TSTP Solution File: LCL250-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL250-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n024.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 12:51:08 EDT 2022

% Result   : Unsatisfiable 105.35s 105.55s
% Output   : CNFRefutation 105.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   56 (  30 unt;   0 nHn;  27 RR)
%            Number of literals    :   90 (   0 equ;  35 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-1 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  150 (   6 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
    axiom(or(not(or(A,A)),A)) ).

cnf(axiom_1_3,axiom,
    axiom(or(not(A),or(B,A))) ).

cnf(axiom_1_4,axiom,
    axiom(or(not(or(A,B)),or(B,A))) ).

cnf(axiom_1_5,axiom,
    axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) ).

cnf(axiom_1_6,axiom,
    axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) ).

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

cnf(rule_2,axiom,
    ( theorem(X)
    | ~ axiom(or(not(Y),X))
    | ~ theorem(Y) ) ).

cnf(rule_3,axiom,
    ( theorem(or(not(X),Z))
    | ~ axiom(or(not(X),Y))
    | ~ theorem(or(not(Y),Z)) ) ).

cnf(prove_this,negated_conjecture,
    ~ theorem(or(not(or(not(q),r)),or(not(not(or(not(p),not(q)))),r))) ).

cnf(refute_0_0,plain,
    ( ~ axiom(or(not(or(A,B)),or(B,A)))
    | ~ theorem(or(not(or(B,A)),X_322))
    | theorem(or(not(or(A,B)),X_322)) ),
    inference(subst,[],[rule_3:[bind(X,$fot(or(A,B))),bind(Y,$fot(or(B,A))),bind(Z,$fot(X_322))]]) ).

cnf(refute_0_1,plain,
    ( ~ theorem(or(not(or(B,A)),X_322))
    | theorem(or(not(or(A,B)),X_322)) ),
    inference(resolve,[$cnf( axiom(or(not(or(A,B)),or(B,A))) )],[axiom_1_4,refute_0_0]) ).

cnf(refute_0_2,plain,
    ( ~ theorem(or(not(or(X_154888,X_154887)),or(not(not(or(X_154886,X_154887))),X_154888)))
    | theorem(or(not(or(X_154887,X_154888)),or(not(not(or(X_154886,X_154887))),X_154888))) ),
    inference(subst,[],[refute_0_1:[bind(A,$fot(X_154887)),bind(B,$fot(X_154888)),bind(X_322,$fot(or(not(not(or(X_154886,X_154887))),X_154888)))]]) ).

cnf(refute_0_3,plain,
    axiom(or(not(X_320),or(B,X_320))),
    inference(subst,[],[axiom_1_3:[bind(A,$fot(X_320))]]) ).

cnf(refute_0_4,plain,
    ( ~ axiom(or(not(X_320),or(B,X_320)))
    | ~ theorem(or(not(or(B,X_320)),X_322))
    | theorem(or(not(X_320),X_322)) ),
    inference(subst,[],[rule_3:[bind(X,$fot(X_320)),bind(Y,$fot(or(B,X_320))),bind(Z,$fot(X_322))]]) ).

cnf(refute_0_5,plain,
    ( ~ theorem(or(not(or(B,X_320)),X_322))
    | theorem(or(not(X_320),X_322)) ),
    inference(resolve,[$cnf( axiom(or(not(X_320),or(B,X_320))) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( ~ theorem(or(not(or(X_154864,or(X_154866,X_154865))),or(not(not(or(X_154864,X_154865))),X_154866)))
    | theorem(or(not(or(X_154866,X_154865)),or(not(not(or(X_154864,X_154865))),X_154866))) ),
    inference(subst,[],[refute_0_5:[bind(B,$fot(X_154864)),bind(X_320,$fot(or(X_154866,X_154865))),bind(X_322,$fot(or(not(not(or(X_154864,X_154865))),X_154866)))]]) ).

cnf(refute_0_7,plain,
    ( ~ axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
    | ~ theorem(or(A,or(B,C)))
    | theorem(or(B,or(A,C))) ),
    inference(subst,[],[rule_2:[bind(X,$fot(or(B,or(A,C)))),bind(Y,$fot(or(A,or(B,C))))]]) ).

cnf(refute_0_8,plain,
    ( ~ theorem(or(A,or(B,C)))
    | theorem(or(B,or(A,C))) ),
    inference(resolve,[$cnf( axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) )],[axiom_1_5,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( ~ theorem(or(not(not(or(X_154850,X_154851))),or(not(or(X_154850,or(X_154852,X_154851))),X_154852)))
    | theorem(or(not(or(X_154850,or(X_154852,X_154851))),or(not(not(or(X_154850,X_154851))),X_154852))) ),
    inference(subst,[],[refute_0_8:[bind(A,$fot(not(not(or(X_154850,X_154851))))),bind(B,$fot(not(or(X_154850,or(X_154852,X_154851))))),bind(C,$fot(X_154852))]]) ).

cnf(refute_0_10,plain,
    ( ~ theorem(or(not(or(X_154846,not(or(X_154844,X_154845)))),or(not(or(X_154844,or(X_154846,X_154845))),X_154846)))
    | theorem(or(not(not(or(X_154844,X_154845))),or(not(or(X_154844,or(X_154846,X_154845))),X_154846))) ),
    inference(subst,[],[refute_0_5:[bind(B,$fot(X_154846)),bind(X_320,$fot(not(or(X_154844,X_154845)))),bind(X_322,$fot(or(not(or(X_154844,or(X_154846,X_154845))),X_154846)))]]) ).

cnf(refute_0_11,plain,
    ( ~ theorem(or(not(or(not(or(X_154834,X_154835)),X_154836)),or(not(or(X_154834,or(X_154836,X_154835))),X_154836)))
    | theorem(or(not(or(X_154836,not(or(X_154834,X_154835)))),or(not(or(X_154834,or(X_154836,X_154835))),X_154836))) ),
    inference(subst,[],[refute_0_1:[bind(A,$fot(X_154836)),bind(B,$fot(not(or(X_154834,X_154835)))),bind(X_322,$fot(or(not(or(X_154834,or(X_154836,X_154835))),X_154836)))]]) ).

cnf(refute_0_12,plain,
    ( ~ axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B))))
    | ~ theorem(or(not(or(not(or(C,A)),or(C,B))),X_322))
    | theorem(or(not(or(not(A),B)),X_322)) ),
    inference(subst,[],[rule_3:[bind(X,$fot(or(not(A),B))),bind(Y,$fot(or(not(or(C,A)),or(C,B)))),bind(Z,$fot(X_322))]]) ).

cnf(refute_0_13,plain,
    ( ~ theorem(or(not(or(not(or(C,A)),or(C,B))),X_322))
    | theorem(or(not(or(not(A),B)),X_322)) ),
    inference(resolve,[$cnf( axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) )],[axiom_1_6,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( ~ theorem(or(not(or(not(or(X_154829,or(X_154826,X_154828))),or(X_154829,X_154829))),or(not(or(X_154826,or(X_154829,X_154828))),X_154829)))
    | theorem(or(not(or(not(or(X_154826,X_154828)),X_154829)),or(not(or(X_154826,or(X_154829,X_154828))),X_154829))) ),
    inference(subst,[],[refute_0_13:[bind(A,$fot(or(X_154826,X_154828))),bind(B,$fot(X_154829)),bind(C,$fot(X_154829)),bind(X_322,$fot(or(not(or(X_154826,or(X_154829,X_154828))),X_154829)))]]) ).

cnf(refute_0_15,plain,
    ( ~ theorem(or(not(or(X_49328,or(X_49329,X_49330))),or(not(or(not(or(X_49329,or(X_49328,X_49330))),or(X_49331,X_49331))),X_49331)))
    | theorem(or(not(or(not(or(X_49329,or(X_49328,X_49330))),or(X_49331,X_49331))),or(not(or(X_49328,or(X_49329,X_49330))),X_49331))) ),
    inference(subst,[],[refute_0_8:[bind(A,$fot(not(or(X_49328,or(X_49329,X_49330))))),bind(B,$fot(not(or(not(or(X_49329,or(X_49328,X_49330))),or(X_49331,X_49331))))),bind(C,$fot(X_49331))]]) ).

cnf(refute_0_16,plain,
    ( ~ theorem(or(not(or(X_553,or(X_552,X_552))),or(X_553,X_552)))
    | theorem(or(X_553,or(not(or(X_553,or(X_552,X_552))),X_552))) ),
    inference(subst,[],[refute_0_8:[bind(A,$fot(not(or(X_553,or(X_552,X_552))))),bind(B,$fot(X_553)),bind(C,$fot(X_552))]]) ).

cnf(refute_0_17,plain,
    ( ~ axiom(or(not(or(A,A)),A))
    | theorem(or(not(or(A,A)),A)) ),
    inference(subst,[],[rule_1:[bind(X,$fot(or(not(or(A,A)),A)))]]) ).

cnf(refute_0_18,plain,
    theorem(or(not(or(A,A)),A)),
    inference(resolve,[$cnf( axiom(or(not(or(A,A)),A)) )],[axiom_1_2,refute_0_17]) ).

cnf(refute_0_19,plain,
    theorem(or(not(or(X_548,X_548)),X_548)),
    inference(subst,[],[refute_0_18:[bind(A,$fot(X_548))]]) ).

cnf(refute_0_20,plain,
    ( ~ axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B))))
    | ~ theorem(or(not(A),B))
    | theorem(or(not(or(C,A)),or(C,B))) ),
    inference(subst,[],[rule_2:[bind(X,$fot(or(not(or(C,A)),or(C,B)))),bind(Y,$fot(or(not(A),B)))]]) ).

cnf(refute_0_21,plain,
    ( ~ theorem(or(not(A),B))
    | theorem(or(not(or(C,A)),or(C,B))) ),
    inference(resolve,[$cnf( axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) )],[axiom_1_6,refute_0_20]) ).

cnf(refute_0_22,plain,
    ( ~ theorem(or(not(or(X_548,X_548)),X_548))
    | theorem(or(not(or(X_549,or(X_548,X_548))),or(X_549,X_548))) ),
    inference(subst,[],[refute_0_21:[bind(A,$fot(or(X_548,X_548))),bind(B,$fot(X_548)),bind(C,$fot(X_549))]]) ).

cnf(refute_0_23,plain,
    theorem(or(not(or(X_549,or(X_548,X_548))),or(X_549,X_548))),
    inference(resolve,[$cnf( theorem(or(not(or(X_548,X_548)),X_548)) )],[refute_0_19,refute_0_22]) ).

cnf(refute_0_24,plain,
    theorem(or(not(or(X_553,or(X_552,X_552))),or(X_553,X_552))),
    inference(subst,[],[refute_0_23:[bind(X_548,$fot(X_552)),bind(X_549,$fot(X_553))]]) ).

cnf(refute_0_25,plain,
    theorem(or(X_553,or(not(or(X_553,or(X_552,X_552))),X_552))),
    inference(resolve,[$cnf( theorem(or(not(or(X_553,or(X_552,X_552))),or(X_553,X_552))) )],[refute_0_24,refute_0_16]) ).

cnf(refute_0_26,plain,
    theorem(or(not(or(X_1179,or(X_1178,X_1180))),or(not(or(not(or(X_1179,or(X_1178,X_1180))),or(X_552,X_552))),X_552))),
    inference(subst,[],[refute_0_25:[bind(X_553,$fot(not(or(X_1179,or(X_1178,X_1180)))))]]) ).

cnf(refute_0_27,plain,
    ( ~ axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
    | ~ theorem(or(not(or(B,or(A,C))),X_322))
    | theorem(or(not(or(A,or(B,C))),X_322)) ),
    inference(subst,[],[rule_3:[bind(X,$fot(or(A,or(B,C)))),bind(Y,$fot(or(B,or(A,C)))),bind(Z,$fot(X_322))]]) ).

cnf(refute_0_28,plain,
    ( ~ theorem(or(not(or(B,or(A,C))),X_322))
    | theorem(or(not(or(A,or(B,C))),X_322)) ),
    inference(resolve,[$cnf( axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) )],[axiom_1_5,refute_0_27]) ).

cnf(refute_0_29,plain,
    ( ~ theorem(or(not(or(X_1179,or(X_1178,X_1180))),or(not(or(not(or(X_1179,or(X_1178,X_1180))),or(X_552,X_552))),X_552)))
    | theorem(or(not(or(X_1178,or(X_1179,X_1180))),or(not(or(not(or(X_1179,or(X_1178,X_1180))),or(X_552,X_552))),X_552))) ),
    inference(subst,[],[refute_0_28:[bind(A,$fot(X_1178)),bind(B,$fot(X_1179)),bind(C,$fot(X_1180)),bind(X_322,$fot(or(not(or(not(or(X_1179,or(X_1178,X_1180))),or(X_552,X_552))),X_552)))]]) ).

cnf(refute_0_30,plain,
    theorem(or(not(or(X_1178,or(X_1179,X_1180))),or(not(or(not(or(X_1179,or(X_1178,X_1180))),or(X_552,X_552))),X_552))),
    inference(resolve,[$cnf( theorem(or(not(or(X_1179,or(X_1178,X_1180))),or(not(or(not(or(X_1179,or(X_1178,X_1180))),or(X_552,X_552))),X_552))) )],[refute_0_26,refute_0_29]) ).

cnf(refute_0_31,plain,
    theorem(or(not(or(X_49328,or(X_49329,X_49330))),or(not(or(not(or(X_49329,or(X_49328,X_49330))),or(X_49331,X_49331))),X_49331))),
    inference(subst,[],[refute_0_30:[bind(X_1178,$fot(X_49328)),bind(X_1179,$fot(X_49329)),bind(X_1180,$fot(X_49330)),bind(X_552,$fot(X_49331))]]) ).

cnf(refute_0_32,plain,
    theorem(or(not(or(not(or(X_49329,or(X_49328,X_49330))),or(X_49331,X_49331))),or(not(or(X_49328,or(X_49329,X_49330))),X_49331))),
    inference(resolve,[$cnf( theorem(or(not(or(X_49328,or(X_49329,X_49330))),or(not(or(not(or(X_49329,or(X_49328,X_49330))),or(X_49331,X_49331))),X_49331))) )],[refute_0_31,refute_0_15]) ).

cnf(refute_0_33,plain,
    theorem(or(not(or(not(or(X_154829,or(X_154826,X_154828))),or(X_154829,X_154829))),or(not(or(X_154826,or(X_154829,X_154828))),X_154829))),
    inference(subst,[],[refute_0_32:[bind(X_49328,$fot(X_154826)),bind(X_49329,$fot(X_154829)),bind(X_49330,$fot(X_154828)),bind(X_49331,$fot(X_154829))]]) ).

cnf(refute_0_34,plain,
    theorem(or(not(or(not(or(X_154826,X_154828)),X_154829)),or(not(or(X_154826,or(X_154829,X_154828))),X_154829))),
    inference(resolve,[$cnf( theorem(or(not(or(not(or(X_154829,or(X_154826,X_154828))),or(X_154829,X_154829))),or(not(or(X_154826,or(X_154829,X_154828))),X_154829))) )],[refute_0_33,refute_0_14]) ).

cnf(refute_0_35,plain,
    theorem(or(not(or(not(or(X_154834,X_154835)),X_154836)),or(not(or(X_154834,or(X_154836,X_154835))),X_154836))),
    inference(subst,[],[refute_0_34:[bind(X_154826,$fot(X_154834)),bind(X_154828,$fot(X_154835)),bind(X_154829,$fot(X_154836))]]) ).

cnf(refute_0_36,plain,
    theorem(or(not(or(X_154836,not(or(X_154834,X_154835)))),or(not(or(X_154834,or(X_154836,X_154835))),X_154836))),
    inference(resolve,[$cnf( theorem(or(not(or(not(or(X_154834,X_154835)),X_154836)),or(not(or(X_154834,or(X_154836,X_154835))),X_154836))) )],[refute_0_35,refute_0_11]) ).

cnf(refute_0_37,plain,
    theorem(or(not(or(X_154846,not(or(X_154844,X_154845)))),or(not(or(X_154844,or(X_154846,X_154845))),X_154846))),
    inference(subst,[],[refute_0_36:[bind(X_154834,$fot(X_154844)),bind(X_154835,$fot(X_154845)),bind(X_154836,$fot(X_154846))]]) ).

cnf(refute_0_38,plain,
    theorem(or(not(not(or(X_154844,X_154845))),or(not(or(X_154844,or(X_154846,X_154845))),X_154846))),
    inference(resolve,[$cnf( theorem(or(not(or(X_154846,not(or(X_154844,X_154845)))),or(not(or(X_154844,or(X_154846,X_154845))),X_154846))) )],[refute_0_37,refute_0_10]) ).

cnf(refute_0_39,plain,
    theorem(or(not(not(or(X_154850,X_154851))),or(not(or(X_154850,or(X_154852,X_154851))),X_154852))),
    inference(subst,[],[refute_0_38:[bind(X_154844,$fot(X_154850)),bind(X_154845,$fot(X_154851)),bind(X_154846,$fot(X_154852))]]) ).

cnf(refute_0_40,plain,
    theorem(or(not(or(X_154850,or(X_154852,X_154851))),or(not(not(or(X_154850,X_154851))),X_154852))),
    inference(resolve,[$cnf( theorem(or(not(not(or(X_154850,X_154851))),or(not(or(X_154850,or(X_154852,X_154851))),X_154852))) )],[refute_0_39,refute_0_9]) ).

cnf(refute_0_41,plain,
    theorem(or(not(or(X_154864,or(X_154866,X_154865))),or(not(not(or(X_154864,X_154865))),X_154866))),
    inference(subst,[],[refute_0_40:[bind(X_154850,$fot(X_154864)),bind(X_154851,$fot(X_154865)),bind(X_154852,$fot(X_154866))]]) ).

cnf(refute_0_42,plain,
    theorem(or(not(or(X_154866,X_154865)),or(not(not(or(X_154864,X_154865))),X_154866))),
    inference(resolve,[$cnf( theorem(or(not(or(X_154864,or(X_154866,X_154865))),or(not(not(or(X_154864,X_154865))),X_154866))) )],[refute_0_41,refute_0_6]) ).

cnf(refute_0_43,plain,
    theorem(or(not(or(X_154888,X_154887)),or(not(not(or(X_154886,X_154887))),X_154888))),
    inference(subst,[],[refute_0_42:[bind(X_154864,$fot(X_154886)),bind(X_154865,$fot(X_154887)),bind(X_154866,$fot(X_154888))]]) ).

cnf(refute_0_44,plain,
    theorem(or(not(or(X_154887,X_154888)),or(not(not(or(X_154886,X_154887))),X_154888))),
    inference(resolve,[$cnf( theorem(or(not(or(X_154888,X_154887)),or(not(not(or(X_154886,X_154887))),X_154888))) )],[refute_0_43,refute_0_2]) ).

cnf(refute_0_45,plain,
    theorem(or(not(or(not(q),r)),or(not(not(or(not(p),not(q)))),r))),
    inference(subst,[],[refute_0_44:[bind(X_154886,$fot(not(p))),bind(X_154887,$fot(not(q))),bind(X_154888,$fot(r))]]) ).

cnf(refute_0_46,plain,
    $false,
    inference(resolve,[$cnf( theorem(or(not(or(not(q),r)),or(not(not(or(not(p),not(q)))),r))) )],[refute_0_45,prove_this]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : LCL250-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.07/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n024.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 : Sun Jul  3 04:02:15 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 105.35/105.55  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 105.35/105.55  
% 105.35/105.55  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 105.35/105.56  
%------------------------------------------------------------------------------