TSTP Solution File: SYN071+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN071+1 : TPTP v8.1.0. Released v2.0.0.
% 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 : Thu Jul 21 08:59:17 EDT 2022

% Result   : Theorem 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   47 (  12 unt;   0 def)
%            Number of atoms       :   92 (  91 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   81 (  36   ~;  42   |;   1   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :    5 (   0 sgn   0   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(pel48_1,axiom,
    ( a = b
    | c = d ) ).

fof(pel48_2,axiom,
    ( a = c
    | b = d ) ).

fof(pel48,conjecture,
    ( a = d
    | b = c ) ).

fof(subgoal_0,plain,
    ( a != d
   => b = c ),
    inference(strip,[],[pel48]) ).

fof(negate_0_0,plain,
    ~ ( a != d
     => b = c ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( a = c
    | b = d ),
    inference(canonicalize,[],[pel48_2]) ).

fof(normalize_0_1,plain,
    ( a != d
    & b != c ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_2,plain,
    a != d,
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ( a = b
    | c = d ),
    inference(canonicalize,[],[pel48_1]) ).

fof(normalize_0_4,plain,
    b != c,
    inference(conjunct,[],[normalize_0_1]) ).

cnf(refute_0_0,plain,
    ( a = c
    | b = d ),
    inference(canonicalize,[],[normalize_0_0]) ).

cnf(refute_0_1,plain,
    a != d,
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_2,plain,
    ( a = b
    | c = d ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_3,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_4,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_5,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( c != d
    | d = c ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(c)),bind(Y,$fot(d))]]) ).

cnf(refute_0_7,plain,
    ( a = b
    | d = c ),
    inference(resolve,[$cnf( $equal(c,d) )],[refute_0_2,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( a != c
    | d != c
    | a = d ),
    introduced(tautology,[equality,[$cnf( ~ $equal(a,d) ),[1],$fot(c)]]) ).

cnf(refute_0_9,plain,
    ( a != c
    | a = b
    | a = d ),
    inference(resolve,[$cnf( $equal(d,c) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( a != c
    | a = b ),
    inference(resolve,[$cnf( $equal(a,d) )],[refute_0_9,refute_0_1]) ).

cnf(refute_0_11,plain,
    ( b != d
    | d = b ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(b)),bind(Y,$fot(d))]]) ).

cnf(refute_0_12,plain,
    ( a = c
    | d = b ),
    inference(resolve,[$cnf( $equal(b,d) )],[refute_0_0,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( c != d
    | d != b
    | c = b ),
    introduced(tautology,[equality,[$cnf( ~ $equal(c,b) ),[0],$fot(d)]]) ).

cnf(refute_0_14,plain,
    ( c != d
    | a = c
    | c = b ),
    inference(resolve,[$cnf( $equal(d,b) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( a = b
    | a = c
    | c = b ),
    inference(resolve,[$cnf( $equal(c,d) )],[refute_0_2,refute_0_14]) ).

cnf(refute_0_16,plain,
    b != c,
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_17,plain,
    ( c != b
    | b = c ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(c)),bind(Y,$fot(b))]]) ).

cnf(refute_0_18,plain,
    c != b,
    inference(resolve,[$cnf( $equal(b,c) )],[refute_0_17,refute_0_16]) ).

cnf(refute_0_19,plain,
    ( a = b
    | a = c ),
    inference(resolve,[$cnf( $equal(c,b) )],[refute_0_15,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( a != c
    | c = a ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(a)),bind(Y,$fot(c))]]) ).

cnf(refute_0_21,plain,
    ( a = b
    | c = a ),
    inference(resolve,[$cnf( $equal(a,c) )],[refute_0_19,refute_0_20]) ).

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

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

cnf(refute_0_24,plain,
    ( a != a
    | a = b ),
    inference(resolve,[$cnf( $equal(a,c) )],[refute_0_23,refute_0_10]) ).

cnf(refute_0_25,plain,
    a = a,
    introduced(tautology,[refl,[$fot(a)]]) ).

cnf(refute_0_26,plain,
    a = b,
    inference(resolve,[$cnf( $equal(a,a) )],[refute_0_25,refute_0_24]) ).

cnf(refute_0_27,plain,
    ( a != b
    | b = a ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).

cnf(refute_0_28,plain,
    b = a,
    inference(resolve,[$cnf( $equal(a,b) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    ( b != a
    | b != d
    | a = d ),
    introduced(tautology,[equality,[$cnf( $equal(b,d) ),[0],$fot(a)]]) ).

cnf(refute_0_30,plain,
    ( b != d
    | a = d ),
    inference(resolve,[$cnf( $equal(b,a) )],[refute_0_28,refute_0_29]) ).

cnf(refute_0_31,plain,
    ( a = c
    | a = d ),
    inference(resolve,[$cnf( $equal(b,d) )],[refute_0_0,refute_0_30]) ).

cnf(refute_0_32,plain,
    ( a != c
    | b != a
    | b = c ),
    introduced(tautology,[equality,[$cnf( $equal(b,a) ),[1],$fot(c)]]) ).

cnf(refute_0_33,plain,
    ( a != c
    | b = c ),
    inference(resolve,[$cnf( $equal(b,a) )],[refute_0_28,refute_0_32]) ).

cnf(refute_0_34,plain,
    a != c,
    inference(resolve,[$cnf( $equal(b,c) )],[refute_0_33,refute_0_16]) ).

cnf(refute_0_35,plain,
    a = d,
    inference(resolve,[$cnf( $equal(a,c) )],[refute_0_31,refute_0_34]) ).

cnf(refute_0_36,plain,
    $false,
    inference(resolve,[$cnf( $equal(a,d) )],[refute_0_35,refute_0_1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN071+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n022.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 : Mon Jul 11 16:01:25 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34  
% 0.12/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.34  
%------------------------------------------------------------------------------