TSTP Solution File: LCL201-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL201-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n009.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 12:50:32 EDT 2022

% Result   : Unsatisfiable 0.81s 0.99s
% Output   : CNFRefutation 0.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   34 (  19 unt;   0 nHn;  18 RR)
%            Number of literals    :   54 (   0 equ;  21 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-1 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   78 (  15 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(axiom_1_3,axiom,
    axiom(or(not(A),or(B,A))) ).

cnf(axiom_1_4,axiom,
    axiom(or(not(or(A,B)),or(B,A))) ).

cnf(axiom_1_5,axiom,
    axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) ).

cnf(rule_1,axiom,
    ( theorem(X)
    | ~ axiom(X) ) ).

cnf(rule_2,axiom,
    ( theorem(X)
    | ~ axiom(or(not(Y),X))
    | ~ theorem(Y) ) ).

cnf(rule_3,axiom,
    ( theorem(or(not(X),Z))
    | ~ axiom(or(not(X),Y))
    | ~ theorem(or(not(Y),Z)) ) ).

cnf(prove_this,negated_conjecture,
    ~ theorem(or(not(not(or(p,q))),or(not(p),q))) ).

cnf(refute_0_0,plain,
    ( ~ axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
    | ~ theorem(or(A,or(B,C)))
    | theorem(or(B,or(A,C))) ),
    inference(subst,[],[rule_2:[bind(X,$fot(or(B,or(A,C)))),bind(Y,$fot(or(A,or(B,C))))]]) ).

cnf(refute_0_1,plain,
    ( ~ theorem(or(A,or(B,C)))
    | theorem(or(B,or(A,C))) ),
    inference(resolve,[$cnf( axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) )],[axiom_1_5,refute_0_0]) ).

cnf(refute_0_2,plain,
    ( ~ theorem(or(not(X_2466),or(not(not(or(X_2466,X_2465))),X_2464)))
    | theorem(or(not(not(or(X_2466,X_2465))),or(not(X_2466),X_2464))) ),
    inference(subst,[],[refute_0_1:[bind(A,$fot(not(X_2466))),bind(B,$fot(not(not(or(X_2466,X_2465))))),bind(C,$fot(X_2464))]]) ).

cnf(refute_0_3,plain,
    axiom(or(not(X_332),or(B,X_332))),
    inference(subst,[],[axiom_1_3:[bind(A,$fot(X_332))]]) ).

cnf(refute_0_4,plain,
    ( ~ axiom(or(not(X_332),or(B,X_332)))
    | ~ theorem(or(not(or(B,X_332)),X_334))
    | theorem(or(not(X_332),X_334)) ),
    inference(subst,[],[rule_3:[bind(X,$fot(X_332)),bind(Y,$fot(or(B,X_332))),bind(Z,$fot(X_334))]]) ).

cnf(refute_0_5,plain,
    ( ~ theorem(or(not(or(B,X_332)),X_334))
    | theorem(or(not(X_332),X_334)) ),
    inference(resolve,[$cnf( axiom(or(not(X_332),or(B,X_332))) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( ~ theorem(or(not(or(X_2399,X_2400)),or(not(not(or(X_2400,X_2399))),X_2398)))
    | theorem(or(not(X_2400),or(not(not(or(X_2400,X_2399))),X_2398))) ),
    inference(subst,[],[refute_0_5:[bind(B,$fot(X_2399)),bind(X_332,$fot(X_2400)),bind(X_334,$fot(or(not(not(or(X_2400,X_2399))),X_2398)))]]) ).

cnf(refute_0_7,plain,
    ( ~ theorem(or(not(X_1117),or(X_1117,X_1116)))
    | theorem(or(X_1117,or(not(X_1117),X_1116))) ),
    inference(subst,[],[refute_0_1:[bind(A,$fot(not(X_1117))),bind(B,$fot(X_1117)),bind(C,$fot(X_1116))]]) ).

cnf(refute_0_8,plain,
    ( ~ axiom(or(not(or(X_7,X_8)),or(X_8,X_7)))
    | theorem(or(not(or(X_7,X_8)),or(X_8,X_7))) ),
    inference(subst,[],[rule_1:[bind(X,$fot(or(not(or(X_7,X_8)),or(X_8,X_7))))]]) ).

cnf(refute_0_9,plain,
    axiom(or(not(or(X_7,X_8)),or(X_8,X_7))),
    inference(subst,[],[axiom_1_4:[bind(A,$fot(X_7)),bind(B,$fot(X_8))]]) ).

cnf(refute_0_10,plain,
    theorem(or(not(or(X_7,X_8)),or(X_8,X_7))),
    inference(resolve,[$cnf( axiom(or(not(or(X_7,X_8)),or(X_8,X_7))) )],[refute_0_9,refute_0_8]) ).

cnf(refute_0_11,plain,
    theorem(or(not(or(X_1113,X_1114)),or(X_1114,X_1113))),
    inference(subst,[],[refute_0_10:[bind(X_7,$fot(X_1113)),bind(X_8,$fot(X_1114))]]) ).

cnf(refute_0_12,plain,
    ( ~ theorem(or(not(or(X_1113,X_1114)),or(X_1114,X_1113)))
    | theorem(or(not(X_1114),or(X_1114,X_1113))) ),
    inference(subst,[],[refute_0_5:[bind(B,$fot(X_1113)),bind(X_332,$fot(X_1114)),bind(X_334,$fot(or(X_1114,X_1113)))]]) ).

cnf(refute_0_13,plain,
    theorem(or(not(X_1114),or(X_1114,X_1113))),
    inference(resolve,[$cnf( theorem(or(not(or(X_1113,X_1114)),or(X_1114,X_1113))) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    theorem(or(not(X_1117),or(X_1117,X_1116))),
    inference(subst,[],[refute_0_13:[bind(X_1113,$fot(X_1116)),bind(X_1114,$fot(X_1117))]]) ).

cnf(refute_0_15,plain,
    theorem(or(X_1117,or(not(X_1117),X_1116))),
    inference(resolve,[$cnf( theorem(or(not(X_1117),or(X_1117,X_1116))) )],[refute_0_14,refute_0_7]) ).

cnf(refute_0_16,plain,
    theorem(or(not(or(X_2294,X_2293)),or(not(not(or(X_2294,X_2293))),X_1116))),
    inference(subst,[],[refute_0_15:[bind(X_1117,$fot(not(or(X_2294,X_2293))))]]) ).

cnf(refute_0_17,plain,
    ( ~ axiom(or(not(or(A,B)),or(B,A)))
    | ~ theorem(or(not(or(B,A)),X_334))
    | theorem(or(not(or(A,B)),X_334)) ),
    inference(subst,[],[rule_3:[bind(X,$fot(or(A,B))),bind(Y,$fot(or(B,A))),bind(Z,$fot(X_334))]]) ).

cnf(refute_0_18,plain,
    ( ~ theorem(or(not(or(B,A)),X_334))
    | theorem(or(not(or(A,B)),X_334)) ),
    inference(resolve,[$cnf( axiom(or(not(or(A,B)),or(B,A))) )],[axiom_1_4,refute_0_17]) ).

cnf(refute_0_19,plain,
    ( ~ theorem(or(not(or(X_2294,X_2293)),or(not(not(or(X_2294,X_2293))),X_1116)))
    | theorem(or(not(or(X_2293,X_2294)),or(not(not(or(X_2294,X_2293))),X_1116))) ),
    inference(subst,[],[refute_0_18:[bind(A,$fot(X_2293)),bind(B,$fot(X_2294)),bind(X_334,$fot(or(not(not(or(X_2294,X_2293))),X_1116)))]]) ).

cnf(refute_0_20,plain,
    theorem(or(not(or(X_2293,X_2294)),or(not(not(or(X_2294,X_2293))),X_1116))),
    inference(resolve,[$cnf( theorem(or(not(or(X_2294,X_2293)),or(not(not(or(X_2294,X_2293))),X_1116))) )],[refute_0_16,refute_0_19]) ).

cnf(refute_0_21,plain,
    theorem(or(not(or(X_2399,X_2400)),or(not(not(or(X_2400,X_2399))),X_2398))),
    inference(subst,[],[refute_0_20:[bind(X_1116,$fot(X_2398)),bind(X_2293,$fot(X_2399)),bind(X_2294,$fot(X_2400))]]) ).

cnf(refute_0_22,plain,
    theorem(or(not(X_2400),or(not(not(or(X_2400,X_2399))),X_2398))),
    inference(resolve,[$cnf( theorem(or(not(or(X_2399,X_2400)),or(not(not(or(X_2400,X_2399))),X_2398))) )],[refute_0_21,refute_0_6]) ).

cnf(refute_0_23,plain,
    theorem(or(not(X_2466),or(not(not(or(X_2466,X_2465))),X_2464))),
    inference(subst,[],[refute_0_22:[bind(X_2398,$fot(X_2464)),bind(X_2399,$fot(X_2465)),bind(X_2400,$fot(X_2466))]]) ).

cnf(refute_0_24,plain,
    theorem(or(not(not(or(X_2466,X_2465))),or(not(X_2466),X_2464))),
    inference(resolve,[$cnf( theorem(or(not(X_2466),or(not(not(or(X_2466,X_2465))),X_2464))) )],[refute_0_23,refute_0_2]) ).

cnf(refute_0_25,plain,
    theorem(or(not(not(or(p,q))),or(not(p),q))),
    inference(subst,[],[refute_0_24:[bind(X_2464,$fot(q)),bind(X_2465,$fot(q)),bind(X_2466,$fot(p))]]) ).

cnf(refute_0_26,plain,
    $false,
    inference(resolve,[$cnf( theorem(or(not(not(or(p,q))),or(not(p),q))) )],[refute_0_25,prove_this]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL201-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.14/0.33  % Computer : n009.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 600
% 0.14/0.33  % DateTime : Sun Jul  3 13:48:37 EDT 2022
% 0.14/0.33  % CPUTime  : 
% 0.14/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.81/0.99  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.81/0.99  
% 0.81/0.99  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.81/1.00  
%------------------------------------------------------------------------------