TSTP Solution File: GRP029-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP029-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n020.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 : Sat Jul 16 10:32:33 EDT 2022

% Result   : Unsatisfiable 0.20s 0.47s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   23 (  13 unt;   0 nHn;  15 RR)
%            Number of literals    :   42 (   0 equ;  21 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   39 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(associativity1,axiom,
    ( ~ product(X,Y,U)
    | ~ product(Y,Z,V)
    | ~ product(U,Z,W)
    | product(X,V,W) ) ).

cnf(associativity2,axiom,
    ( ~ product(X,Y,U)
    | ~ product(Y,Z,V)
    | ~ product(X,V,W)
    | product(U,Z,W) ) ).

cnf(left_identity,axiom,
    product(identity,A,A) ).

cnf(left_inverse,axiom,
    product(inverse(A),A,identity) ).

cnf(prove_there_is_a_right_identity,negated_conjecture,
    ~ product(not_right_identity(A),A,not_right_identity(A)) ).

cnf(refute_0_0,plain,
    ~ product(not_right_identity(identity),identity,not_right_identity(identity)),
    inference(subst,[],[prove_there_is_a_right_identity:[bind(A,$fot(identity))]]) ).

cnf(refute_0_1,plain,
    product(identity,identity,identity),
    inference(subst,[],[left_identity:[bind(A,$fot(identity))]]) ).

cnf(refute_0_2,plain,
    ( ~ product(X_76,identity,X_75)
    | ~ product(identity,identity,identity)
    | product(X_75,identity,X_75) ),
    inference(subst,[],[associativity2:[bind(U,$fot(X_75)),bind(V,$fot(identity)),bind(W,$fot(X_75)),bind(X,$fot(X_76)),bind(Y,$fot(identity)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_3,plain,
    ( ~ product(X_76,identity,X_75)
    | product(X_75,identity,X_75) ),
    inference(resolve,[$cnf( product(identity,identity,identity) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ product(inverse(inverse(X_180)),identity,X_180)
    | product(X_180,identity,X_180) ),
    inference(subst,[],[refute_0_3:[bind(X_75,$fot(X_180)),bind(X_76,$fot(inverse(inverse(X_180))))]]) ).

cnf(refute_0_5,plain,
    product(inverse(inverse(X_178)),inverse(X_178),identity),
    inference(subst,[],[left_inverse:[bind(A,$fot(inverse(X_178)))]]) ).

cnf(refute_0_6,plain,
    product(inverse(X_173),X_173,identity),
    inference(subst,[],[left_inverse:[bind(A,$fot(X_173))]]) ).

cnf(refute_0_7,plain,
    product(identity,X_168,X_168),
    inference(subst,[],[left_identity:[bind(A,$fot(X_168))]]) ).

cnf(refute_0_8,plain,
    ( ~ product(X_169,X_170,identity)
    | ~ product(X_170,X_168,X_167)
    | ~ product(identity,X_168,X_168)
    | product(X_169,X_167,X_168) ),
    inference(subst,[],[associativity1:[bind(U,$fot(identity)),bind(V,$fot(X_167)),bind(W,$fot(X_168)),bind(X,$fot(X_169)),bind(Y,$fot(X_170)),bind(Z,$fot(X_168))]]) ).

cnf(refute_0_9,plain,
    ( ~ product(X_169,X_170,identity)
    | ~ product(X_170,X_168,X_167)
    | product(X_169,X_167,X_168) ),
    inference(resolve,[$cnf( product(identity,X_168,X_168) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( ~ product(X_174,inverse(X_173),identity)
    | ~ product(inverse(X_173),X_173,identity)
    | product(X_174,identity,X_173) ),
    inference(subst,[],[refute_0_9:[bind(X_167,$fot(identity)),bind(X_168,$fot(X_173)),bind(X_169,$fot(X_174)),bind(X_170,$fot(inverse(X_173)))]]) ).

cnf(refute_0_11,plain,
    ( ~ product(X_174,inverse(X_173),identity)
    | product(X_174,identity,X_173) ),
    inference(resolve,[$cnf( product(inverse(X_173),X_173,identity) )],[refute_0_6,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( ~ product(inverse(inverse(X_178)),inverse(X_178),identity)
    | product(inverse(inverse(X_178)),identity,X_178) ),
    inference(subst,[],[refute_0_11:[bind(X_173,$fot(X_178)),bind(X_174,$fot(inverse(inverse(X_178))))]]) ).

cnf(refute_0_13,plain,
    product(inverse(inverse(X_178)),identity,X_178),
    inference(resolve,[$cnf( product(inverse(inverse(X_178)),inverse(X_178),identity) )],[refute_0_5,refute_0_12]) ).

cnf(refute_0_14,plain,
    product(inverse(inverse(X_180)),identity,X_180),
    inference(subst,[],[refute_0_13:[bind(X_178,$fot(X_180))]]) ).

cnf(refute_0_15,plain,
    product(X_180,identity,X_180),
    inference(resolve,[$cnf( product(inverse(inverse(X_180)),identity,X_180) )],[refute_0_14,refute_0_4]) ).

cnf(refute_0_16,plain,
    product(not_right_identity(identity),identity,not_right_identity(identity)),
    inference(subst,[],[refute_0_15:[bind(X_180,$fot(not_right_identity(identity)))]]) ).

cnf(refute_0_17,plain,
    $false,
    inference(resolve,[$cnf( product(not_right_identity(identity),identity,not_right_identity(identity)) )],[refute_0_16,refute_0_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP029-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n020.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 : Tue Jun 14 13:10:35 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.47  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47  
% 0.20/0.47  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.47  
%------------------------------------------------------------------------------