TSTP Solution File: PUZ018-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : PUZ018-1 : TPTP v8.1.0. Bugfixed v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n028.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 : Mon Jul 18 18:20:37 EDT 2022

% Result   : Unsatisfiable 0.18s 0.54s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   23
% Syntax   : Number of clauses     :   84 (  26 unt;  36 nHn;  79 RR)
%            Number of literals    :  261 (   0 equ;  89 neg)
%            Maximal clause size   :    8 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;  10 con; 0-0 aty)
%            Number of variables   :   48 (  17 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(all_on_a_on,axiom,
    ( ~ all_on(X)
    | on(a,X) ) ).

cnf(all_on_b_on,axiom,
    ( ~ all_on(X)
    | on(b,X) ) ).

cnf(all_on_c_on,axiom,
    ( ~ all_on(X)
    | on(c,X) ) ).

cnf(monday_follows_sunday,axiom,
    consecutive(sunday,monday) ).

cnf(tuesday_follows_monday,axiom,
    consecutive(monday,tuesday) ).

cnf(wednesday_follows_tuesday,axiom,
    consecutive(tuesday,wednesday) ).

cnf(thursday_follows_wednesday,axiom,
    consecutive(wednesday,thursday) ).

cnf(friday_follows_thursday,axiom,
    consecutive(thursday,friday) ).

cnf(a_not_b,axiom,
    ~ same_person(a,b) ).

cnf(a_not_c,axiom,
    ~ same_person(a,c) ).

cnf(sunday_not_tuesday,axiom,
    ~ same_day(sunday,tuesday) ).

cnf(sunday_not_thursday,axiom,
    ~ same_day(sunday,thursday) ).

cnf(tuesday_not_thursday,axiom,
    ~ same_day(tuesday,thursday) ).

cnf(all_on_one_day,hypothesis,
    ( all_on(sunday)
    | all_on(monday)
    | all_on(tuesday)
    | all_on(wednesday)
    | all_on(thursday)
    | all_on(friday)
    | all_on(saturday) ) ).

cnf(not_on_for_3_days,hypothesis,
    ( ~ consecutive(X,Y)
    | ~ consecutive(Y,Z)
    | ~ consecutive(Z,W)
    | ~ on(U,X)
    | ~ on(U,Y)
    | ~ on(U,Z) ) ).

cnf(no_two_off_twice_together,hypothesis,
    ( on(X,Y)
    | on(X,Z)
    | on(W,Y)
    | on(W,Z)
    | same_person(X,W)
    | same_day(Y,Z) ) ).

cnf(a_off_sunday,hypothesis,
    ~ on(a,sunday) ).

cnf(a_off_tuesday,hypothesis,
    ~ on(a,tuesday) ).

cnf(a_off_thursday,hypothesis,
    ~ on(a,thursday) ).

cnf(b_off_thursday,hypothesis,
    ~ on(b,thursday) ).

cnf(b_off_saturday,hypothesis,
    ~ on(b,saturday) ).

cnf(c_off_sunday,hypothesis,
    ~ on(c,sunday) ).

cnf(prove_all_on_friday,negated_conjecture,
    ~ all_on(friday) ).

cnf(refute_0_0,plain,
    ( on(a,X_19)
    | on(a,X_20)
    | on(b,X_19)
    | on(b,X_20)
    | same_day(X_19,X_20)
    | same_person(a,b) ),
    inference(subst,[],[no_two_off_twice_together:[bind(W,$fot(b)),bind(X,$fot(a)),bind(Y,$fot(X_19)),bind(Z,$fot(X_20))]]) ).

cnf(refute_0_1,plain,
    ( on(a,X_19)
    | on(a,X_20)
    | on(b,X_19)
    | on(b,X_20)
    | same_day(X_19,X_20) ),
    inference(resolve,[$cnf( same_person(a,b) )],[refute_0_0,a_not_b]) ).

cnf(refute_0_2,plain,
    ( on(a,thursday)
    | on(a,tuesday)
    | on(b,thursday)
    | on(b,tuesday)
    | same_day(tuesday,thursday) ),
    inference(subst,[],[refute_0_1:[bind(X_19,$fot(tuesday)),bind(X_20,$fot(thursday))]]) ).

cnf(refute_0_3,plain,
    ( on(a,thursday)
    | on(a,tuesday)
    | on(b,thursday)
    | on(b,tuesday) ),
    inference(resolve,[$cnf( same_day(tuesday,thursday) )],[refute_0_2,tuesday_not_thursday]) ).

cnf(refute_0_4,plain,
    ( on(a,tuesday)
    | on(b,thursday)
    | on(b,tuesday) ),
    inference(resolve,[$cnf( on(a,thursday) )],[refute_0_3,a_off_thursday]) ).

cnf(refute_0_5,plain,
    ( on(b,thursday)
    | on(b,tuesday) ),
    inference(resolve,[$cnf( on(a,tuesday) )],[refute_0_4,a_off_tuesday]) ).

cnf(refute_0_6,plain,
    on(b,tuesday),
    inference(resolve,[$cnf( on(b,thursday) )],[refute_0_5,b_off_thursday]) ).

cnf(refute_0_7,plain,
    ( on(a,sunday)
    | on(a,thursday)
    | on(b,sunday)
    | on(b,thursday)
    | same_day(sunday,thursday) ),
    inference(subst,[],[refute_0_1:[bind(X_19,$fot(sunday)),bind(X_20,$fot(thursday))]]) ).

cnf(refute_0_8,plain,
    ( on(a,sunday)
    | on(a,thursday)
    | on(b,sunday)
    | on(b,thursday) ),
    inference(resolve,[$cnf( same_day(sunday,thursday) )],[refute_0_7,sunday_not_thursday]) ).

cnf(refute_0_9,plain,
    ( on(a,thursday)
    | on(b,sunday)
    | on(b,thursday) ),
    inference(resolve,[$cnf( on(a,sunday) )],[refute_0_8,a_off_sunday]) ).

cnf(refute_0_10,plain,
    ( on(b,sunday)
    | on(b,thursday) ),
    inference(resolve,[$cnf( on(a,thursday) )],[refute_0_9,a_off_thursday]) ).

cnf(refute_0_11,plain,
    on(b,sunday),
    inference(resolve,[$cnf( on(b,thursday) )],[refute_0_10,b_off_thursday]) ).

cnf(refute_0_12,plain,
    ( ~ consecutive(X_65,X_66)
    | ~ consecutive(X_66,X_63)
    | ~ consecutive(sunday,X_65)
    | ~ on(b,X_65)
    | ~ on(b,X_66)
    | ~ on(b,sunday) ),
    inference(subst,[],[not_on_for_3_days:[bind(U,$fot(b)),bind(W,$fot(X_63)),bind(X,$fot(sunday)),bind(Y,$fot(X_65)),bind(Z,$fot(X_66))]]) ).

cnf(refute_0_13,plain,
    ( ~ consecutive(X_65,X_66)
    | ~ consecutive(X_66,X_63)
    | ~ consecutive(sunday,X_65)
    | ~ on(b,X_65)
    | ~ on(b,X_66) ),
    inference(resolve,[$cnf( on(b,sunday) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( ~ consecutive(X_76,tuesday)
    | ~ consecutive(sunday,X_76)
    | ~ consecutive(tuesday,X_75)
    | ~ on(b,X_76)
    | ~ on(b,tuesday) ),
    inference(subst,[],[refute_0_13:[bind(X_63,$fot(X_75)),bind(X_65,$fot(X_76)),bind(X_66,$fot(tuesday))]]) ).

cnf(refute_0_15,plain,
    ( ~ consecutive(X_76,tuesday)
    | ~ consecutive(sunday,X_76)
    | ~ consecutive(tuesday,X_75)
    | ~ on(b,X_76) ),
    inference(resolve,[$cnf( on(b,tuesday) )],[refute_0_6,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( ~ consecutive(monday,tuesday)
    | ~ consecutive(sunday,monday)
    | ~ consecutive(tuesday,X_75)
    | ~ on(b,monday) ),
    inference(subst,[],[refute_0_15:[bind(X_76,$fot(monday))]]) ).

cnf(refute_0_17,plain,
    ( ~ all_on(monday)
    | on(b,monday) ),
    inference(subst,[],[all_on_b_on:[bind(X,$fot(monday))]]) ).

cnf(refute_0_18,plain,
    ( ~ all_on(saturday)
    | on(b,saturday) ),
    inference(subst,[],[all_on_b_on:[bind(X,$fot(saturday))]]) ).

cnf(refute_0_19,plain,
    ( ~ all_on(sunday)
    | on(c,sunday) ),
    inference(subst,[],[all_on_c_on:[bind(X,$fot(sunday))]]) ).

cnf(refute_0_20,plain,
    ( ~ all_on(thursday)
    | on(a,thursday) ),
    inference(subst,[],[all_on_a_on:[bind(X,$fot(thursday))]]) ).

cnf(refute_0_21,plain,
    ( ~ all_on(tuesday)
    | on(a,tuesday) ),
    inference(subst,[],[all_on_a_on:[bind(X,$fot(tuesday))]]) ).

cnf(refute_0_22,plain,
    ( ~ all_on(wednesday)
    | on(c,wednesday) ),
    inference(subst,[],[all_on_c_on:[bind(X,$fot(wednesday))]]) ).

cnf(refute_0_23,plain,
    ( all_on(monday)
    | all_on(saturday)
    | all_on(sunday)
    | all_on(thursday)
    | all_on(tuesday)
    | all_on(wednesday) ),
    inference(resolve,[$cnf( all_on(friday) )],[all_on_one_day,prove_all_on_friday]) ).

cnf(refute_0_24,plain,
    ( all_on(monday)
    | all_on(saturday)
    | all_on(sunday)
    | all_on(thursday)
    | all_on(tuesday)
    | on(c,wednesday) ),
    inference(resolve,[$cnf( all_on(wednesday) )],[refute_0_23,refute_0_22]) ).

cnf(refute_0_25,plain,
    ( on(a,X_19)
    | on(a,X_20)
    | on(c,X_19)
    | on(c,X_20)
    | same_day(X_19,X_20)
    | same_person(a,c) ),
    inference(subst,[],[no_two_off_twice_together:[bind(W,$fot(c)),bind(X,$fot(a)),bind(Y,$fot(X_19)),bind(Z,$fot(X_20))]]) ).

cnf(refute_0_26,plain,
    ( on(a,X_19)
    | on(a,X_20)
    | on(c,X_19)
    | on(c,X_20)
    | same_day(X_19,X_20) ),
    inference(resolve,[$cnf( same_person(a,c) )],[refute_0_25,a_not_c]) ).

cnf(refute_0_27,plain,
    ( on(a,sunday)
    | on(a,thursday)
    | on(c,sunday)
    | on(c,thursday)
    | same_day(sunday,thursday) ),
    inference(subst,[],[refute_0_26:[bind(X_19,$fot(sunday)),bind(X_20,$fot(thursday))]]) ).

cnf(refute_0_28,plain,
    ( on(a,sunday)
    | on(a,thursday)
    | on(c,sunday)
    | on(c,thursday) ),
    inference(resolve,[$cnf( same_day(sunday,thursday) )],[refute_0_27,sunday_not_thursday]) ).

cnf(refute_0_29,plain,
    ( on(a,thursday)
    | on(c,sunday)
    | on(c,thursday) ),
    inference(resolve,[$cnf( on(a,sunday) )],[refute_0_28,a_off_sunday]) ).

cnf(refute_0_30,plain,
    ( on(c,sunday)
    | on(c,thursday) ),
    inference(resolve,[$cnf( on(a,thursday) )],[refute_0_29,a_off_thursday]) ).

cnf(refute_0_31,plain,
    on(c,thursday),
    inference(resolve,[$cnf( on(c,sunday) )],[refute_0_30,c_off_sunday]) ).

cnf(refute_0_32,plain,
    ( on(a,sunday)
    | on(a,tuesday)
    | on(c,sunday)
    | on(c,tuesday)
    | same_day(sunday,tuesday) ),
    inference(subst,[],[refute_0_26:[bind(X_19,$fot(sunday)),bind(X_20,$fot(tuesday))]]) ).

cnf(refute_0_33,plain,
    ( on(a,sunday)
    | on(a,tuesday)
    | on(c,sunday)
    | on(c,tuesday) ),
    inference(resolve,[$cnf( same_day(sunday,tuesday) )],[refute_0_32,sunday_not_tuesday]) ).

cnf(refute_0_34,plain,
    ( on(a,tuesday)
    | on(c,sunday)
    | on(c,tuesday) ),
    inference(resolve,[$cnf( on(a,sunday) )],[refute_0_33,a_off_sunday]) ).

cnf(refute_0_35,plain,
    ( on(c,sunday)
    | on(c,tuesday) ),
    inference(resolve,[$cnf( on(a,tuesday) )],[refute_0_34,a_off_tuesday]) ).

cnf(refute_0_36,plain,
    on(c,tuesday),
    inference(resolve,[$cnf( on(c,sunday) )],[refute_0_35,c_off_sunday]) ).

cnf(refute_0_37,plain,
    ( ~ consecutive(X_65,X_66)
    | ~ consecutive(X_66,X_63)
    | ~ consecutive(tuesday,X_65)
    | ~ on(c,X_65)
    | ~ on(c,X_66)
    | ~ on(c,tuesday) ),
    inference(subst,[],[not_on_for_3_days:[bind(U,$fot(c)),bind(W,$fot(X_63)),bind(X,$fot(tuesday)),bind(Y,$fot(X_65)),bind(Z,$fot(X_66))]]) ).

cnf(refute_0_38,plain,
    ( ~ consecutive(X_65,X_66)
    | ~ consecutive(X_66,X_63)
    | ~ consecutive(tuesday,X_65)
    | ~ on(c,X_65)
    | ~ on(c,X_66) ),
    inference(resolve,[$cnf( on(c,tuesday) )],[refute_0_36,refute_0_37]) ).

cnf(refute_0_39,plain,
    ( ~ consecutive(X_159,thursday)
    | ~ consecutive(thursday,X_158)
    | ~ consecutive(tuesday,X_159)
    | ~ on(c,X_159)
    | ~ on(c,thursday) ),
    inference(subst,[],[refute_0_38:[bind(X_63,$fot(X_158)),bind(X_65,$fot(X_159)),bind(X_66,$fot(thursday))]]) ).

cnf(refute_0_40,plain,
    ( ~ consecutive(X_159,thursday)
    | ~ consecutive(thursday,X_158)
    | ~ consecutive(tuesday,X_159)
    | ~ on(c,X_159) ),
    inference(resolve,[$cnf( on(c,thursday) )],[refute_0_31,refute_0_39]) ).

cnf(refute_0_41,plain,
    ( ~ consecutive(thursday,X_172)
    | ~ consecutive(tuesday,wednesday)
    | ~ consecutive(wednesday,thursday)
    | ~ on(c,wednesday) ),
    inference(subst,[],[refute_0_40:[bind(X_158,$fot(X_172)),bind(X_159,$fot(wednesday))]]) ).

cnf(refute_0_42,plain,
    ( ~ consecutive(thursday,X_172)
    | ~ consecutive(tuesday,wednesday)
    | ~ consecutive(wednesday,thursday)
    | all_on(monday)
    | all_on(saturday)
    | all_on(sunday)
    | all_on(thursday)
    | all_on(tuesday) ),
    inference(resolve,[$cnf( on(c,wednesday) )],[refute_0_24,refute_0_41]) ).

cnf(refute_0_43,plain,
    ( ~ consecutive(thursday,X_172)
    | ~ consecutive(wednesday,thursday)
    | all_on(monday)
    | all_on(saturday)
    | all_on(sunday)
    | all_on(thursday)
    | all_on(tuesday) ),
    inference(resolve,[$cnf( consecutive(tuesday,wednesday) )],[wednesday_follows_tuesday,refute_0_42]) ).

cnf(refute_0_44,plain,
    ( ~ consecutive(thursday,X_172)
    | all_on(monday)
    | all_on(saturday)
    | all_on(sunday)
    | all_on(thursday)
    | all_on(tuesday) ),
    inference(resolve,[$cnf( consecutive(wednesday,thursday) )],[thursday_follows_wednesday,refute_0_43]) ).

cnf(refute_0_45,plain,
    ( ~ consecutive(thursday,friday)
    | all_on(monday)
    | all_on(saturday)
    | all_on(sunday)
    | all_on(thursday)
    | all_on(tuesday) ),
    inference(subst,[],[refute_0_44:[bind(X_172,$fot(friday))]]) ).

cnf(refute_0_46,plain,
    ( all_on(monday)
    | all_on(saturday)
    | all_on(sunday)
    | all_on(thursday)
    | all_on(tuesday) ),
    inference(resolve,[$cnf( consecutive(thursday,friday) )],[friday_follows_thursday,refute_0_45]) ).

cnf(refute_0_47,plain,
    ( all_on(monday)
    | all_on(saturday)
    | all_on(sunday)
    | all_on(thursday)
    | on(a,tuesday) ),
    inference(resolve,[$cnf( all_on(tuesday) )],[refute_0_46,refute_0_21]) ).

cnf(refute_0_48,plain,
    ( all_on(monday)
    | all_on(saturday)
    | all_on(sunday)
    | all_on(thursday) ),
    inference(resolve,[$cnf( on(a,tuesday) )],[refute_0_47,a_off_tuesday]) ).

cnf(refute_0_49,plain,
    ( all_on(monday)
    | all_on(saturday)
    | all_on(sunday)
    | on(a,thursday) ),
    inference(resolve,[$cnf( all_on(thursday) )],[refute_0_48,refute_0_20]) ).

cnf(refute_0_50,plain,
    ( all_on(monday)
    | all_on(saturday)
    | all_on(sunday) ),
    inference(resolve,[$cnf( on(a,thursday) )],[refute_0_49,a_off_thursday]) ).

cnf(refute_0_51,plain,
    ( all_on(monday)
    | all_on(saturday)
    | on(c,sunday) ),
    inference(resolve,[$cnf( all_on(sunday) )],[refute_0_50,refute_0_19]) ).

cnf(refute_0_52,plain,
    ( all_on(monday)
    | all_on(saturday) ),
    inference(resolve,[$cnf( on(c,sunday) )],[refute_0_51,c_off_sunday]) ).

cnf(refute_0_53,plain,
    ( all_on(monday)
    | on(b,saturday) ),
    inference(resolve,[$cnf( all_on(saturday) )],[refute_0_52,refute_0_18]) ).

cnf(refute_0_54,plain,
    all_on(monday),
    inference(resolve,[$cnf( on(b,saturday) )],[refute_0_53,b_off_saturday]) ).

cnf(refute_0_55,plain,
    on(b,monday),
    inference(resolve,[$cnf( all_on(monday) )],[refute_0_54,refute_0_17]) ).

cnf(refute_0_56,plain,
    ( ~ consecutive(monday,tuesday)
    | ~ consecutive(sunday,monday)
    | ~ consecutive(tuesday,X_75) ),
    inference(resolve,[$cnf( on(b,monday) )],[refute_0_55,refute_0_16]) ).

cnf(refute_0_57,plain,
    ( ~ consecutive(sunday,monday)
    | ~ consecutive(tuesday,X_75) ),
    inference(resolve,[$cnf( consecutive(monday,tuesday) )],[tuesday_follows_monday,refute_0_56]) ).

cnf(refute_0_58,plain,
    ~ consecutive(tuesday,X_75),
    inference(resolve,[$cnf( consecutive(sunday,monday) )],[monday_follows_sunday,refute_0_57]) ).

cnf(refute_0_59,plain,
    ~ consecutive(tuesday,wednesday),
    inference(subst,[],[refute_0_58:[bind(X_75,$fot(wednesday))]]) ).

cnf(refute_0_60,plain,
    $false,
    inference(resolve,[$cnf( consecutive(tuesday,wednesday) )],[wednesday_follows_tuesday,refute_0_59]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : PUZ018-1 : TPTP v8.1.0. Bugfixed v1.2.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n028.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 May 29 00:36:47 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.54  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.54  
% 0.18/0.54  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.54  
%------------------------------------------------------------------------------