TSTP Solution File: LCL158-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : LCL158-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n008.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 14:20:38 EDT 2022

% Result   : Unsatisfiable 0.53s 0.73s
% Output   : Refutation 0.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   35 (  35 unt;   0 nHn;   8 RR)
%            Number of literals    :   35 (  34 equ;   5 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-2 aty)
%            Number of variables   :   42 (   3 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
    implies(truth,X) = X,
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).

cnf(wajsberg_3,axiom,
    implies(implies(X,Y),Y) = implies(implies(Y,X),X),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).

cnf(wajsberg_4,axiom,
    implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_4) ).

cnf(or_definition,axiom,
    or(X,Y) = implies(not(X),Y),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',or_definition) ).

cnf(and_definition,axiom,
    and(X,Y) = not(or(not(X),not(Y))),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',and_definition) ).

cnf(8,plain,
    and(X,Y) = not(implies(not(not(X)),not(Y))),
    inference('REWRITE',[status(thm)],[and_definition,or_definition,theory(equality)]) ).

cnf(xor_definition,axiom,
    xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',xor_definition) ).

cnf(10,plain,
    xor(X,Y) = implies(not(and(X,not(Y))),and(not(X),Y)),
    inference('REWRITE',[status(thm)],[xor_definition,or_definition,theory(equality)]) ).

cnf(and_star_definition,axiom,
    and_star(X,Y) = not(or(not(X),not(Y))),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',and_star_definition) ).

cnf(12,plain,
    and_star(X,Y) = and(X,Y),
    inference('REWRITE',[status(thm)],[and_star_definition,8,or_definition,theory(equality)]) ).

cnf(false_definition,axiom,
    not(truth) = falsehood,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',false_definition) ).

cnf(prove_alternative_wajsberg_axiom,negated_conjecture,
    and_star(xor(truth,x),x) != falsehood,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).

cnf(16,plain,
    and(implies(not(and(truth,not(x))),and(falsehood,x)),x) != falsehood,
    inference('REWRITE',[status(thm)],[prove_alternative_wajsberg_axiom,12,false_definition,10,theory(equality)]) ).

cnf(17,plain,
    implies(not(X),Y) = implies(not(Y),X),
    inference('PARAMODULATE',[status(thm)],[or_definition,or_definition,theory(equality)]) ).

cnf(18,plain,
    and(implies(not(and(falsehood,x)),and(truth,not(x))),x) != falsehood,
    inference('REWRITE',[status(thm)],[16,17,theory(equality)]) ).

cnf(100,plain,
    implies(X,X) = implies(implies(X,truth),truth),
    inference('PARAMODULATE',[status(thm)],[wajsberg_3,wajsberg_1,theory(equality)]) ).

cnf(102,plain,
    implies(implies(not(X),falsehood),X) = truth,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[wajsberg_4,wajsberg_1,theory(equality)]),false_definition,theory(equality)]) ).

cnf(106,plain,
    and(truth,X) = not(implies(not(falsehood),not(X))),
    inference('PARAMODULATE',[status(thm)],[8,false_definition,theory(equality)]) ).

cnf(112,plain,
    implies(X,implies(implies(X,Y),Y)) = truth,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[wajsberg_2,wajsberg_1,theory(equality)]),wajsberg_1,theory(equality)]) ).

cnf(126,plain,
    implies(falsehood,X) = implies(not(X),truth),
    inference('PARAMODULATE',[status(thm)],[17,false_definition,theory(equality)]) ).

cnf(135,plain,
    implies(not(X),not(X)) = implies(implies(falsehood,X),truth),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[100,17,theory(equality)]),false_definition,theory(equality)]) ).

cnf(141,plain,
    implies(implies(not(falsehood),X),X) = truth,
    inference('PARAMODULATE',[status(thm)],[102,17,theory(equality)]) ).

cnf(161,plain,
    truth = implies(X,X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[wajsberg_1,112,theory(equality)]),wajsberg_1,theory(equality)]) ).

cnf(162,plain,
    truth = implies(implies(falsehood,X),truth),
    inference('REWRITE',[status(thm)],[135,161,theory(equality)]) ).

cnf(168,plain,
    implies(falsehood,X) = truth,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[112,126,theory(equality)]),126,162,theory(equality)]) ).

cnf(201,plain,
    not(falsehood) = truth,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[141,161,theory(equality)]),wajsberg_1,theory(equality)]) ).

cnf(202,plain,
    and(truth,X) = not(not(X)),
    inference('REWRITE',[status(thm)],[106,wajsberg_1,201,theory(equality)]) ).

cnf(203,plain,
    and(truth,and(X,Y)) = and(not(not(X)),Y),
    inference('EMBED',[status(thm)],[202]) ).

cnf(204,plain,
    and(implies(not(not(not(not(x)))),and(falsehood,x)),x) != falsehood,
    inference('REWRITE',[status(thm)],[18,17,202,theory(equality)]) ).

cnf(205,plain,
    X = implies(not(X),falsehood),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[17,201,theory(equality)]),wajsberg_1,theory(equality)]) ).

cnf(206,plain,
    and(falsehood,X) = falsehood,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,201,theory(equality)]),168,false_definition,theory(equality)]) ).

cnf(208,plain,
    and(not(not(not(x))),x) != falsehood,
    inference('REWRITE',[status(thm)],[204,205,206,theory(equality)]) ).

cnf(212,plain,
    and(not(not(X)),Y) = not(not(and(X,Y))),
    inference('PARAMODULATE',[status(thm)],[202,203,theory(equality)]) ).

cnf(214,plain,
    $false,
    inference('REWRITE',[status(thm)],[208,false_definition,201,212,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL158-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run-snark %s %d
% 0.12/0.34  % Computer : n008.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sat Jul  2 19:42:08 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.45  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46  * 
% 0.19/0.46  * 
% 0.19/0.47  #<PACKAGE "SNARK-USER">
% 0.19/0.47  * 
% 0.19/0.47  SNARK-TPTP-OPTIONS
% 0.19/0.47  * 
% 0.19/0.47  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.47   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.47   (USE-FACTORING :POS)
% 0.19/0.47   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.47   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.47   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.47   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.47   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.47   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.47   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.47   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.47   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47  * 
% 0.19/0.47  "."
% 0.19/0.47  * 
% 0.19/0.47  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-02T19:42:08
% 0.19/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n008.cluster.edu at 2022-07-02T19:42:08
% 0.19/0.49  
% 0.19/0.49  ; Recognized left identity assertion (= (|implies| |truth| ?X) ?X).
% 0.19/0.49  ; Recognized associativity assertion (= (|or| (|or| ?X ?Y) ?Z) (|or| ?X (|or| ?Y ?Z))).
% 0.19/0.49  ; Recognized commutativity assertion (= (|or| ?X ?Y) (|or| ?Y ?X)).
% 0.19/0.49  ; Recognized associativity assertion (= (|and| (|and| ?X ?Y) ?Z) (|and| ?X (|and| ?Y ?Z))).
% 0.19/0.49  ; Recognized commutativity assertion (= (|and| ?X ?Y) (|and| ?Y ?X)).
% 0.19/0.49  ; Recognized commutativity assertion (= (|xor| ?X ?Y) (|xor| ?Y ?X)).
% 0.19/0.49  ; Recognized associativity assertion (= (|and_star| (|and_star| ?X ?Y) ?Z) (|and_star| ?X (|and_star| ?Y ?Z))).
% 0.19/0.49  ; Recognized commutativity assertion (= (|and_star| ?X ?Y) (|and_star| ?Y ?X)).
% 0.19/0.49  ; Declaring or to be commutative.
% 0.19/0.49  ; Declaring or to be associative-commutative.
% 0.19/0.49  ; Declaring and to be commutative.
% 0.19/0.49  ; Declaring and to be associative-commutative.
% 0.19/0.49  ; Declaring xor to be commutative.
% 0.19/0.49  ; Declaring and_star to be commutative.
% 0.53/0.73  ; Declaring and_star to be associative-commutative.
% 0.53/0.73  
% 0.53/0.73  #||
% 0.53/0.73  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.53/0.73  % SZS output start Refutation
% See solution above
% 0.53/0.74  ||#
% 0.53/0.74  
% 0.53/0.74  ; Summary of computation:
% 0.53/0.74  ;       687 formulas have been input or derived (from 34 formulas).
% 0.53/0.74  ;       214 (31%) were retained.  Of these,
% 0.53/0.74  ;           71 (33%) were simplified or subsumed later,
% 0.53/0.74  ;          143 (67%) are still being kept.
% 0.53/0.74  ; 
% 0.53/0.74  ; Run time in seconds excluding printing time:
% 0.53/0.74  ;     0.004   2%   Read assertion file          (1 call)
% 0.53/0.74  ;     0.001   0%   Assert                       (17 calls)
% 0.53/0.74  ;     0.040  15%   Process new row              (630 calls)
% 0.53/0.74  ;     0.002   1%   Resolution                   (66 calls)
% 0.53/0.74  ;     0.015   6%   Paramodulation               (33 calls)
% 0.53/0.74  ;     0.000   0%   Embedding                    (15 calls)
% 0.53/0.74  ;     0.053  20%   Forward simplification       (603 calls)
% 0.53/0.74  ;     0.009   3%   Backward simplification      (199 calls)
% 0.53/0.74  ;     0.117  45%   Ordering                     (14,176 calls)
% 0.53/0.74  ;     0.000   0%   Ordering ac                  (76 calls)
% 0.53/0.74  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.53/0.74  ;     0.000   0%   Purity testing               (1 call)
% 0.53/0.74  ;     0.021   8%   Other
% 0.53/0.74  ;     0.262        Total
% 0.53/0.74  ;     0.265        Real time
% 0.53/0.74  ; 
% 0.53/0.74  ; Term-hash-array has 801 terms in all.
% 0.53/0.74  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.53/0.74  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.53/0.74  ; Path-index has 606 entries (676 at peak, 826 added, 220 deleted).
% 0.53/0.74  ; Path-index has 618 nodes (688 at peak, 799 added, 181 deleted).
% 0.53/0.74  ; Trie-index has 606 entries (676 at peak, 826 added, 220 deleted).
% 0.53/0.74  ; Trie-index has 1,459 nodes (1,834 at peak, 2,051 added, 592 deleted).
% 0.53/0.74  ; Retrieved 10,148 generalization terms in 5,617 calls.
% 0.53/0.74  ; Retrieved 1,811 instance terms in 341 calls.
% 0.53/0.74  ; Retrieved 2,272 unifiable terms in 196 calls.
% 0.53/0.74  ; 
% 0.53/0.74  ; The agenda of rows to process has 21 entries:
% 0.53/0.74  ;     1 with value 17              5 with value 22               3 with value 25
% 0.53/0.74  ;     3 with value 18              2 with value 23               2 with value 27
% 0.53/0.74  ;     1 with value 19              1 with value 24               2 with value 29
% 0.53/0.74  ;     1 with value 20
% 0.53/0.74  ; The agenda of rows to give has 120 entries:
% 0.53/0.74  ;     2 with value (4 11)         11 with value (4 21)          11 with value (4 36)
% 0.53/0.74  ;     1 with value (4 13)          4 with value (4 22)           6 with value (4 37)
% 0.53/0.74  ;     2 with value (4 14)          7 with value (4 23)           6 with value (4 42)
% 0.53/0.74  ;     1 with value (4 15)          2 with value (4 24)           7 with value (4 43)
% 0.53/0.74  ;     2 with value (4 16)          1 with value (4 27)           3 with value (4 44)
% 0.53/0.74  ;     5 with value (4 17)         10 with value (4 28)           2 with value (4 49)
% 0.53/0.74  ;     2 with value (4 18)         15 with value (4 29)           3 with value (4 50)
% 0.53/0.74  ;     5 with value (4 20)         11 with value (4 35)           1 with value (4 56)
% 0.53/0.74  Evaluation took:
% 0.53/0.74    0.266 seconds of real time
% 0.53/0.74    0.237121 seconds of user run time
% 0.53/0.74    0.02824 seconds of system run time
% 0.53/0.74    [Run times include 0.006 seconds GC run time.]
% 0.53/0.74    0 calls to %EVAL
% 0.53/0.74    0 page faults and
% 0.53/0.74    16,793,792 bytes consed.
% 0.53/0.74  :PROOF-FOUND
% 0.53/0.74  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-02T19:42:08
% 0.53/0.74  :PROOF-FOUND
% 0.53/0.74  * 
%------------------------------------------------------------------------------