TSTP Solution File: LCL075-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL075-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n011.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 12:49:13 EDT 2022

% Result   : Unsatisfiable 1.05s 1.27s
% Output   : CNFRefutation 1.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    3
% Syntax   : Number of clauses     :   38 (  23 unt;   0 nHn;  16 RR)
%            Number of literals    :   57 (   0 equ;  20 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :  130 (  38 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
    ( ~ is_a_theorem(implies(X,Y))
    | ~ is_a_theorem(X)
    | is_a_theorem(Y) ) ).

cnf(cn_CAMerideth,axiom,
    is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(not(Z),not(U))),Z),V),implies(implies(V,X),implies(U,X)))) ).

cnf(prove_cn_3,negated_conjecture,
    ~ is_a_theorem(implies(a,implies(not(a),b))) ).

cnf(refute_0_0,plain,
    ( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6),X_3))
    | ~ is_a_theorem(implies(implies(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6),X_3),implies(implies(X_3,X_4),implies(X_2,X_4))))
    | is_a_theorem(implies(implies(X_3,X_4),implies(X_2,X_4))) ),
    inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6),X_3))),bind(Y,$fot(implies(implies(X_3,X_4),implies(X_2,X_4))))]]) ).

cnf(refute_0_1,plain,
    is_a_theorem(implies(implies(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6),X_3),implies(implies(X_3,X_4),implies(X_2,X_4)))),
    inference(subst,[],[cn_CAMerideth:[bind(U,$fot(X_2)),bind(V,$fot(X_3)),bind(X,$fot(X_4)),bind(Y,$fot(X_5)),bind(Z,$fot(X_6))]]) ).

cnf(refute_0_2,plain,
    ( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6),X_3))
    | is_a_theorem(implies(implies(X_3,X_4),implies(X_2,X_4))) ),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6),X_3),implies(implies(X_3,X_4),implies(X_2,X_4)))) )],[refute_0_1,refute_0_0]) ).

cnf(refute_0_3,plain,
    ( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_115),not(X_115))),X_115),implies(X_112,X_115)))
    | is_a_theorem(implies(implies(implies(X_112,X_115),X_4),implies(X_115,X_4))) ),
    inference(subst,[],[refute_0_2:[bind(X_2,$fot(X_115)),bind(X_3,$fot(implies(X_112,X_115))),bind(X_6,$fot(X_115))]]) ).

cnf(refute_0_4,plain,
    ( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6),implies(X_31,implies(X_30,X_30))))
    | is_a_theorem(implies(implies(implies(X_31,implies(X_30,X_30)),X_4),implies(X_2,X_4))) ),
    inference(subst,[],[refute_0_2:[bind(X_3,$fot(implies(X_31,implies(X_30,X_30))))]]) ).

cnf(refute_0_5,plain,
    ( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_18),not(X_2))),X_18),implies(X_18,X_18)))
    | is_a_theorem(implies(implies(implies(X_18,X_18),X_4),implies(X_2,X_4))) ),
    inference(subst,[],[refute_0_2:[bind(X_3,$fot(implies(X_18,X_18))),bind(X_6,$fot(X_18))]]) ).

cnf(refute_0_6,plain,
    ( ~ is_a_theorem(implies(implies(implies(implies(X_15,not(X_2)),implies(not(implies(not(X_2),X_14)),not(X_2))),implies(not(X_2),X_14)),implies(X_16,implies(not(X_2),X_14))))
    | is_a_theorem(implies(implies(implies(X_16,implies(not(X_2),X_14)),X_15),implies(X_2,X_15))) ),
    inference(subst,[],[refute_0_2:[bind(X_3,$fot(implies(X_16,implies(not(X_2),X_14)))),bind(X_4,$fot(X_15)),bind(X_5,$fot(not(X_2))),bind(X_6,$fot(implies(not(X_2),X_14)))]]) ).

cnf(refute_0_7,plain,
    is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(not(implies(not(X_11),not(X_7))),not(U))),implies(not(X_11),not(X_7))),X_11),implies(implies(X_11,X),implies(U,X)))),
    inference(subst,[],[cn_CAMerideth:[bind(V,$fot(X_11)),bind(Z,$fot(implies(not(X_11),not(X_7))))]]) ).

cnf(refute_0_8,plain,
    ( ~ is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(not(implies(not(X_11),not(X_7))),not(U))),implies(not(X_11),not(X_7))),X_11),implies(implies(X_11,X),implies(U,X))))
    | is_a_theorem(implies(implies(implies(implies(X_11,X),implies(U,X)),implies(X,Y)),implies(X_7,implies(X,Y)))) ),
    inference(subst,[],[refute_0_2:[bind(X_2,$fot(X_7)),bind(X_3,$fot(implies(implies(X_11,X),implies(U,X)))),bind(X_4,$fot(implies(X,Y))),bind(X_5,$fot(implies(not(implies(not(X_11),not(X_7))),not(U)))),bind(X_6,$fot(X_11))]]) ).

cnf(refute_0_9,plain,
    is_a_theorem(implies(implies(implies(implies(X_11,X),implies(U,X)),implies(X,Y)),implies(X_7,implies(X,Y)))),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(not(implies(not(X_11),not(X_7))),not(U))),implies(not(X_11),not(X_7))),X_11),implies(implies(X_11,X),implies(U,X)))) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    is_a_theorem(implies(implies(implies(implies(X_15,not(X_2)),implies(not(implies(not(X_2),X_14)),not(X_2))),implies(not(X_2),X_14)),implies(X_16,implies(not(X_2),X_14)))),
    inference(subst,[],[refute_0_9:[bind(U,$fot(not(implies(not(X_2),X_14)))),bind(X,$fot(not(X_2))),bind(Y,$fot(X_14)),bind(X_11,$fot(X_15)),bind(X_7,$fot(X_16))]]) ).

cnf(refute_0_11,plain,
    is_a_theorem(implies(implies(implies(X_16,implies(not(X_2),X_14)),X_15),implies(X_2,X_15))),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_15,not(X_2)),implies(not(implies(not(X_2),X_14)),not(X_2))),implies(not(X_2),X_14)),implies(X_16,implies(not(X_2),X_14)))) )],[refute_0_10,refute_0_6]) ).

cnf(refute_0_12,plain,
    is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_18),not(X_2))),X_18),implies(X_18,X_18))),
    inference(subst,[],[refute_0_11:[bind(X_14,$fot(not(X_2))),bind(X_15,$fot(X_18)),bind(X_16,$fot(implies(X_4,X_5))),bind(X_2,$fot(X_18))]]) ).

cnf(refute_0_13,plain,
    is_a_theorem(implies(implies(implies(X_18,X_18),X_4),implies(X_2,X_4))),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_18),not(X_2))),X_18),implies(X_18,X_18))) )],[refute_0_12,refute_0_5]) ).

cnf(refute_0_14,plain,
    is_a_theorem(implies(implies(implies(X_18,X_18),implies(X_18,X_18)),implies(X_2,implies(X_18,X_18)))),
    inference(subst,[],[refute_0_13:[bind(X_4,$fot(implies(X_18,X_18)))]]) ).

cnf(refute_0_15,plain,
    ( ~ is_a_theorem(implies(implies(X_21,X_21),X_23))
    | ~ is_a_theorem(implies(implies(implies(X_21,X_21),X_23),implies(X_22,X_23)))
    | is_a_theorem(implies(X_22,X_23)) ),
    inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_21,X_21),X_23))),bind(Y,$fot(implies(X_22,X_23)))]]) ).

cnf(refute_0_16,plain,
    is_a_theorem(implies(implies(implies(X_21,X_21),X_23),implies(X_22,X_23))),
    inference(subst,[],[refute_0_13:[bind(X_18,$fot(X_21)),bind(X_2,$fot(X_22)),bind(X_4,$fot(X_23))]]) ).

cnf(refute_0_17,plain,
    ( ~ is_a_theorem(implies(implies(X_21,X_21),X_23))
    | is_a_theorem(implies(X_22,X_23)) ),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_21,X_21),X_23),implies(X_22,X_23))) )],[refute_0_16,refute_0_15]) ).

cnf(refute_0_18,plain,
    ( ~ is_a_theorem(implies(implies(implies(X_18,X_18),implies(X_18,X_18)),implies(X_2,implies(X_18,X_18))))
    | is_a_theorem(implies(X_28,implies(X_2,implies(X_18,X_18)))) ),
    inference(subst,[],[refute_0_17:[bind(X_21,$fot(implies(X_18,X_18))),bind(X_22,$fot(X_28)),bind(X_23,$fot(implies(X_2,implies(X_18,X_18))))]]) ).

cnf(refute_0_19,plain,
    is_a_theorem(implies(X_28,implies(X_2,implies(X_18,X_18)))),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_18,X_18),implies(X_18,X_18)),implies(X_2,implies(X_18,X_18)))) )],[refute_0_14,refute_0_18]) ).

cnf(refute_0_20,plain,
    is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6),implies(X_31,implies(X_30,X_30)))),
    inference(subst,[],[refute_0_19:[bind(X_18,$fot(X_30)),bind(X_2,$fot(X_31)),bind(X_28,$fot(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6)))]]) ).

cnf(refute_0_21,plain,
    is_a_theorem(implies(implies(implies(X_31,implies(X_30,X_30)),X_4),implies(X_2,X_4))),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6),implies(X_31,implies(X_30,X_30)))) )],[refute_0_20,refute_0_4]) ).

cnf(refute_0_22,plain,
    is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_115),not(X_115))),X_115),implies(X_112,X_115))),
    inference(subst,[],[refute_0_21:[bind(X_2,$fot(X_112)),bind(X_30,$fot(not(X_115))),bind(X_31,$fot(implies(X_4,X_5))),bind(X_4,$fot(X_115))]]) ).

cnf(refute_0_23,plain,
    is_a_theorem(implies(implies(implies(X_112,X_115),X_4),implies(X_115,X_4))),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_115),not(X_115))),X_115),implies(X_112,X_115))) )],[refute_0_22,refute_0_3]) ).

cnf(refute_0_24,plain,
    is_a_theorem(implies(implies(implies(not(X_2200),not(X_2201)),X_2200),implies(not(X_2201),X_2200))),
    inference(subst,[],[refute_0_23:[bind(X_112,$fot(not(X_2200))),bind(X_115,$fot(not(X_2201))),bind(X_4,$fot(X_2200))]]) ).

cnf(refute_0_25,plain,
    ( ~ is_a_theorem(implies(implies(implies(implies(not(X_127),not(X_128)),X_127),X_129),implies(X_128,X_129)))
    | ~ is_a_theorem(implies(implies(implies(not(X_127),not(X_128)),X_127),X_129))
    | is_a_theorem(implies(X_128,X_129)) ),
    inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_127),not(X_128)),X_127),X_129))),bind(Y,$fot(implies(X_128,X_129)))]]) ).

cnf(refute_0_26,plain,
    ( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_118),not(X_2))),X_118),implies(implies(not(X_118),not(X_2)),X_118)))
    | is_a_theorem(implies(implies(implies(implies(not(X_118),not(X_2)),X_118),X_4),implies(X_2,X_4))) ),
    inference(subst,[],[refute_0_2:[bind(X_3,$fot(implies(implies(not(X_118),not(X_2)),X_118))),bind(X_6,$fot(X_118))]]) ).

cnf(refute_0_27,plain,
    is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_118),not(X_2))),X_118),implies(implies(not(X_118),not(X_2)),X_118))),
    inference(subst,[],[refute_0_23:[bind(X_112,$fot(implies(X_4,X_5))),bind(X_115,$fot(implies(not(X_118),not(X_2)))),bind(X_4,$fot(X_118))]]) ).

cnf(refute_0_28,plain,
    is_a_theorem(implies(implies(implies(implies(not(X_118),not(X_2)),X_118),X_4),implies(X_2,X_4))),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_118),not(X_2))),X_118),implies(implies(not(X_118),not(X_2)),X_118))) )],[refute_0_27,refute_0_26]) ).

cnf(refute_0_29,plain,
    is_a_theorem(implies(implies(implies(implies(not(X_127),not(X_128)),X_127),X_129),implies(X_128,X_129))),
    inference(subst,[],[refute_0_28:[bind(X_118,$fot(X_127)),bind(X_2,$fot(X_128)),bind(X_4,$fot(X_129))]]) ).

cnf(refute_0_30,plain,
    ( ~ is_a_theorem(implies(implies(implies(not(X_127),not(X_128)),X_127),X_129))
    | is_a_theorem(implies(X_128,X_129)) ),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_127),not(X_128)),X_127),X_129),implies(X_128,X_129))) )],[refute_0_29,refute_0_25]) ).

cnf(refute_0_31,plain,
    ( ~ is_a_theorem(implies(implies(implies(not(X_2200),not(X_2201)),X_2200),implies(not(X_2201),X_2200)))
    | is_a_theorem(implies(X_2201,implies(not(X_2201),X_2200))) ),
    inference(subst,[],[refute_0_30:[bind(X_127,$fot(X_2200)),bind(X_128,$fot(X_2201)),bind(X_129,$fot(implies(not(X_2201),X_2200)))]]) ).

cnf(refute_0_32,plain,
    is_a_theorem(implies(X_2201,implies(not(X_2201),X_2200))),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_2200),not(X_2201)),X_2200),implies(not(X_2201),X_2200))) )],[refute_0_24,refute_0_31]) ).

cnf(refute_0_33,plain,
    is_a_theorem(implies(a,implies(not(a),b))),
    inference(subst,[],[refute_0_32:[bind(X_2200,$fot(b)),bind(X_2201,$fot(a))]]) ).

cnf(refute_0_34,plain,
    $false,
    inference(resolve,[$cnf( is_a_theorem(implies(a,implies(not(a),b))) )],[refute_0_33,prove_cn_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : LCL075-1 : TPTP v8.1.0. Released v1.0.0.
% 0.02/0.09  % Command  : metis --show proof --show saturation %s
% 0.09/0.29  % Computer : n011.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 600
% 0.09/0.29  % DateTime : Sun Jul  3 16:00:35 EDT 2022
% 0.09/0.29  % CPUTime  : 
% 0.09/0.29  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.05/1.27  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.05/1.27  
% 1.05/1.27  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.05/1.27  
%------------------------------------------------------------------------------