TSTP Solution File: NUM004-1 by Metis---2.4

View Problem - Process Solution 
%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM004-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% 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 : Mon Jul 18 12:24:02 EDT 2022

% Result   : Unsatisfiable 17.75s 17.95s
% Output   : CNFRefutation 17.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   23 (  12 unt;   0 nHn;  12 RR)
%            Number of literals    :   39 (   0 equ;  17 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   59 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(reflexivity,axiom,
    equalish(A,A) ).

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(commutativity2,axiom,
    equalish(subtract(add(A,B),C),add(subtract(A,C),B)) ).

cnf(subtract_substitution1,axiom,
    ( ~ equalish(A,B)
    | ~ equalish(C,subtract(A,D))
    | equalish(C,subtract(B,D)) ) ).

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

cnf(refute_0_0,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_1,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_0]) ).

cnf(refute_0_2,plain,
    ( ~ equalish(subtract(add(X_5842,X_5841),X_5843),add(subtract(X_5841,X_5843),X_5842))
    | equalish(subtract(add(X_5842,X_5841),X_5843),add(X_5842,subtract(X_5841,X_5843))) ),
    inference(subst,[],[refute_0_1:[bind(A,$fot(subtract(X_5841,X_5843))),bind(B,$fot(X_5842)),bind(X_25,$fot(subtract(add(X_5842,X_5841),X_5843)))]]) ).

cnf(refute_0_3,plain,
    equalish(subtract(X_208,X_211),subtract(X_208,X_211)),
    inference(subst,[],[reflexivity:[bind(A,$fot(subtract(X_208,X_211)))]]) ).

cnf(refute_0_4,plain,
    ( ~ equalish(X_208,X_209)
    | ~ equalish(subtract(X_208,X_211),subtract(X_208,X_211))
    | equalish(subtract(X_208,X_211),subtract(X_209,X_211)) ),
    inference(subst,[],[subtract_substitution1:[bind(A,$fot(X_208)),bind(B,$fot(X_209)),bind(C,$fot(subtract(X_208,X_211))),bind(D,$fot(X_211))]]) ).

cnf(refute_0_5,plain,
    ( ~ equalish(X_208,X_209)
    | equalish(subtract(X_208,X_211),subtract(X_209,X_211)) ),
    inference(resolve,[$cnf( equalish(subtract(X_208,X_211),subtract(X_208,X_211)) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( ~ equalish(add(A,B),add(B,A))
    | equalish(subtract(add(A,B),X_257),subtract(add(B,A),X_257)) ),
    inference(subst,[],[refute_0_5:[bind(X_208,$fot(add(A,B))),bind(X_209,$fot(add(B,A))),bind(X_211,$fot(X_257))]]) ).

cnf(refute_0_7,plain,
    equalish(subtract(add(A,B),X_257),subtract(add(B,A),X_257)),
    inference(resolve,[$cnf( equalish(add(A,B),add(B,A)) )],[commutativity_of_addition,refute_0_6]) ).

cnf(refute_0_8,plain,
    equalish(subtract(add(X_5759,X_5758),X_5760),subtract(add(X_5758,X_5759),X_5760)),
    inference(subst,[],[refute_0_7:[bind(A,$fot(X_5759)),bind(B,$fot(X_5758)),bind(X_257,$fot(X_5760))]]) ).

cnf(refute_0_9,plain,
    ( ~ equalish(X_25,subtract(add(A,B),C))
    | ~ equalish(subtract(add(A,B),C),add(subtract(A,C),B))
    | equalish(X_25,add(subtract(A,C),B)) ),
    inference(subst,[],[transitivity:[bind(A,$fot(X_25)),bind(B,$fot(subtract(add(A,B),C))),bind(C,$fot(add(subtract(A,C),B)))]]) ).

cnf(refute_0_10,plain,
    ( ~ equalish(X_25,subtract(add(A,B),C))
    | equalish(X_25,add(subtract(A,C),B)) ),
    inference(resolve,[$cnf( equalish(subtract(add(A,B),C),add(subtract(A,C),B)) )],[commutativity2,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( ~ equalish(subtract(add(X_5759,X_5758),X_5760),subtract(add(X_5758,X_5759),X_5760))
    | equalish(subtract(add(X_5759,X_5758),X_5760),add(subtract(X_5758,X_5760),X_5759)) ),
    inference(subst,[],[refute_0_10:[bind(A,$fot(X_5758)),bind(B,$fot(X_5759)),bind(C,$fot(X_5760)),bind(X_25,$fot(subtract(add(X_5759,X_5758),X_5760)))]]) ).

cnf(refute_0_12,plain,
    equalish(subtract(add(X_5759,X_5758),X_5760),add(subtract(X_5758,X_5760),X_5759)),
    inference(resolve,[$cnf( equalish(subtract(add(X_5759,X_5758),X_5760),subtract(add(X_5758,X_5759),X_5760)) )],[refute_0_8,refute_0_11]) ).

cnf(refute_0_13,plain,
    equalish(subtract(add(X_5842,X_5841),X_5843),add(subtract(X_5841,X_5843),X_5842)),
    inference(subst,[],[refute_0_12:[bind(X_5758,$fot(X_5841)),bind(X_5759,$fot(X_5842)),bind(X_5760,$fot(X_5843))]]) ).

cnf(refute_0_14,plain,
    equalish(subtract(add(X_5842,X_5841),X_5843),add(X_5842,subtract(X_5841,X_5843))),
    inference(resolve,[$cnf( equalish(subtract(add(X_5842,X_5841),X_5843),add(subtract(X_5841,X_5843),X_5842)) )],[refute_0_13,refute_0_2]) ).

cnf(refute_0_15,plain,
    equalish(subtract(add(a,b),c),add(a,subtract(b,c))),
    inference(subst,[],[refute_0_14:[bind(X_5841,$fot(b)),bind(X_5842,$fot(a)),bind(X_5843,$fot(c))]]) ).

cnf(refute_0_16,plain,
    $false,
    inference(resolve,[$cnf( equalish(subtract(add(a,b),c),add(a,subtract(b,c))) )],[refute_0_15,prove_equation]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 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 : Tue Jul  5 22:38:23 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 17.75/17.95  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.75/17.95  
% 17.75/17.95  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.75/17.95  
%------------------------------------------------------------------------------