TSTP Solution File: LCL171-3 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL171-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n023.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 12:50:10 EDT 2022

% Result   : Unsatisfiable 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   26 (  16 unt;   0 nHn;  13 RR)
%            Number of literals    :   39 (  17 equ;  14 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   44 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(axiom_1_4,axiom,
    axiom(implies(or(A,B),or(B,A))) ).

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(p,not(q)),implies(q,not(p)))) ).

cnf(refute_0_0,plain,
    ( ~ axiom(implies(or(X_7,X_8),or(X_8,X_7)))
    | theorem(implies(or(X_7,X_8),or(X_8,X_7))) ),
    inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_7,X_8),or(X_8,X_7))))]]) ).

cnf(refute_0_1,plain,
    axiom(implies(or(X_7,X_8),or(X_8,X_7))),
    inference(subst,[],[axiom_1_4:[bind(A,$fot(X_7)),bind(B,$fot(X_8))]]) ).

cnf(refute_0_2,plain,
    theorem(implies(or(X_7,X_8),or(X_8,X_7))),
    inference(resolve,[$cnf( axiom(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_1,refute_0_0]) ).

cnf(refute_0_3,plain,
    theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7))),
    inference(subst,[],[refute_0_2:[bind(X_8,$fot(not(X_11)))]]) ).

cnf(refute_0_4,plain,
    implies(X_11,X_7) = or(not(X_11),X_7),
    inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(X_7))]]) ).

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_11,X_7) != or(not(X_11),X_7)
    | or(not(X_11),X_7) = implies(X_11,X_7) ),
    inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X_11,X_7))),bind(Y0,$fot(or(not(X_11),X_7)))]]) ).

cnf(refute_0_9,plain,
    or(not(X_11),X_7) = implies(X_11,X_7),
    inference(resolve,[$cnf( $equal(implies(X_11,X_7),or(not(X_11),X_7)) )],[refute_0_4,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( or(not(X_11),X_7) != implies(X_11,X_7)
    | ~ theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7)))
    | theorem(implies(or(X_7,not(X_11)),implies(X_11,X_7))) ),
    introduced(tautology,[equality,[$cnf( theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7))) ),[0,1],$fot(implies(X_11,X_7))]]) ).

cnf(refute_0_11,plain,
    ( ~ theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7)))
    | theorem(implies(or(X_7,not(X_11)),implies(X_11,X_7))) ),
    inference(resolve,[$cnf( $equal(or(not(X_11),X_7),implies(X_11,X_7)) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    theorem(implies(or(X_7,not(X_11)),implies(X_11,X_7))),
    inference(resolve,[$cnf( theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7))) )],[refute_0_3,refute_0_11]) ).

cnf(refute_0_13,plain,
    theorem(implies(or(not(X),not(X_14)),implies(X_14,not(X)))),
    inference(subst,[],[refute_0_12:[bind(X_11,$fot(X_14)),bind(X_7,$fot(not(X)))]]) ).

cnf(refute_0_14,plain,
    implies(X,not(X_14)) = or(not(X),not(X_14)),
    inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_14)))]]) ).

cnf(refute_0_15,plain,
    ( implies(X,not(X_14)) != or(not(X),not(X_14))
    | or(not(X),not(X_14)) = implies(X,not(X_14)) ),
    inference(subst,[],[refute_0_7:[bind(X0,$fot(implies(X,not(X_14)))),bind(Y0,$fot(or(not(X),not(X_14))))]]) ).

cnf(refute_0_16,plain,
    or(not(X),not(X_14)) = implies(X,not(X_14)),
    inference(resolve,[$cnf( $equal(implies(X,not(X_14)),or(not(X),not(X_14))) )],[refute_0_14,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( or(not(X),not(X_14)) != implies(X,not(X_14))
    | ~ theorem(implies(or(not(X),not(X_14)),implies(X_14,not(X))))
    | theorem(implies(implies(X,not(X_14)),implies(X_14,not(X)))) ),
    introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),not(X_14)),implies(X_14,not(X)))) ),[0,0],$fot(implies(X,not(X_14)))]]) ).

cnf(refute_0_18,plain,
    ( ~ theorem(implies(or(not(X),not(X_14)),implies(X_14,not(X))))
    | theorem(implies(implies(X,not(X_14)),implies(X_14,not(X)))) ),
    inference(resolve,[$cnf( $equal(or(not(X),not(X_14)),implies(X,not(X_14))) )],[refute_0_16,refute_0_17]) ).

cnf(refute_0_19,plain,
    theorem(implies(implies(X,not(X_14)),implies(X_14,not(X)))),
    inference(resolve,[$cnf( theorem(implies(or(not(X),not(X_14)),implies(X_14,not(X)))) )],[refute_0_13,refute_0_18]) ).

cnf(refute_0_20,plain,
    theorem(implies(implies(p,not(q)),implies(q,not(p)))),
    inference(subst,[],[refute_0_19:[bind(X,$fot(p)),bind(X_14,$fot(q))]]) ).

cnf(refute_0_21,plain,
    $false,
    inference(resolve,[$cnf( theorem(implies(implies(p,not(q)),implies(q,not(p)))) )],[refute_0_20,prove_this]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : LCL171-3 : TPTP v8.1.0. Released v2.3.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n023.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 23:45:27 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
% 0.12/0.35  
%------------------------------------------------------------------------------