TSTP Solution File: NUM001-1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n025.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 : Mon Jul 18 12:24:01 EDT 2022

% Result   : Unsatisfiable 6.75s 6.94s
% Output   : CNFRefutation 6.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   24 (  13 unt;   0 nHn;  14 RR)
%            Number of literals    :   39 (   0 equ;  16 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   64 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(transitivity,axiom,
    ( ~ equalish(A,B)
    | ~ equalish(B,C)
    | equalish(A,C) ) ).

cnf(commutativity_of_addition,axiom,
    equalish(add(A,B),add(B,A)) ).

cnf(associativity_of_addition,axiom,
    equalish(add(A,add(B,C)),add(add(A,B),C)) ).

cnf(prove_equation,negated_conjecture,
    ~ equalish(add(add(a,b),c),add(a,add(b,c))) ).

cnf(refute_0_0,plain,
    ( ~ equalish(add(A,B),add(B,A))
    | ~ equalish(add(B,A),X_27)
    | equalish(add(A,B),X_27) ),
    inference(subst,[],[transitivity:[bind(A,$fot(add(A,B))),bind(B,$fot(add(B,A))),bind(C,$fot(X_27))]]) ).

cnf(refute_0_1,plain,
    ( ~ equalish(add(B,A),X_27)
    | equalish(add(A,B),X_27) ),
    inference(resolve,[$cnf( equalish(add(A,B),add(B,A)) )],[commutativity_of_addition,refute_0_0]) ).

cnf(refute_0_2,plain,
    ( ~ equalish(add(X_3295,add(X_3296,X_3297)),add(X_3296,add(X_3297,X_3295)))
    | equalish(add(add(X_3296,X_3297),X_3295),add(X_3296,add(X_3297,X_3295))) ),
    inference(subst,[],[refute_0_1:[bind(A,$fot(add(X_3296,X_3297))),bind(B,$fot(X_3295)),bind(X_27,$fot(add(X_3296,add(X_3297,X_3295))))]]) ).

cnf(refute_0_3,plain,
    equalish(add(X_29,add(B,C)),add(add(X_29,B),C)),
    inference(subst,[],[associativity_of_addition:[bind(A,$fot(X_29))]]) ).

cnf(refute_0_4,plain,
    ( ~ equalish(add(X_29,add(B,C)),add(add(X_29,B),C))
    | equalish(add(add(B,C),X_29),add(add(X_29,B),C)) ),
    inference(subst,[],[refute_0_1:[bind(A,$fot(add(B,C))),bind(B,$fot(X_29)),bind(X_27,$fot(add(add(X_29,B),C)))]]) ).

cnf(refute_0_5,plain,
    equalish(add(add(B,C),X_29),add(add(X_29,B),C)),
    inference(resolve,[$cnf( equalish(add(X_29,add(B,C)),add(add(X_29,B),C)) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    equalish(add(add(B,X_75),X_29),add(add(X_29,B),X_75)),
    inference(subst,[],[refute_0_5:[bind(C,$fot(X_75))]]) ).

cnf(refute_0_7,plain,
    ( ~ equalish(X_25,add(A,B))
    | ~ equalish(add(A,B),add(B,A))
    | equalish(X_25,add(B,A)) ),
    inference(subst,[],[transitivity:[bind(A,$fot(X_25)),bind(B,$fot(add(A,B))),bind(C,$fot(add(B,A)))]]) ).

cnf(refute_0_8,plain,
    ( ~ equalish(X_25,add(A,B))
    | equalish(X_25,add(B,A)) ),
    inference(resolve,[$cnf( equalish(add(A,B),add(B,A)) )],[commutativity_of_addition,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( ~ equalish(add(add(B,X_75),X_29),add(add(X_29,B),X_75))
    | equalish(add(add(B,X_75),X_29),add(X_75,add(X_29,B))) ),
    inference(subst,[],[refute_0_8:[bind(A,$fot(add(X_29,B))),bind(B,$fot(X_75)),bind(X_25,$fot(add(add(B,X_75),X_29)))]]) ).

cnf(refute_0_10,plain,
    equalish(add(add(B,X_75),X_29),add(X_75,add(X_29,B))),
    inference(resolve,[$cnf( equalish(add(add(B,X_75),X_29),add(add(X_29,B),X_75)) )],[refute_0_6,refute_0_9]) ).

cnf(refute_0_11,plain,
    equalish(add(add(X_3243,X_3244),X_3245),add(X_3244,add(X_3245,X_3243))),
    inference(subst,[],[refute_0_10:[bind(B,$fot(X_3243)),bind(X_29,$fot(X_3245)),bind(X_75,$fot(X_3244))]]) ).

cnf(refute_0_12,plain,
    ( ~ equalish(add(A,add(B,C)),add(add(A,B),C))
    | ~ equalish(add(add(A,B),C),X_27)
    | equalish(add(A,add(B,C)),X_27) ),
    inference(subst,[],[transitivity:[bind(A,$fot(add(A,add(B,C)))),bind(B,$fot(add(add(A,B),C))),bind(C,$fot(X_27))]]) ).

cnf(refute_0_13,plain,
    ( ~ equalish(add(add(A,B),C),X_27)
    | equalish(add(A,add(B,C)),X_27) ),
    inference(resolve,[$cnf( equalish(add(A,add(B,C)),add(add(A,B),C)) )],[associativity_of_addition,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( ~ equalish(add(add(X_3243,X_3244),X_3245),add(X_3244,add(X_3245,X_3243)))
    | equalish(add(X_3243,add(X_3244,X_3245)),add(X_3244,add(X_3245,X_3243))) ),
    inference(subst,[],[refute_0_13:[bind(A,$fot(X_3243)),bind(B,$fot(X_3244)),bind(C,$fot(X_3245)),bind(X_27,$fot(add(X_3244,add(X_3245,X_3243))))]]) ).

cnf(refute_0_15,plain,
    equalish(add(X_3243,add(X_3244,X_3245)),add(X_3244,add(X_3245,X_3243))),
    inference(resolve,[$cnf( equalish(add(add(X_3243,X_3244),X_3245),add(X_3244,add(X_3245,X_3243))) )],[refute_0_11,refute_0_14]) ).

cnf(refute_0_16,plain,
    equalish(add(X_3295,add(X_3296,X_3297)),add(X_3296,add(X_3297,X_3295))),
    inference(subst,[],[refute_0_15:[bind(X_3243,$fot(X_3295)),bind(X_3244,$fot(X_3296)),bind(X_3245,$fot(X_3297))]]) ).

cnf(refute_0_17,plain,
    equalish(add(add(X_3296,X_3297),X_3295),add(X_3296,add(X_3297,X_3295))),
    inference(resolve,[$cnf( equalish(add(X_3295,add(X_3296,X_3297)),add(X_3296,add(X_3297,X_3295))) )],[refute_0_16,refute_0_2]) ).

cnf(refute_0_18,plain,
    equalish(add(add(a,b),c),add(a,add(b,c))),
    inference(subst,[],[refute_0_17:[bind(X_3295,$fot(c)),bind(X_3296,$fot(a)),bind(X_3297,$fot(b))]]) ).

cnf(refute_0_19,plain,
    $false,
    inference(resolve,[$cnf( equalish(add(add(a,b),c),add(a,add(b,c))) )],[refute_0_18,prove_equation]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12  % Problem  : NUM001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n025.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 : Wed Jul  6 03:33:12 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 6.75/6.94  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.75/6.94  
% 6.75/6.94  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.75/6.95  
%------------------------------------------------------------------------------