TSTP Solution File: ROB010-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : ROB010-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n028.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 20:54:33 EDT 2022

% Result   : Unsatisfiable 0.12s 0.33s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   17
% Syntax   : Number of clauses     :   38 (  21 unt;   0 nHn;  34 RR)
%            Number of literals    :   63 (  62 equ;  27 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   13 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(commutativity_of_add,axiom,
    add(X,Y) = add(Y,X) ).

cnf(robbins_axiom,axiom,
    negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ).

cnf(condition,hypothesis,
    negate(add(a,negate(b))) = c ).

cnf(prove_result,negated_conjecture,
    negate(add(c,negate(add(b,a)))) != a ).

cnf(refute_0_0,plain,
    negate(add(negate(add(a,b)),negate(add(a,negate(b))))) = a,
    inference(subst,[],[robbins_axiom:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).

cnf(refute_0_1,plain,
    ( negate(add(a,negate(b))) != c
    | negate(add(negate(add(a,b)),negate(add(a,negate(b))))) != a
    | negate(add(negate(add(a,b)),c)) = a ),
    introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(a,b)),negate(add(a,negate(b))))),a) ),[0,0,1],$fot(c)]]) ).

cnf(refute_0_2,plain,
    ( negate(add(negate(add(a,b)),negate(add(a,negate(b))))) != a
    | negate(add(negate(add(a,b)),c)) = a ),
    inference(resolve,[$cnf( $equal(negate(add(a,negate(b))),c) )],[condition,refute_0_1]) ).

cnf(refute_0_3,plain,
    negate(add(negate(add(a,b)),c)) = a,
    inference(resolve,[$cnf( $equal(negate(add(negate(add(a,b)),negate(add(a,negate(b))))),a) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_5,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_6,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( add(X,Y) != add(Y,X)
    | add(Y,X) = add(X,Y) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).

cnf(refute_0_8,plain,
    add(Y,X) = add(X,Y),
    inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutativity_of_add,refute_0_7]) ).

cnf(refute_0_9,plain,
    add(negate(add(a,b)),c) = add(c,negate(add(a,b))),
    inference(subst,[],[refute_0_8:[bind(X,$fot(c)),bind(Y,$fot(negate(add(a,b))))]]) ).

cnf(refute_0_10,plain,
    negate(add(negate(add(a,b)),c)) = negate(add(negate(add(a,b)),c)),
    introduced(tautology,[refl,[$fot(negate(add(negate(add(a,b)),c)))]]) ).

cnf(refute_0_11,plain,
    ( add(negate(add(a,b)),c) != add(c,negate(add(a,b)))
    | negate(add(negate(add(a,b)),c)) != negate(add(negate(add(a,b)),c))
    | negate(add(negate(add(a,b)),c)) = negate(add(c,negate(add(a,b)))) ),
    introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(a,b)),c)),negate(add(negate(add(a,b)),c))) ),[1,0],$fot(add(c,negate(add(a,b))))]]) ).

cnf(refute_0_12,plain,
    ( add(negate(add(a,b)),c) != add(c,negate(add(a,b)))
    | negate(add(negate(add(a,b)),c)) = negate(add(c,negate(add(a,b)))) ),
    inference(resolve,[$cnf( $equal(negate(add(negate(add(a,b)),c)),negate(add(negate(add(a,b)),c))) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    negate(add(negate(add(a,b)),c)) = negate(add(c,negate(add(a,b)))),
    inference(resolve,[$cnf( $equal(add(negate(add(a,b)),c),add(c,negate(add(a,b)))) )],[refute_0_9,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( negate(add(negate(add(a,b)),c)) != a
    | negate(add(negate(add(a,b)),c)) != negate(add(c,negate(add(a,b))))
    | negate(add(c,negate(add(a,b)))) = a ),
    introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(a,b)),c)),a) ),[0],$fot(negate(add(c,negate(add(a,b)))))]]) ).

cnf(refute_0_15,plain,
    ( negate(add(negate(add(a,b)),c)) != a
    | negate(add(c,negate(add(a,b)))) = a ),
    inference(resolve,[$cnf( $equal(negate(add(negate(add(a,b)),c)),negate(add(c,negate(add(a,b))))) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    negate(add(c,negate(add(a,b)))) = a,
    inference(resolve,[$cnf( $equal(negate(add(negate(add(a,b)),c)),a) )],[refute_0_3,refute_0_15]) ).

cnf(refute_0_17,plain,
    add(b,a) = add(a,b),
    inference(subst,[],[refute_0_8:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).

cnf(refute_0_18,plain,
    negate(add(b,a)) = negate(add(b,a)),
    introduced(tautology,[refl,[$fot(negate(add(b,a)))]]) ).

cnf(refute_0_19,plain,
    ( add(b,a) != add(a,b)
    | negate(add(b,a)) != negate(add(b,a))
    | negate(add(b,a)) = negate(add(a,b)) ),
    introduced(tautology,[equality,[$cnf( $equal(negate(add(b,a)),negate(add(b,a))) ),[1,0],$fot(add(a,b))]]) ).

cnf(refute_0_20,plain,
    ( add(b,a) != add(a,b)
    | negate(add(b,a)) = negate(add(a,b)) ),
    inference(resolve,[$cnf( $equal(negate(add(b,a)),negate(add(b,a))) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    negate(add(b,a)) = negate(add(a,b)),
    inference(resolve,[$cnf( $equal(add(b,a),add(a,b)) )],[refute_0_17,refute_0_20]) ).

cnf(refute_0_22,plain,
    add(c,negate(add(b,a))) = add(c,negate(add(b,a))),
    introduced(tautology,[refl,[$fot(add(c,negate(add(b,a))))]]) ).

cnf(refute_0_23,plain,
    ( add(c,negate(add(b,a))) != add(c,negate(add(b,a)))
    | negate(add(b,a)) != negate(add(a,b))
    | add(c,negate(add(b,a))) = add(c,negate(add(a,b))) ),
    introduced(tautology,[equality,[$cnf( $equal(add(c,negate(add(b,a))),add(c,negate(add(b,a)))) ),[1,1],$fot(negate(add(a,b)))]]) ).

cnf(refute_0_24,plain,
    ( negate(add(b,a)) != negate(add(a,b))
    | add(c,negate(add(b,a))) = add(c,negate(add(a,b))) ),
    inference(resolve,[$cnf( $equal(add(c,negate(add(b,a))),add(c,negate(add(b,a)))) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    add(c,negate(add(b,a))) = add(c,negate(add(a,b))),
    inference(resolve,[$cnf( $equal(negate(add(b,a)),negate(add(a,b))) )],[refute_0_21,refute_0_24]) ).

cnf(refute_0_26,plain,
    negate(add(c,negate(add(b,a)))) = negate(add(c,negate(add(b,a)))),
    introduced(tautology,[refl,[$fot(negate(add(c,negate(add(b,a)))))]]) ).

cnf(refute_0_27,plain,
    ( add(c,negate(add(b,a))) != add(c,negate(add(a,b)))
    | negate(add(c,negate(add(b,a)))) != negate(add(c,negate(add(b,a))))
    | negate(add(c,negate(add(b,a)))) = negate(add(c,negate(add(a,b)))) ),
    introduced(tautology,[equality,[$cnf( $equal(negate(add(c,negate(add(b,a)))),negate(add(c,negate(add(b,a))))) ),[1,0],$fot(add(c,negate(add(a,b))))]]) ).

cnf(refute_0_28,plain,
    ( add(c,negate(add(b,a))) != add(c,negate(add(a,b)))
    | negate(add(c,negate(add(b,a)))) = negate(add(c,negate(add(a,b)))) ),
    inference(resolve,[$cnf( $equal(negate(add(c,negate(add(b,a)))),negate(add(c,negate(add(b,a))))) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    negate(add(c,negate(add(b,a)))) = negate(add(c,negate(add(a,b)))),
    inference(resolve,[$cnf( $equal(add(c,negate(add(b,a))),add(c,negate(add(a,b)))) )],[refute_0_25,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( negate(add(c,negate(add(a,b)))) != a
    | negate(add(c,negate(add(b,a)))) != negate(add(c,negate(add(a,b))))
    | negate(add(c,negate(add(b,a)))) = a ),
    introduced(tautology,[equality,[$cnf( $equal(negate(add(c,negate(add(b,a)))),negate(add(c,negate(add(a,b))))) ),[1],$fot(a)]]) ).

cnf(refute_0_31,plain,
    ( negate(add(c,negate(add(a,b)))) != a
    | negate(add(c,negate(add(b,a)))) = a ),
    inference(resolve,[$cnf( $equal(negate(add(c,negate(add(b,a)))),negate(add(c,negate(add(a,b))))) )],[refute_0_29,refute_0_30]) ).

cnf(refute_0_32,plain,
    negate(add(c,negate(add(a,b)))) != a,
    inference(resolve,[$cnf( $equal(negate(add(c,negate(add(b,a)))),a) )],[refute_0_31,prove_result]) ).

cnf(refute_0_33,plain,
    $false,
    inference(resolve,[$cnf( $equal(negate(add(c,negate(add(a,b)))),a) )],[refute_0_16,refute_0_32]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : ROB010-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.11  % Command  : metis --show proof --show saturation %s
% 0.12/0.32  % Computer : n028.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 600
% 0.12/0.32  % DateTime : Thu Jun  9 15:23:32 EDT 2022
% 0.12/0.32  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.33  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33  
% 0.12/0.33  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.33  
%------------------------------------------------------------------------------