0.62  
% 0.38/0.62  ; Summary of computation:
% 0.38/0.62  ;      2264 formulas have been input or derived (from 92 formulas).
% 0.38/0.62  ;       352 (16%) were retained.  Of these,
% 0.38/0.62  ;          118 (34%) were simplified or subsumed later,
% 0.38/0.62  ;          234 (66%) are still being kept.
% 0.38/0.62  ; 
% 0.38/0.62  ; Run time in seconds excluding printing time:
% 0.38/0.62  ;     0.002   1%   Read assertion file          (1 call)
% 0.38/0.62  ;     0.000   0%   Assert                       (9 calls)
% 0.38/0.62  ;     0.035  23%   Process new row              (1,969 calls)
% 0.38/0.62  ;     0.009   6%   Resolution                   (182 calls)
% 0.38/0.62  ;     0.025  16%   Paramodulation               (91 calls)
% 0.38/0.62  ;     0.000   0%   Condensing                   (45 calls)
% 0.38/0.62  ;     0.000   0%   Forward subsumption          (45 calls)
% 0.38/0.62  ;     0.000   0%   Backward subsumption         (12 calls)
% 0.38/0.62  ;     0.000   0%   Clause clause subsumption    (49 calls)
% 0.38/0.62  ;     0.031  20%   Forward simplification       (1,960 calls)
% 0.38/0.62  ;     0.007   5%   Backward simplification      (351 calls)
% 0.38/0.62  ;     0.002   1%   Ordering                     (2,118 calls)
% 0.38/0.62  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.38/0.62  ;     0.000   0%   Purity testing               (1 call)
% 0.38/0.62  ;     0.043  28%   Other
% 0.38/0.62  ;     0.154        Total
% 0.38/0.62  ;     0.158        Real time
% 0.38/0.62  ; 
% 0.38/0.62  ; Term-hash-array has 745 terms in all.
% 0.38/0.62  ; Feature-vector-row-index has 9 entries (10 at peak, 12 added, 3 deleted).
% 0.38/0.62  ; Feature-vector-row-index has 32 nodes (39 at peak, 53 added, 21 deleted).
% 0.38/0.62  ;  Retrieved 59 possibly forward subsuming rows in 45 calls.
% 0.38/0.62  ;  Retrieved 2 possibly backward subsumed rows in 12 calls.
% 0.38/0.62  ; Path-index has 540 entries (607 at peak, 766 added, 226 deleted).
% 0.38/0.62  ; Path-index has 1,330 nodes (1,400 at peak, 1,618 added, 288 deleted).
% 0.38/0.62  ; Trie-index has 540 entries (607 at peak, 766 added, 226 deleted).
% 0.38/0.62  ; Trie-index has 1,857 nodes (2,057 at peak, 2,775 added, 918 deleted).
% 0.38/0.62  ; Retrieved 8,475 generalization terms in 6,468 calls.
% 0.38/0.62  ; Retrieved 756 instance terms in 339 calls.
% 0.38/0.62  ; Retrieved 3,433 unifiable terms in 672 calls.
% 0.38/0.62  ; 
% 0.38/0.62  ; The agenda of backward simplifiable rows to process has 2 entries:
% 0.38/0.62  ;     2 with value 0
% 0.38/0.62  ; The agenda of rows to process has 20 entries:
% 0.38/0.62  ;     7 with value 22              1 with value 24               4 with value 25
% 0.38/0.62  ;     8 with value 23
% 0.38/0.62  ; The agenda of rows to give has 164 entries:
% 0.38/0.62  ;     1 with value (4 14)         46 with value (4 20)           3 with value (4 24)
% 0.38/0.62  ;    17 with value (4 17)         30 with value (4 21)           3 with value (4 25)
% 0.38/0.62  ;    17 with value (4 18)         10 with value (4 22)           2 with value (4 27)
% 0.38/0.62  ;    14 with value (4 19)         21 with value (4 23)
% 0.38/0.62  Evaluation took:
% 0.38/0.62    0.158 seconds of real time
% 0.38/0.62    0.134021 seconds of user run time
% 0.38/0.62    0.023916 seconds of system run time
% 0.38/0.62    0 calls to %EVAL
% 0.38/0.62    0 page faults and
% 0.38/0.62    10,809,896 bytes consed.
% 0.38/0.62  :PROOF-FOUND
% 0.38/0.62  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-03T06:41:48
% 0.38/0.62  :PROOF-FOUND
% 0.38/0.62  * 
%------------------------------------------------------------------------------