TSTP Solution File: LCL173-3 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL173-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n003.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 : Sun Jul 17 12:50:12 EDT 2022

% Result   : Unsatisfiable 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   33 (  19 unt;   0 nHn;  16 RR)
%            Number of literals    :   52 (  31 equ;  20 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   77 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(axiom_1_6,axiom,
    axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ).

cnf(implies_definition,axiom,
    implies(X,Y) = or(not(X),Y) ).

cnf(rule_1,axiom,
    ( theorem(X)
    | ~ axiom(X) ) ).

cnf(prove_this,negated_conjecture,
    ~ theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))) ).

cnf(refute_0_0,plain,
    ( ~ axiom(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26))))
    | theorem(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26)))) ),
    inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26)))))]]) ).

cnf(refute_0_1,plain,
    axiom(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26)))),
    inference(subst,[],[axiom_1_6:[bind(A,$fot(X_25)),bind(B,$fot(X_26)),bind(C,$fot(X_27))]]) ).

cnf(refute_0_2,plain,
    theorem(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26)))),
    inference(resolve,[$cnf( axiom(implies(implies(X_25,X_26),implies(or(X_27,X_25),or(X_27,X_26)))) )],[refute_0_1,refute_0_0]) ).

cnf(refute_0_3,plain,
    theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),or(not(X),X_47)))),
    inference(subst,[],[refute_0_2:[bind(X_25,$fot(X_46)),bind(X_26,$fot(X_47)),bind(X_27,$fot(not(X)))]]) ).

cnf(refute_0_4,plain,
    implies(X,X_47) = or(not(X),X_47),
    inference(subst,[],[implies_definition:[bind(Y,$fot(X_47))]]) ).

cnf(refute_0_5,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_6,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_7,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( implies(X,X_47) != or(not(X),X_47)
    | or(not(X),X_47) = implies(X,X_47) ),
    inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,X_47))),bind(Y0,$fot(or(not(X),X_47)))]]) ).

cnf(refute_0_9,plain,
    or(not(X),X_47) = implies(X,X_47),
    inference(resolve,[$cnf( $equal(implies(X,X_47),or(not(X),X_47)) )],[refute_0_4,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( or(not(X),X_47) != implies(X,X_47)
    | ~ theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),or(not(X),X_47))))
    | theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))) ),
    introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),or(not(X),X_47)))) ),[0,1,1],$fot(implies(X,X_47))]]) ).

cnf(refute_0_11,plain,
    ( ~ theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),or(not(X),X_47))))
    | theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))) ),
    inference(resolve,[$cnf( $equal(or(not(X),X_47),implies(X,X_47)) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))),
    inference(resolve,[$cnf( theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),or(not(X),X_47)))) )],[refute_0_3,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( implies(X,Y) != or(not(X),Y)
    | or(not(X),Y) = implies(X,Y) ),
    inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).

cnf(refute_0_14,plain,
    or(not(X),Y) = implies(X,Y),
    inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_13]) ).

cnf(refute_0_15,plain,
    or(not(X),X_46) = implies(X,X_46),
    inference(subst,[],[refute_0_14:[bind(Y,$fot(X_46))]]) ).

cnf(refute_0_16,plain,
    implies(or(not(X),X_46),implies(X,X_47)) = implies(or(not(X),X_46),implies(X,X_47)),
    introduced(tautology,[refl,[$fot(implies(or(not(X),X_46),implies(X,X_47)))]]) ).

cnf(refute_0_17,plain,
    ( implies(or(not(X),X_46),implies(X,X_47)) != implies(or(not(X),X_46),implies(X,X_47))
    | or(not(X),X_46) != implies(X,X_46)
    | implies(or(not(X),X_46),implies(X,X_47)) = implies(implies(X,X_46),implies(X,X_47)) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),X_46),implies(X,X_47)),implies(or(not(X),X_46),implies(X,X_47))) ),[1,0],$fot(implies(X,X_46))]]) ).

cnf(refute_0_18,plain,
    ( or(not(X),X_46) != implies(X,X_46)
    | implies(or(not(X),X_46),implies(X,X_47)) = implies(implies(X,X_46),implies(X,X_47)) ),
    inference(resolve,[$cnf( $equal(implies(or(not(X),X_46),implies(X,X_47)),implies(or(not(X),X_46),implies(X,X_47))) )],[refute_0_16,refute_0_17]) ).

cnf(refute_0_19,plain,
    implies(or(not(X),X_46),implies(X,X_47)) = implies(implies(X,X_46),implies(X,X_47)),
    inference(resolve,[$cnf( $equal(or(not(X),X_46),implies(X,X_46)) )],[refute_0_15,refute_0_18]) ).

cnf(refute_0_20,plain,
    implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))) = implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))),
    introduced(tautology,[refl,[$fot(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))))]]) ).

cnf(refute_0_21,plain,
    ( implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))) != implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))
    | implies(or(not(X),X_46),implies(X,X_47)) != implies(implies(X,X_46),implies(X,X_47))
    | implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))) = implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47))) ),
    introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))),implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))) ),[1,1],$fot(implies(implies(X,X_46),implies(X,X_47)))]]) ).

cnf(refute_0_22,plain,
    ( implies(or(not(X),X_46),implies(X,X_47)) != implies(implies(X,X_46),implies(X,X_47))
    | implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))) = implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47))) ),
    inference(resolve,[$cnf( $equal(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))),implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))) )],[refute_0_20,refute_0_21]) ).

cnf(refute_0_23,plain,
    implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))) = implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47))),
    inference(resolve,[$cnf( $equal(implies(or(not(X),X_46),implies(X,X_47)),implies(implies(X,X_46),implies(X,X_47))) )],[refute_0_19,refute_0_22]) ).

cnf(refute_0_24,plain,
    ( implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))) != implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47)))
    | ~ theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))))
    | theorem(implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47)))) ),
    introduced(tautology,[equality,[$cnf( theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))) ),[0],$fot(implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47))))]]) ).

cnf(refute_0_25,plain,
    ( ~ theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))))
    | theorem(implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47)))) ),
    inference(resolve,[$cnf( $equal(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47))),implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47)))) )],[refute_0_23,refute_0_24]) ).

cnf(refute_0_26,plain,
    theorem(implies(implies(X_46,X_47),implies(implies(X,X_46),implies(X,X_47)))),
    inference(resolve,[$cnf( theorem(implies(implies(X_46,X_47),implies(or(not(X),X_46),implies(X,X_47)))) )],[refute_0_12,refute_0_25]) ).

cnf(refute_0_27,plain,
    theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))),
    inference(subst,[],[refute_0_26:[bind(X,$fot(p)),bind(X_46,$fot(q)),bind(X_47,$fot(r))]]) ).

cnf(refute_0_28,plain,
    $false,
    inference(resolve,[$cnf( theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))) )],[refute_0_27,prove_this]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : LCL173-3 : TPTP v8.1.0. Released v2.3.0.
% 0.10/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n003.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 : Mon Jul  4 16:22:40 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35  
% 0.12/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36  
%------------------------------------------------------------------------------