TSTP Solution File: ROB013-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : ROB013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n032.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 20:54:34 EDT 2022

% Result   : Unsatisfiable 0.14s 0.30s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   30 (  17 unt;   0 nHn;  26 RR)
%            Number of literals    :   49 (  48 equ;  21 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,b)) = c ).

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

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

cnf(refute_0_3,plain,
    negate(add(c,negate(add(a,negate(b))))) = 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(b),a) = add(a,negate(b)),
    inference(subst,[],[refute_0_8:[bind(X,$fot(a)),bind(Y,$fot(negate(b)))]]) ).

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

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

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

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

cnf(refute_0_14,plain,
    add(c,negate(add(negate(b),a))) = add(c,negate(add(negate(b),a))),
    introduced(tautology,[refl,[$fot(add(c,negate(add(negate(b),a))))]]) ).

cnf(refute_0_15,plain,
    ( add(c,negate(add(negate(b),a))) != add(c,negate(add(negate(b),a)))
    | negate(add(negate(b),a)) != negate(add(a,negate(b)))
    | add(c,negate(add(negate(b),a))) = add(c,negate(add(a,negate(b)))) ),
    introduced(tautology,[equality,[$cnf( $equal(add(c,negate(add(negate(b),a))),add(c,negate(add(negate(b),a)))) ),[1,1],$fot(negate(add(a,negate(b))))]]) ).

cnf(refute_0_16,plain,
    ( negate(add(negate(b),a)) != negate(add(a,negate(b)))
    | add(c,negate(add(negate(b),a))) = add(c,negate(add(a,negate(b)))) ),
    inference(resolve,[$cnf( $equal(add(c,negate(add(negate(b),a))),add(c,negate(add(negate(b),a)))) )],[refute_0_14,refute_0_15]) ).

cnf(refute_0_17,plain,
    add(c,negate(add(negate(b),a))) = add(c,negate(add(a,negate(b)))),
    inference(resolve,[$cnf( $equal(negate(add(negate(b),a)),negate(add(a,negate(b)))) )],[refute_0_13,refute_0_16]) ).

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

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

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

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

cnf(refute_0_22,plain,
    ( negate(add(c,negate(add(a,negate(b))))) != a
    | negate(add(c,negate(add(negate(b),a)))) != negate(add(c,negate(add(a,negate(b)))))
    | negate(add(c,negate(add(negate(b),a)))) = a ),
    introduced(tautology,[equality,[$cnf( $equal(negate(add(c,negate(add(negate(b),a)))),negate(add(c,negate(add(a,negate(b)))))) ),[1],$fot(a)]]) ).

cnf(refute_0_23,plain,
    ( negate(add(c,negate(add(a,negate(b))))) != a
    | negate(add(c,negate(add(negate(b),a)))) = a ),
    inference(resolve,[$cnf( $equal(negate(add(c,negate(add(negate(b),a)))),negate(add(c,negate(add(a,negate(b)))))) )],[refute_0_21,refute_0_22]) ).

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

cnf(refute_0_25,plain,
    $false,
    inference(resolve,[$cnf( $equal(negate(add(c,negate(add(a,negate(b))))),a) )],[refute_0_3,refute_0_24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : ROB013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.10  % Command  : metis --show proof --show saturation %s
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit : 300
% 0.10/0.29  % WCLimit  : 600
% 0.10/0.29  % DateTime : Thu Jun  9 13:37:22 EDT 2022
% 0.14/0.29  % CPUTime  : 
% 0.14/0.29  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.30  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.30  
% 0.14/0.30  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.30  
%------------------------------------------------------------------------------