TSTP Solution File: ROB002-1 by Metis---2.4

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : ROB002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n022.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 20:54:30 EDT 2022

% Result   : Unsatisfiable 0.13s 0.38s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   40 (  23 unt;   0 nHn;  24 RR)
%            Number of literals    :   65 (  64 equ;  27 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   58 (   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(double_negation,hypothesis,
    negate(negate(X)) = X ).

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

cnf(refute_0_0,plain,
    negate(negate(b)) = b,
    inference(subst,[],[double_negation:[bind(X,$fot(b))]]) ).

cnf(refute_0_1,plain,
    negate(negate(add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2)))))) = add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2)))),
    inference(subst,[],[double_negation:[bind(X,$fot(add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2))))))]]) ).

cnf(refute_0_2,plain,
    negate(add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2))))) = X_1,
    inference(subst,[],[robbins_axiom:[bind(X,$fot(X_1)),bind(Y,$fot(X_2))]]) ).

cnf(refute_0_3,plain,
    ( negate(add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2))))) != X_1
    | negate(negate(add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2)))))) != add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2))))
    | negate(X_1) = add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2)))) ),
    introduced(tautology,[equality,[$cnf( $equal(negate(negate(add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2)))))),add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2))))) ),[0,0],$fot(X_1)]]) ).

cnf(refute_0_4,plain,
    ( negate(negate(add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2)))))) != add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2))))
    | negate(X_1) = add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2)))) ),
    inference(resolve,[$cnf( $equal(negate(add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2))))),X_1) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    negate(X_1) = add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2)))),
    inference(resolve,[$cnf( $equal(negate(negate(add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2)))))),add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2))))) )],[refute_0_1,refute_0_4]) ).

cnf(refute_0_6,plain,
    negate(X_5) = add(negate(add(X_5,X_6)),negate(add(X_5,negate(X_6)))),
    inference(subst,[],[refute_0_5:[bind(X_1,$fot(X_5)),bind(X_2,$fot(X_6))]]) ).

cnf(refute_0_7,plain,
    add(negate(X_6),X_5) = add(X_5,negate(X_6)),
    inference(subst,[],[commutativity_of_add:[bind(X,$fot(negate(X_6))),bind(Y,$fot(X_5))]]) ).

cnf(refute_0_8,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_9,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_10,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( add(negate(X_6),X_5) != add(X_5,negate(X_6))
    | add(X_5,negate(X_6)) = add(negate(X_6),X_5) ),
    inference(subst,[],[refute_0_10:[bind(X0,$fot(add(negate(X_6),X_5))),bind(Y0,$fot(add(X_5,negate(X_6))))]]) ).

cnf(refute_0_12,plain,
    add(X_5,negate(X_6)) = add(negate(X_6),X_5),
    inference(resolve,[$cnf( $equal(add(negate(X_6),X_5),add(X_5,negate(X_6))) )],[refute_0_7,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( add(X_5,negate(X_6)) != add(negate(X_6),X_5)
    | negate(X_5) != add(negate(add(X_5,X_6)),negate(add(X_5,negate(X_6))))
    | negate(X_5) = add(negate(add(X_5,X_6)),negate(add(negate(X_6),X_5))) ),
    introduced(tautology,[equality,[$cnf( $equal(negate(X_5),add(negate(add(X_5,X_6)),negate(add(X_5,negate(X_6))))) ),[1,1,0],$fot(add(negate(X_6),X_5))]]) ).

cnf(refute_0_14,plain,
    ( negate(X_5) != add(negate(add(X_5,X_6)),negate(add(X_5,negate(X_6))))
    | negate(X_5) = add(negate(add(X_5,X_6)),negate(add(negate(X_6),X_5))) ),
    inference(resolve,[$cnf( $equal(add(X_5,negate(X_6)),add(negate(X_6),X_5)) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    negate(X_5) = add(negate(add(X_5,X_6)),negate(add(negate(X_6),X_5))),
    inference(resolve,[$cnf( $equal(negate(X_5),add(negate(add(X_5,X_6)),negate(add(X_5,negate(X_6))))) )],[refute_0_6,refute_0_14]) ).

cnf(refute_0_16,plain,
    negate(X_10) = add(negate(add(X_10,X_11)),negate(add(negate(X_11),X_10))),
    inference(subst,[],[refute_0_15:[bind(X_5,$fot(X_10)),bind(X_6,$fot(X_11))]]) ).

cnf(refute_0_17,plain,
    add(X_11,X_10) = add(X_10,X_11),
    inference(subst,[],[commutativity_of_add:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).

cnf(refute_0_18,plain,
    ( add(X_11,X_10) != add(X_10,X_11)
    | add(X_10,X_11) = add(X_11,X_10) ),
    inference(subst,[],[refute_0_10:[bind(X0,$fot(add(X_11,X_10))),bind(Y0,$fot(add(X_10,X_11)))]]) ).

cnf(refute_0_19,plain,
    add(X_10,X_11) = add(X_11,X_10),
    inference(resolve,[$cnf( $equal(add(X_11,X_10),add(X_10,X_11)) )],[refute_0_17,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( add(X_10,X_11) != add(X_11,X_10)
    | negate(X_10) != add(negate(add(X_10,X_11)),negate(add(negate(X_11),X_10)))
    | negate(X_10) = add(negate(add(X_11,X_10)),negate(add(negate(X_11),X_10))) ),
    introduced(tautology,[equality,[$cnf( $equal(negate(X_10),add(negate(add(X_10,X_11)),negate(add(negate(X_11),X_10)))) ),[1,0,0],$fot(add(X_11,X_10))]]) ).

cnf(refute_0_21,plain,
    ( negate(X_10) != add(negate(add(X_10,X_11)),negate(add(negate(X_11),X_10)))
    | negate(X_10) = add(negate(add(X_11,X_10)),negate(add(negate(X_11),X_10))) ),
    inference(resolve,[$cnf( $equal(add(X_10,X_11),add(X_11,X_10)) )],[refute_0_19,refute_0_20]) ).

cnf(refute_0_22,plain,
    negate(X_10) = add(negate(add(X_11,X_10)),negate(add(negate(X_11),X_10))),
    inference(resolve,[$cnf( $equal(negate(X_10),add(negate(add(X_10,X_11)),negate(add(negate(X_11),X_10)))) )],[refute_0_16,refute_0_21]) ).

cnf(refute_0_23,plain,
    ( negate(X_10) != add(negate(add(X_11,X_10)),negate(add(negate(X_11),X_10)))
    | add(negate(add(X_11,X_10)),negate(add(negate(X_11),X_10))) = negate(X_10) ),
    inference(subst,[],[refute_0_10:[bind(X0,$fot(negate(X_10))),bind(Y0,$fot(add(negate(add(X_11,X_10)),negate(add(negate(X_11),X_10)))))]]) ).

cnf(refute_0_24,plain,
    add(negate(add(X_11,X_10)),negate(add(negate(X_11),X_10))) = negate(X_10),
    inference(resolve,[$cnf( $equal(negate(X_10),add(negate(add(X_11,X_10)),negate(add(negate(X_11),X_10)))) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = negate(negate(b)),
    inference(subst,[],[refute_0_24:[bind(X_10,$fot(negate(b))),bind(X_11,$fot(a))]]) ).

cnf(refute_0_26,plain,
    ( Y0 != X0
    | Y0 != Z
    | X0 = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).

cnf(refute_0_27,plain,
    ( X0 != Y0
    | Y0 != Z
    | X0 = Z ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_10,refute_0_26]) ).

cnf(refute_0_28,plain,
    ( add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != negate(negate(b))
    | negate(negate(b)) != b
    | add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b ),
    inference(subst,[],[refute_0_27:[bind(X0,$fot(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))))),bind(Y0,$fot(negate(negate(b)))),bind(Z,$fot(b))]]) ).

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

cnf(refute_0_30,plain,
    add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b,
    inference(resolve,[$cnf( $equal(negate(negate(b)),b) )],[refute_0_0,refute_0_29]) ).

cnf(refute_0_31,plain,
    ( add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b
    | b != b
    | add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b ),
    introduced(tautology,[equality,[$cnf( ~ $equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b) ),[0],$fot(b)]]) ).

cnf(refute_0_32,plain,
    ( b != b
    | add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b ),
    inference(resolve,[$cnf( $equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b) )],[refute_0_30,refute_0_31]) ).

cnf(refute_0_33,plain,
    b != b,
    inference(resolve,[$cnf( $equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b) )],[refute_0_32,prove_huntingtons_axiom]) ).

cnf(refute_0_34,plain,
    b = b,
    introduced(tautology,[refl,[$fot(b)]]) ).

cnf(refute_0_35,plain,
    $false,
    inference(resolve,[$cnf( $equal(b,b) )],[refute_0_34,refute_0_33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ROB002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun  9 16:06:04 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.38  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38  
% 0.13/0.38  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.39  
%------------------------------------------------------------------------------