TSTP Solution File: LCL101-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL101-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n004.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 12:49:29 EDT 2022

% Result   : Unsatisfiable 0.19s 0.48s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   47 (  28 unt;   0 nHn;  19 RR)
%            Number of literals    :   71 (   0 equ;  25 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :  175 (   0 sgn)

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

cnf(lg_2,axiom,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),U),U)) ).

cnf(p_4,axiom,
    is_a_theorem(equivalent(X,equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X))) ).

cnf(prove_p_1,negated_conjecture,
    ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))) ).

cnf(refute_0_0,plain,
    ( ~ is_a_theorem(equivalent(equivalent(X_24,X_25),equivalent(X_24,X_26)))
    | ~ is_a_theorem(equivalent(equivalent(equivalent(X_24,X_25),equivalent(X_24,X_26)),equivalent(X_25,X_26)))
    | is_a_theorem(equivalent(X_25,X_26)) ),
    inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X_24,X_25),equivalent(X_24,X_26)))),bind(Y,$fot(equivalent(X_25,X_26)))]]) ).

cnf(refute_0_1,plain,
    ( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_3,X_4),equivalent(X_3,X_5)),equivalent(X_4,X_5)),X_2))
    | ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_3,X_4),equivalent(X_3,X_5)),equivalent(X_4,X_5)),X_2),X_2))
    | is_a_theorem(X_2) ),
    inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(equivalent(equivalent(X_3,X_4),equivalent(X_3,X_5)),equivalent(X_4,X_5)),X_2))),bind(Y,$fot(X_2))]]) ).

cnf(refute_0_2,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_3,X_4),equivalent(X_3,X_5)),equivalent(X_4,X_5)),X_2),X_2)),
    inference(subst,[],[lg_2:[bind(U,$fot(X_2)),bind(X,$fot(X_3)),bind(Y,$fot(X_4)),bind(Z,$fot(X_5))]]) ).

cnf(refute_0_3,plain,
    ( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_3,X_4),equivalent(X_3,X_5)),equivalent(X_4,X_5)),X_2))
    | is_a_theorem(X_2) ),
    inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_3,X_4),equivalent(X_3,X_5)),equivalent(X_4,X_5)),X_2),X_2)) )],[refute_0_2,refute_0_1]) ).

cnf(refute_0_4,plain,
    ( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_19,X_20),equivalent(X_19,X_18)),equivalent(X_20,X_18)),equivalent(equivalent(equivalent(X_21,X_22),equivalent(X_21,X_23)),equivalent(X_22,X_23))))
    | is_a_theorem(equivalent(equivalent(equivalent(X_21,X_22),equivalent(X_21,X_23)),equivalent(X_22,X_23))) ),
    inference(subst,[],[refute_0_3:[bind(X_2,$fot(equivalent(equivalent(equivalent(X_21,X_22),equivalent(X_21,X_23)),equivalent(X_22,X_23)))),bind(X_3,$fot(X_19)),bind(X_4,$fot(X_20)),bind(X_5,$fot(X_18))]]) ).

cnf(refute_0_5,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13))))),
    inference(subst,[],[p_4:[bind(X,$fot(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13))))]]) ).

cnf(refute_0_6,plain,
    ( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)))))
    | is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)))) ),
    inference(subst,[],[refute_0_3:[bind(X_2,$fot(equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13))))),bind(X_3,$fot(X_11)),bind(X_4,$fot(X_12)),bind(X_5,$fot(X_13))]]) ).

cnf(refute_0_7,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)))),
    inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13))))) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_19,X_20),equivalent(X_19,X_18)),equivalent(X_20,X_18)),equivalent(equivalent(equivalent(X_21,X_22),equivalent(X_21,X_23)),equivalent(X_22,X_23)))),
    inference(subst,[],[refute_0_7:[bind(U,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(X_20)),bind(X_11,$fot(X_21)),bind(X_12,$fot(X_22)),bind(X_13,$fot(X_23))]]) ).

cnf(refute_0_9,plain,
    is_a_theorem(equivalent(equivalent(equivalent(X_21,X_22),equivalent(X_21,X_23)),equivalent(X_22,X_23))),
    inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_19,X_20),equivalent(X_19,X_18)),equivalent(X_20,X_18)),equivalent(equivalent(equivalent(X_21,X_22),equivalent(X_21,X_23)),equivalent(X_22,X_23)))) )],[refute_0_8,refute_0_4]) ).

cnf(refute_0_10,plain,
    is_a_theorem(equivalent(equivalent(equivalent(X_24,X_25),equivalent(X_24,X_26)),equivalent(X_25,X_26))),
    inference(subst,[],[refute_0_9:[bind(X_21,$fot(X_24)),bind(X_22,$fot(X_25)),bind(X_23,$fot(X_26))]]) ).

cnf(refute_0_11,plain,
    ( ~ is_a_theorem(equivalent(equivalent(X_24,X_25),equivalent(X_24,X_26)))
    | is_a_theorem(equivalent(X_25,X_26)) ),
    inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_24,X_25),equivalent(X_24,X_26)),equivalent(X_25,X_26))) )],[refute_0_10,refute_0_0]) ).

cnf(refute_0_12,plain,
    ( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_60,X_61),equivalent(X_60,X_59)),equivalent(X_61,X_59)),equivalent(equivalent(equivalent(X_60,X_61),equivalent(X_60,X_59)),equivalent(equivalent(equivalent(equivalent(X_57,X_58),equivalent(X_57,X_55)),equivalent(X_58,X_55)),equivalent(equivalent(X_60,X_61),equivalent(X_60,X_59))))))
    | is_a_theorem(equivalent(equivalent(X_61,X_59),equivalent(equivalent(equivalent(equivalent(X_57,X_58),equivalent(X_57,X_55)),equivalent(X_58,X_55)),equivalent(equivalent(X_60,X_61),equivalent(X_60,X_59))))) ),
    inference(subst,[],[refute_0_11:[bind(X_24,$fot(equivalent(equivalent(X_60,X_61),equivalent(X_60,X_59)))),bind(X_25,$fot(equivalent(X_61,X_59))),bind(X_26,$fot(equivalent(equivalent(equivalent(equivalent(X_57,X_58),equivalent(X_57,X_55)),equivalent(X_58,X_55)),equivalent(equivalent(X_60,X_61),equivalent(X_60,X_59)))))]]) ).

cnf(refute_0_13,plain,
    ( ~ is_a_theorem(X_7)
    | ~ is_a_theorem(equivalent(X_7,equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_6)),equivalent(X_9,X_6)),X_7)))
    | is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_6)),equivalent(X_9,X_6)),X_7)) ),
    inference(subst,[],[condensed_detachment:[bind(X,$fot(X_7)),bind(Y,$fot(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_6)),equivalent(X_9,X_6)),X_7)))]]) ).

cnf(refute_0_14,plain,
    is_a_theorem(equivalent(X_7,equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_6)),equivalent(X_9,X_6)),X_7))),
    inference(subst,[],[p_4:[bind(U,$fot(X_6)),bind(X,$fot(X_7)),bind(Y,$fot(X_8)),bind(Z,$fot(X_9))]]) ).

cnf(refute_0_15,plain,
    ( ~ is_a_theorem(X_7)
    | is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_6)),equivalent(X_9,X_6)),X_7)) ),
    inference(resolve,[$cnf( is_a_theorem(equivalent(X_7,equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_6)),equivalent(X_9,X_6)),X_7))) )],[refute_0_14,refute_0_13]) ).

cnf(refute_0_16,plain,
    ( ~ is_a_theorem(equivalent(X,equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X)))
    | is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_16,X_17),equivalent(X_16,X_14)),equivalent(X_17,X_14)),equivalent(X,equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X)))) ),
    inference(subst,[],[refute_0_15:[bind(X_6,$fot(X_14)),bind(X_7,$fot(equivalent(X,equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X)))),bind(X_8,$fot(X_16)),bind(X_9,$fot(X_17))]]) ).

cnf(refute_0_17,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_16,X_17),equivalent(X_16,X_14)),equivalent(X_17,X_14)),equivalent(X,equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X)))),
    inference(resolve,[$cnf( is_a_theorem(equivalent(X,equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X))) )],[p_4,refute_0_16]) ).

cnf(refute_0_18,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_60,X_61),equivalent(X_60,X_59)),equivalent(X_61,X_59)),equivalent(equivalent(equivalent(X_60,X_61),equivalent(X_60,X_59)),equivalent(equivalent(equivalent(equivalent(X_57,X_58),equivalent(X_57,X_55)),equivalent(X_58,X_55)),equivalent(equivalent(X_60,X_61),equivalent(X_60,X_59)))))),
    inference(subst,[],[refute_0_17:[bind(U,$fot(X_55)),bind(X,$fot(equivalent(equivalent(X_60,X_61),equivalent(X_60,X_59)))),bind(Y,$fot(X_57)),bind(Z,$fot(X_58)),bind(X_14,$fot(X_59)),bind(X_16,$fot(X_60)),bind(X_17,$fot(X_61))]]) ).

cnf(refute_0_19,plain,
    is_a_theorem(equivalent(equivalent(X_61,X_59),equivalent(equivalent(equivalent(equivalent(X_57,X_58),equivalent(X_57,X_55)),equivalent(X_58,X_55)),equivalent(equivalent(X_60,X_61),equivalent(X_60,X_59))))),
    inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_60,X_61),equivalent(X_60,X_59)),equivalent(X_61,X_59)),equivalent(equivalent(equivalent(X_60,X_61),equivalent(X_60,X_59)),equivalent(equivalent(equivalent(equivalent(X_57,X_58),equivalent(X_57,X_55)),equivalent(X_58,X_55)),equivalent(equivalent(X_60,X_61),equivalent(X_60,X_59)))))) )],[refute_0_18,refute_0_12]) ).

cnf(refute_0_20,plain,
    is_a_theorem(equivalent(equivalent(equivalent(X_57,X_55),X_59),equivalent(equivalent(equivalent(equivalent(X_57,X_58),equivalent(X_57,X_55)),equivalent(X_58,X_55)),equivalent(equivalent(equivalent(X_57,X_58),equivalent(X_57,X_55)),equivalent(equivalent(X_57,X_58),X_59))))),
    inference(subst,[],[refute_0_19:[bind(X_60,$fot(equivalent(X_57,X_58))),bind(X_61,$fot(equivalent(X_57,X_55)))]]) ).

cnf(refute_0_21,plain,
    ( ~ is_a_theorem(equivalent(X_63,equivalent(equivalent(X_62,X_64),equivalent(X_62,X_65))))
    | ~ is_a_theorem(equivalent(equivalent(X_63,equivalent(equivalent(X_62,X_64),equivalent(X_62,X_65))),equivalent(X_63,equivalent(X_64,X_65))))
    | is_a_theorem(equivalent(X_63,equivalent(X_64,X_65))) ),
    inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_63,equivalent(equivalent(X_62,X_64),equivalent(X_62,X_65))))),bind(Y,$fot(equivalent(X_63,equivalent(X_64,X_65))))]]) ).

cnf(refute_0_22,plain,
    ( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_3,X_4),equivalent(X_3,X_5)),equivalent(X_4,X_5)),equivalent(equivalent(X_38,equivalent(equivalent(X_3,X_4),equivalent(X_3,X_5))),equivalent(X_38,equivalent(X_4,X_5)))))
    | is_a_theorem(equivalent(equivalent(X_38,equivalent(equivalent(X_3,X_4),equivalent(X_3,X_5))),equivalent(X_38,equivalent(X_4,X_5)))) ),
    inference(subst,[],[refute_0_3:[bind(X_2,$fot(equivalent(equivalent(X_38,equivalent(equivalent(X_3,X_4),equivalent(X_3,X_5))),equivalent(X_38,equivalent(X_4,X_5)))))]]) ).

cnf(refute_0_23,plain,
    ( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_35,X_36),equivalent(X_35,X_34)),equivalent(X_36,X_34)),equivalent(equivalent(equivalent(X_35,X_36),equivalent(X_35,X_34)),equivalent(equivalent(X_35,X_36),equivalent(X_35,X_34)))))
    | is_a_theorem(equivalent(equivalent(X_36,X_34),equivalent(equivalent(X_35,X_36),equivalent(X_35,X_34)))) ),
    inference(subst,[],[refute_0_11:[bind(X_24,$fot(equivalent(equivalent(X_35,X_36),equivalent(X_35,X_34)))),bind(X_25,$fot(equivalent(X_36,X_34))),bind(X_26,$fot(equivalent(equivalent(X_35,X_36),equivalent(X_35,X_34))))]]) ).

cnf(refute_0_24,plain,
    ( ~ is_a_theorem(equivalent(X_32,X_32))
    | is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_6)),equivalent(X_9,X_6)),equivalent(X_32,X_32))) ),
    inference(subst,[],[refute_0_15:[bind(X_7,$fot(equivalent(X_32,X_32)))]]) ).

cnf(refute_0_25,plain,
    ( ~ is_a_theorem(equivalent(equivalent(X_31,X_30),equivalent(X_31,X_30)))
    | is_a_theorem(equivalent(X_30,X_30)) ),
    inference(subst,[],[refute_0_11:[bind(X_24,$fot(X_31)),bind(X_25,$fot(X_30)),bind(X_26,$fot(X_30))]]) ).

cnf(refute_0_26,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)))),
    inference(subst,[],[refute_0_7:[bind(X_11,$fot(Y)),bind(X_12,$fot(Z)),bind(X_13,$fot(U))]]) ).

cnf(refute_0_27,plain,
    ( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U))))
    | is_a_theorem(equivalent(equivalent(Z,U),equivalent(Z,U))) ),
    inference(subst,[],[refute_0_11:[bind(X_24,$fot(equivalent(equivalent(Y,Z),equivalent(Y,U)))),bind(X_25,$fot(equivalent(Z,U))),bind(X_26,$fot(equivalent(Z,U)))]]) ).

cnf(refute_0_28,plain,
    is_a_theorem(equivalent(equivalent(Z,U),equivalent(Z,U))),
    inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)))) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    is_a_theorem(equivalent(equivalent(X_31,X_30),equivalent(X_31,X_30))),
    inference(subst,[],[refute_0_28:[bind(U,$fot(X_30)),bind(Z,$fot(X_31))]]) ).

cnf(refute_0_30,plain,
    is_a_theorem(equivalent(X_30,X_30)),
    inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_31,X_30),equivalent(X_31,X_30))) )],[refute_0_29,refute_0_25]) ).

cnf(refute_0_31,plain,
    is_a_theorem(equivalent(X_32,X_32)),
    inference(subst,[],[refute_0_30:[bind(X_30,$fot(X_32))]]) ).

cnf(refute_0_32,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_6)),equivalent(X_9,X_6)),equivalent(X_32,X_32))),
    inference(resolve,[$cnf( is_a_theorem(equivalent(X_32,X_32)) )],[refute_0_31,refute_0_24]) ).

cnf(refute_0_33,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_35,X_36),equivalent(X_35,X_34)),equivalent(X_36,X_34)),equivalent(equivalent(equivalent(X_35,X_36),equivalent(X_35,X_34)),equivalent(equivalent(X_35,X_36),equivalent(X_35,X_34))))),
    inference(subst,[],[refute_0_32:[bind(X_32,$fot(equivalent(equivalent(X_35,X_36),equivalent(X_35,X_34)))),bind(X_6,$fot(X_34)),bind(X_8,$fot(X_35)),bind(X_9,$fot(X_36))]]) ).

cnf(refute_0_34,plain,
    is_a_theorem(equivalent(equivalent(X_36,X_34),equivalent(equivalent(X_35,X_36),equivalent(X_35,X_34)))),
    inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_35,X_36),equivalent(X_35,X_34)),equivalent(X_36,X_34)),equivalent(equivalent(equivalent(X_35,X_36),equivalent(X_35,X_34)),equivalent(equivalent(X_35,X_36),equivalent(X_35,X_34))))) )],[refute_0_33,refute_0_23]) ).

cnf(refute_0_35,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_3,X_4),equivalent(X_3,X_5)),equivalent(X_4,X_5)),equivalent(equivalent(X_38,equivalent(equivalent(X_3,X_4),equivalent(X_3,X_5))),equivalent(X_38,equivalent(X_4,X_5))))),
    inference(subst,[],[refute_0_34:[bind(X_34,$fot(equivalent(X_4,X_5))),bind(X_35,$fot(X_38)),bind(X_36,$fot(equivalent(equivalent(X_3,X_4),equivalent(X_3,X_5))))]]) ).

cnf(refute_0_36,plain,
    is_a_theorem(equivalent(equivalent(X_38,equivalent(equivalent(X_3,X_4),equivalent(X_3,X_5))),equivalent(X_38,equivalent(X_4,X_5)))),
    inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_3,X_4),equivalent(X_3,X_5)),equivalent(X_4,X_5)),equivalent(equivalent(X_38,equivalent(equivalent(X_3,X_4),equivalent(X_3,X_5))),equivalent(X_38,equivalent(X_4,X_5))))) )],[refute_0_35,refute_0_22]) ).

cnf(refute_0_37,plain,
    is_a_theorem(equivalent(equivalent(X_63,equivalent(equivalent(X_62,X_64),equivalent(X_62,X_65))),equivalent(X_63,equivalent(X_64,X_65)))),
    inference(subst,[],[refute_0_36:[bind(X_3,$fot(X_62)),bind(X_38,$fot(X_63)),bind(X_4,$fot(X_64)),bind(X_5,$fot(X_65))]]) ).

cnf(refute_0_38,plain,
    ( ~ is_a_theorem(equivalent(X_63,equivalent(equivalent(X_62,X_64),equivalent(X_62,X_65))))
    | is_a_theorem(equivalent(X_63,equivalent(X_64,X_65))) ),
    inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_63,equivalent(equivalent(X_62,X_64),equivalent(X_62,X_65))),equivalent(X_63,equivalent(X_64,X_65)))) )],[refute_0_37,refute_0_21]) ).

cnf(refute_0_39,plain,
    ( ~ is_a_theorem(equivalent(equivalent(equivalent(X_57,X_55),X_59),equivalent(equivalent(equivalent(equivalent(X_57,X_58),equivalent(X_57,X_55)),equivalent(X_58,X_55)),equivalent(equivalent(equivalent(X_57,X_58),equivalent(X_57,X_55)),equivalent(equivalent(X_57,X_58),X_59)))))
    | is_a_theorem(equivalent(equivalent(equivalent(X_57,X_55),X_59),equivalent(equivalent(X_58,X_55),equivalent(equivalent(X_57,X_58),X_59)))) ),
    inference(subst,[],[refute_0_38:[bind(X_62,$fot(equivalent(equivalent(X_57,X_58),equivalent(X_57,X_55)))),bind(X_63,$fot(equivalent(equivalent(X_57,X_55),X_59))),bind(X_64,$fot(equivalent(X_58,X_55))),bind(X_65,$fot(equivalent(equivalent(X_57,X_58),X_59)))]]) ).

cnf(refute_0_40,plain,
    is_a_theorem(equivalent(equivalent(equivalent(X_57,X_55),X_59),equivalent(equivalent(X_58,X_55),equivalent(equivalent(X_57,X_58),X_59)))),
    inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_57,X_55),X_59),equivalent(equivalent(equivalent(equivalent(X_57,X_58),equivalent(X_57,X_55)),equivalent(X_58,X_55)),equivalent(equivalent(equivalent(X_57,X_58),equivalent(X_57,X_55)),equivalent(equivalent(X_57,X_58),X_59))))) )],[refute_0_20,refute_0_39]) ).

cnf(refute_0_41,plain,
    is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
    inference(subst,[],[refute_0_40:[bind(X_55,$fot(b)),bind(X_57,$fot(a)),bind(X_58,$fot(e)),bind(X_59,$fot(c))]]) ).

cnf(refute_0_42,plain,
    $false,
    inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))) )],[refute_0_41,prove_p_1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL101-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n004.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jul  2 23:37:08 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.48  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.48  
% 0.19/0.48  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.49  
%------------------------------------------------------------------------------