TSTP Solution File: GRP702-11 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP702-11 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n012.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 : Sat Jul 16 10:50:20 EDT 2022

% Result   : Unsatisfiable 0.12s 0.36s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   17
% Syntax   : Number of clauses     :   40 (  20 unt;   0 nHn;  35 RR)
%            Number of literals    :   70 (  69 equ;  32 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   20 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(f02,axiom,
    ld(A,mult(A,B)) = B ).

cnf(f09,axiom,
    mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ).

cnf(f11,axiom,
    op_d = ld(A,mult(op_c,A)) ).

cnf(goal,negated_conjecture,
    mult(x0,mult(x1,op_d)) != mult(mult(x0,x1),op_d) ).

cnf(refute_0_0,plain,
    op_d = ld(op_c,mult(op_c,op_c)),
    inference(subst,[],[f11:[bind(A,$fot(op_c))]]) ).

cnf(refute_0_1,plain,
    ld(op_c,mult(op_c,op_c)) = op_c,
    inference(subst,[],[f02:[bind(A,$fot(op_c)),bind(B,$fot(op_c))]]) ).

cnf(refute_0_2,plain,
    ( ld(op_c,mult(op_c,op_c)) != op_c
    | op_d != ld(op_c,mult(op_c,op_c))
    | op_d = op_c ),
    introduced(tautology,[equality,[$cnf( $equal(op_d,ld(op_c,mult(op_c,op_c))) ),[1],$fot(op_c)]]) ).

cnf(refute_0_3,plain,
    ( op_d != ld(op_c,mult(op_c,op_c))
    | op_d = op_c ),
    inference(resolve,[$cnf( $equal(ld(op_c,mult(op_c,op_c)),op_c) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    op_d = op_c,
    inference(resolve,[$cnf( $equal(op_d,ld(op_c,mult(op_c,op_c))) )],[refute_0_0,refute_0_3]) ).

cnf(refute_0_5,plain,
    mult(x1,op_d) = mult(x1,op_d),
    introduced(tautology,[refl,[$fot(mult(x1,op_d))]]) ).

cnf(refute_0_6,plain,
    ( mult(x1,op_d) != mult(x1,op_d)
    | op_d != op_c
    | mult(x1,op_d) = mult(x1,op_c) ),
    introduced(tautology,[equality,[$cnf( $equal(mult(x1,op_d),mult(x1,op_d)) ),[1,1],$fot(op_c)]]) ).

cnf(refute_0_7,plain,
    ( op_d != op_c
    | mult(x1,op_d) = mult(x1,op_c) ),
    inference(resolve,[$cnf( $equal(mult(x1,op_d),mult(x1,op_d)) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    mult(x1,op_d) = mult(x1,op_c),
    inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_0_4,refute_0_7]) ).

cnf(refute_0_9,plain,
    mult(x0,mult(x1,op_d)) = mult(x0,mult(x1,op_d)),
    introduced(tautology,[refl,[$fot(mult(x0,mult(x1,op_d)))]]) ).

cnf(refute_0_10,plain,
    ( mult(x0,mult(x1,op_d)) != mult(x0,mult(x1,op_d))
    | mult(x1,op_d) != mult(x1,op_c)
    | mult(x0,mult(x1,op_d)) = mult(x0,mult(x1,op_c)) ),
    introduced(tautology,[equality,[$cnf( $equal(mult(x0,mult(x1,op_d)),mult(x0,mult(x1,op_d))) ),[1,1],$fot(mult(x1,op_c))]]) ).

cnf(refute_0_11,plain,
    ( mult(x1,op_d) != mult(x1,op_c)
    | mult(x0,mult(x1,op_d)) = mult(x0,mult(x1,op_c)) ),
    inference(resolve,[$cnf( $equal(mult(x0,mult(x1,op_d)),mult(x0,mult(x1,op_d))) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    mult(x0,mult(x1,op_d)) = mult(x0,mult(x1,op_c)),
    inference(resolve,[$cnf( $equal(mult(x1,op_d),mult(x1,op_c)) )],[refute_0_8,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( mult(x0,mult(x1,op_c)) != mult(mult(x0,x1),op_d)
    | mult(x0,mult(x1,op_d)) != mult(x0,mult(x1,op_c))
    | mult(x0,mult(x1,op_d)) = mult(mult(x0,x1),op_d) ),
    introduced(tautology,[equality,[$cnf( $equal(mult(x0,mult(x1,op_d)),mult(x0,mult(x1,op_c))) ),[1],$fot(mult(mult(x0,x1),op_d))]]) ).

cnf(refute_0_14,plain,
    ( mult(x0,mult(x1,op_c)) != mult(mult(x0,x1),op_d)
    | mult(x0,mult(x1,op_d)) = mult(mult(x0,x1),op_d) ),
    inference(resolve,[$cnf( $equal(mult(x0,mult(x1,op_d)),mult(x0,mult(x1,op_c))) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_16,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_17,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_15,refute_0_16]) ).

cnf(refute_0_18,plain,
    ( mult(A,mult(B,op_c)) != mult(mult(A,B),op_c)
    | mult(mult(A,B),op_c) = mult(A,mult(B,op_c)) ),
    inference(subst,[],[refute_0_17:[bind(X,$fot(mult(A,mult(B,op_c)))),bind(Y,$fot(mult(mult(A,B),op_c)))]]) ).

cnf(refute_0_19,plain,
    mult(mult(A,B),op_c) = mult(A,mult(B,op_c)),
    inference(resolve,[$cnf( $equal(mult(A,mult(B,op_c)),mult(mult(A,B),op_c)) )],[f09,refute_0_18]) ).

cnf(refute_0_20,plain,
    mult(mult(x0,x1),op_c) = mult(x0,mult(x1,op_c)),
    inference(subst,[],[refute_0_19:[bind(A,$fot(x0)),bind(B,$fot(x1))]]) ).

cnf(refute_0_21,plain,
    mult(mult(x0,x1),op_d) = mult(mult(x0,x1),op_d),
    introduced(tautology,[refl,[$fot(mult(mult(x0,x1),op_d))]]) ).

cnf(refute_0_22,plain,
    ( mult(mult(x0,x1),op_d) != mult(mult(x0,x1),op_d)
    | op_d != op_c
    | mult(mult(x0,x1),op_d) = mult(mult(x0,x1),op_c) ),
    introduced(tautology,[equality,[$cnf( $equal(mult(mult(x0,x1),op_d),mult(mult(x0,x1),op_d)) ),[1,1],$fot(op_c)]]) ).

cnf(refute_0_23,plain,
    ( op_d != op_c
    | mult(mult(x0,x1),op_d) = mult(mult(x0,x1),op_c) ),
    inference(resolve,[$cnf( $equal(mult(mult(x0,x1),op_d),mult(mult(x0,x1),op_d)) )],[refute_0_21,refute_0_22]) ).

cnf(refute_0_24,plain,
    mult(mult(x0,x1),op_d) = mult(mult(x0,x1),op_c),
    inference(resolve,[$cnf( $equal(op_d,op_c) )],[refute_0_4,refute_0_23]) ).

cnf(refute_0_25,plain,
    ( Y != X
    | Y != Z
    | X = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).

cnf(refute_0_26,plain,
    ( X != Y
    | Y != Z
    | X = Z ),
    inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_17,refute_0_25]) ).

cnf(refute_0_27,plain,
    ( mult(mult(x0,x1),op_c) != mult(x0,mult(x1,op_c))
    | mult(mult(x0,x1),op_d) != mult(mult(x0,x1),op_c)
    | mult(mult(x0,x1),op_d) = mult(x0,mult(x1,op_c)) ),
    inference(subst,[],[refute_0_26:[bind(X,$fot(mult(mult(x0,x1),op_d))),bind(Y,$fot(mult(mult(x0,x1),op_c))),bind(Z,$fot(mult(x0,mult(x1,op_c))))]]) ).

cnf(refute_0_28,plain,
    ( mult(mult(x0,x1),op_c) != mult(x0,mult(x1,op_c))
    | mult(mult(x0,x1),op_d) = mult(x0,mult(x1,op_c)) ),
    inference(resolve,[$cnf( $equal(mult(mult(x0,x1),op_d),mult(mult(x0,x1),op_c)) )],[refute_0_24,refute_0_27]) ).

cnf(refute_0_29,plain,
    mult(mult(x0,x1),op_d) = mult(x0,mult(x1,op_c)),
    inference(resolve,[$cnf( $equal(mult(mult(x0,x1),op_c),mult(x0,mult(x1,op_c))) )],[refute_0_20,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( mult(mult(x0,x1),op_d) != mult(x0,mult(x1,op_c))
    | mult(x0,mult(x1,op_c)) != mult(x0,mult(x1,op_c))
    | mult(x0,mult(x1,op_c)) = mult(mult(x0,x1),op_d) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(mult(x0,mult(x1,op_c)),mult(mult(x0,x1),op_d)) ),[1],$fot(mult(x0,mult(x1,op_c)))]]) ).

cnf(refute_0_31,plain,
    ( mult(x0,mult(x1,op_c)) != mult(x0,mult(x1,op_c))
    | mult(x0,mult(x1,op_c)) = mult(mult(x0,x1),op_d) ),
    inference(resolve,[$cnf( $equal(mult(mult(x0,x1),op_d),mult(x0,mult(x1,op_c))) )],[refute_0_29,refute_0_30]) ).

cnf(refute_0_32,plain,
    ( mult(x0,mult(x1,op_c)) != mult(x0,mult(x1,op_c))
    | mult(x0,mult(x1,op_d)) = mult(mult(x0,x1),op_d) ),
    inference(resolve,[$cnf( $equal(mult(x0,mult(x1,op_c)),mult(mult(x0,x1),op_d)) )],[refute_0_31,refute_0_14]) ).

cnf(refute_0_33,plain,
    mult(x0,mult(x1,op_c)) != mult(x0,mult(x1,op_c)),
    inference(resolve,[$cnf( $equal(mult(x0,mult(x1,op_d)),mult(mult(x0,x1),op_d)) )],[refute_0_32,goal]) ).

cnf(refute_0_34,plain,
    mult(x0,mult(x1,op_c)) = mult(x0,mult(x1,op_c)),
    introduced(tautology,[refl,[$fot(mult(x0,mult(x1,op_c)))]]) ).

cnf(refute_0_35,plain,
    $false,
    inference(resolve,[$cnf( $equal(mult(x0,mult(x1,op_c)),mult(x0,mult(x1,op_c))) )],[refute_0_34,refute_0_33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP702-11 : TPTP v8.1.0. Released v8.1.0.
% 0.06/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n012.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 Jun 14 05:25:10 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36  
% 0.12/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37  
%------------------------------------------------------------------------------