TSTP Solution File: GEO212+2 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GEO212+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n003.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  : 300s
% DateTime : Wed Jul 27 12:54:51 EDT 2022

% Result   : Theorem 1.75s 1.96s
% Output   : Refutation 1.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   15 (   8 unt;   7 nHn;   8 RR)
%            Number of literals    :   26 (   0 equ;   6 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   14 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ~ convergent_lines(A,A),
    file('GEO212+2.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ convergent_lines(A,B)
    | convergent_lines(A,C)
    | convergent_lines(B,C) ),
    file('GEO212+2.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ convergent_lines(A,B)
    | ~ unorthogonal_lines(A,B)
    | convergent_lines(A,C)
    | unorthogonal_lines(B,C) ),
    file('GEO212+2.p',unknown),
    [] ).

cnf(24,axiom,
    ~ convergent_lines(dollar_c3,dollar_c1),
    file('GEO212+2.p',unknown),
    [] ).

cnf(25,axiom,
    ~ unorthogonal_lines(dollar_c2,dollar_c1),
    file('GEO212+2.p',unknown),
    [] ).

cnf(26,axiom,
    ( convergent_lines(A,B)
    | unorthogonal_lines(A,B) ),
    file('GEO212+2.p',unknown),
    [] ).

cnf(27,axiom,
    unorthogonal_lines(dollar_c3,dollar_c2),
    file('GEO212+2.p',unknown),
    [] ).

cnf(28,plain,
    convergent_lines(dollar_c2,dollar_c1),
    inference(hyper,[status(thm)],[26,25]),
    [iquote('hyper,26,25')] ).

cnf(31,plain,
    ( convergent_lines(dollar_c2,A)
    | convergent_lines(dollar_c1,A) ),
    inference(hyper,[status(thm)],[28,6]),
    [iquote('hyper,28,6')] ).

cnf(40,plain,
    ( convergent_lines(dollar_c2,A)
    | convergent_lines(dollar_c1,B)
    | convergent_lines(A,B) ),
    inference(hyper,[status(thm)],[31,6]),
    [iquote('hyper,31,6')] ).

cnf(118,plain,
    convergent_lines(dollar_c2,dollar_c3),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[40,24]),3]),
    [iquote('hyper,40,24,unit_del,3')] ).

cnf(126,plain,
    ( convergent_lines(dollar_c2,A)
    | convergent_lines(dollar_c3,A) ),
    inference(hyper,[status(thm)],[118,6]),
    [iquote('hyper,118,6')] ).

cnf(262,plain,
    ( convergent_lines(dollar_c3,A)
    | unorthogonal_lines(dollar_c2,A) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[126,18,27]),3]),
    [iquote('hyper,126,18,27,unit_del,3')] ).

cnf(360,plain,
    convergent_lines(dollar_c3,dollar_c1),
    inference(hyper,[status(thm)],[262,25]),
    [iquote('hyper,262,25')] ).

cnf(361,plain,
    $false,
    inference(binary,[status(thm)],[360,24]),
    [iquote('binary,360.1,24.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : GEO212+2 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n003.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  : 300
% 0.12/0.33  % DateTime : Wed Jul 27 07:06:41 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.67/1.89  ----- Otter 3.3f, August 2004 -----
% 1.67/1.89  The process was started by sandbox on n003.cluster.edu,
% 1.67/1.89  Wed Jul 27 07:06:41 2022
% 1.67/1.89  The command was "./otter".  The process ID is 13590.
% 1.67/1.89  
% 1.67/1.89  set(prolog_style_variables).
% 1.67/1.89  set(auto).
% 1.67/1.89     dependent: set(auto1).
% 1.67/1.89     dependent: set(process_input).
% 1.67/1.89     dependent: clear(print_kept).
% 1.67/1.89     dependent: clear(print_new_demod).
% 1.67/1.89     dependent: clear(print_back_demod).
% 1.67/1.89     dependent: clear(print_back_sub).
% 1.67/1.89     dependent: set(control_memory).
% 1.67/1.89     dependent: assign(max_mem, 12000).
% 1.67/1.89     dependent: assign(pick_given_ratio, 4).
% 1.67/1.89     dependent: assign(stats_level, 1).
% 1.67/1.89     dependent: assign(max_seconds, 10800).
% 1.67/1.89  clear(print_given).
% 1.67/1.89  
% 1.67/1.89  formula_list(usable).
% 1.67/1.89  all X (-distinct_points(X,X)).
% 1.67/1.89  all X (-distinct_lines(X,X)).
% 1.67/1.89  all X (-convergent_lines(X,X)).
% 1.67/1.89  all X Y Z (distinct_points(X,Y)->distinct_points(X,Z)|distinct_points(Y,Z)).
% 1.67/1.89  all X Y Z (distinct_lines(X,Y)->distinct_lines(X,Z)|distinct_lines(Y,Z)).
% 1.67/1.89  all X Y Z (convergent_lines(X,Y)->convergent_lines(X,Z)|convergent_lines(Y,Z)).
% 1.67/1.89  all X Y Z (distinct_points(X,Y)-> (apart_point_and_line(Z,line_connecting(X,Y))->distinct_points(Z,X)&distinct_points(Z,Y))).
% 1.67/1.89  all X Y Z (convergent_lines(X,Y)-> (apart_point_and_line(Z,X)|apart_point_and_line(Z,Y)->distinct_points(Z,intersection_point(X,Y)))).
% 1.67/1.89  all X Y U V (distinct_points(X,Y)&distinct_lines(U,V)->apart_point_and_line(X,U)|apart_point_and_line(X,V)|apart_point_and_line(Y,U)|apart_point_and_line(Y,V)).
% 1.67/1.89  all X Y Z (apart_point_and_line(X,Y)->distinct_points(X,Z)|apart_point_and_line(Z,Y)).
% 1.67/1.89  all X Y Z (apart_point_and_line(X,Y)->distinct_lines(Y,Z)|apart_point_and_line(X,Z)).
% 1.67/1.89  all X Y (convergent_lines(X,Y)->distinct_lines(X,Y)).
% 1.67/1.89  all X Y (-convergent_lines(parallel_through_point(Y,X),Y)).
% 1.67/1.89  all X Y (-apart_point_and_line(X,parallel_through_point(Y,X))).
% 1.67/1.89  all X Y Z (distinct_lines(Y,Z)->apart_point_and_line(X,Y)|apart_point_and_line(X,Z)|convergent_lines(Y,Z)).
% 1.67/1.89  all L M (convergent_lines(L,M)|unorthogonal_lines(L,M)).
% 1.67/1.89  all L M N (convergent_lines(L,M)&unorthogonal_lines(L,M)->convergent_lines(L,N)&unorthogonal_lines(L,N)|convergent_lines(M,N)&unorthogonal_lines(M,N)).
% 1.67/1.89  all A L (-unorthogonal_lines(orthogonal_through_point(L,A),L)).
% 1.67/1.89  all A L (-apart_point_and_line(A,orthogonal_through_point(L,A))).
% 1.67/1.89  all A L M N (distinct_lines(L,M)->apart_point_and_line(A,L)|apart_point_and_line(A,M)|unorthogonal_lines(L,N)|unorthogonal_lines(M,N)).
% 1.67/1.89  -(all L M N (unorthogonal_lines(L,M)->convergent_lines(L,N)|unorthogonal_lines(M,N))).
% 1.67/1.89  end_of_list.
% 1.67/1.89  
% 1.67/1.89  -------> usable clausifies to:
% 1.67/1.89  
% 1.67/1.89  list(usable).
% 1.67/1.89  0 [] -distinct_points(X,X).
% 1.67/1.89  0 [] -distinct_lines(X,X).
% 1.67/1.89  0 [] -convergent_lines(X,X).
% 1.67/1.89  0 [] -distinct_points(X,Y)|distinct_points(X,Z)|distinct_points(Y,Z).
% 1.67/1.89  0 [] -distinct_lines(X,Y)|distinct_lines(X,Z)|distinct_lines(Y,Z).
% 1.67/1.89  0 [] -convergent_lines(X,Y)|convergent_lines(X,Z)|convergent_lines(Y,Z).
% 1.67/1.89  0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,X).
% 1.67/1.89  0 [] -distinct_points(X,Y)| -apart_point_and_line(Z,line_connecting(X,Y))|distinct_points(Z,Y).
% 1.67/1.89  0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,X)|distinct_points(Z,intersection_point(X,Y)).
% 1.67/1.89  0 [] -convergent_lines(X,Y)| -apart_point_and_line(Z,Y)|distinct_points(Z,intersection_point(X,Y)).
% 1.67/1.89  0 [] -distinct_points(X,Y)| -distinct_lines(U,V)|apart_point_and_line(X,U)|apart_point_and_line(X,V)|apart_point_and_line(Y,U)|apart_point_and_line(Y,V).
% 1.67/1.89  0 [] -apart_point_and_line(X,Y)|distinct_points(X,Z)|apart_point_and_line(Z,Y).
% 1.67/1.89  0 [] -apart_point_and_line(X,Y)|distinct_lines(Y,Z)|apart_point_and_line(X,Z).
% 1.67/1.89  0 [] -convergent_lines(X,Y)|distinct_lines(X,Y).
% 1.67/1.89  0 [] -convergent_lines(parallel_through_point(Y,X),Y).
% 1.67/1.89  0 [] -apart_point_and_line(X,parallel_through_point(Y,X)).
% 1.67/1.89  0 [] -distinct_lines(Y,Z)|apart_point_and_line(X,Y)|apart_point_and_line(X,Z)|convergent_lines(Y,Z).
% 1.67/1.89  0 [] convergent_lines(L,M)|unorthogonal_lines(L,M).
% 1.67/1.89  0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|convergent_lines(L,N)|convergent_lines(M,N).
% 1.67/1.89  0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|convergent_lines(L,N)|unorthogonal_lines(M,N).
% 1.67/1.89  0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|unorthogonal_lines(L,N)|convergent_lines(M,N).
% 1.75/1.96  0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|unorthogonal_lines(L,N)|unorthogonal_lines(M,N).
% 1.75/1.96  0 [] -unorthogonal_lines(orthogonal_through_point(L,A),L).
% 1.75/1.96  0 [] -apart_point_and_line(A,orthogonal_through_point(L,A)).
% 1.75/1.96  0 [] -distinct_lines(L,M)|apart_point_and_line(A,L)|apart_point_and_line(A,M)|unorthogonal_lines(L,N)|unorthogonal_lines(M,N).
% 1.75/1.96  0 [] unorthogonal_lines($c3,$c2).
% 1.75/1.96  0 [] -convergent_lines($c3,$c1).
% 1.75/1.96  0 [] -unorthogonal_lines($c2,$c1).
% 1.75/1.96  end_of_list.
% 1.75/1.96  
% 1.75/1.96  SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.75/1.96  
% 1.75/1.96  This is a non-Horn set without equality.  The strategy will
% 1.75/1.96  be ordered hyper_res, unit deletion, and factoring, with
% 1.75/1.96  satellites in sos and with nuclei in usable.
% 1.75/1.96  
% 1.75/1.96     dependent: set(hyper_res).
% 1.75/1.96     dependent: set(factor).
% 1.75/1.96     dependent: set(unit_deletion).
% 1.75/1.96  
% 1.75/1.96  ------------> process usable:
% 1.75/1.96  ** KEPT (pick-wt=3): 1 [] -distinct_points(A,A).
% 1.75/1.96  ** KEPT (pick-wt=3): 2 [] -distinct_lines(A,A).
% 1.75/1.96  ** KEPT (pick-wt=3): 3 [] -convergent_lines(A,A).
% 1.75/1.96  ** KEPT (pick-wt=9): 4 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 1.75/1.96  ** KEPT (pick-wt=9): 5 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 1.75/1.96  ** KEPT (pick-wt=9): 6 [] -convergent_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 1.75/1.96  ** KEPT (pick-wt=11): 7 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,A).
% 1.75/1.96  ** KEPT (pick-wt=11): 8 [] -distinct_points(A,B)| -apart_point_and_line(C,line_connecting(A,B))|distinct_points(C,B).
% 1.75/1.96  ** KEPT (pick-wt=11): 9 [] -convergent_lines(A,B)| -apart_point_and_line(C,A)|distinct_points(C,intersection_point(A,B)).
% 1.75/1.96  ** KEPT (pick-wt=11): 10 [] -convergent_lines(A,B)| -apart_point_and_line(C,B)|distinct_points(C,intersection_point(A,B)).
% 1.75/1.96  ** KEPT (pick-wt=18): 11 [] -distinct_points(A,B)| -distinct_lines(C,D)|apart_point_and_line(A,C)|apart_point_and_line(A,D)|apart_point_and_line(B,C)|apart_point_and_line(B,D).
% 1.75/1.96  ** KEPT (pick-wt=9): 12 [] -apart_point_and_line(A,B)|distinct_points(A,C)|apart_point_and_line(C,B).
% 1.75/1.96  ** KEPT (pick-wt=9): 13 [] -apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C).
% 1.75/1.96  ** KEPT (pick-wt=6): 14 [] -convergent_lines(A,B)|distinct_lines(A,B).
% 1.75/1.96  ** KEPT (pick-wt=5): 15 [] -convergent_lines(parallel_through_point(A,B),A).
% 1.75/1.96  ** KEPT (pick-wt=5): 16 [] -apart_point_and_line(A,parallel_through_point(B,A)).
% 1.75/1.96  ** KEPT (pick-wt=12): 17 [] -distinct_lines(A,B)|apart_point_and_line(C,A)|apart_point_and_line(C,B)|convergent_lines(A,B).
% 1.75/1.96    Following clause subsumed by 6 during input processing: 0 [] -convergent_lines(A,B)| -unorthogonal_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 1.75/1.96  ** KEPT (pick-wt=12): 18 [] -convergent_lines(A,B)| -unorthogonal_lines(A,B)|convergent_lines(A,C)|unorthogonal_lines(B,C).
% 1.75/1.96  ** KEPT (pick-wt=12): 19 [] -convergent_lines(A,B)| -unorthogonal_lines(A,B)|unorthogonal_lines(A,C)|convergent_lines(B,C).
% 1.75/1.96  ** KEPT (pick-wt=12): 20 [] -convergent_lines(A,B)| -unorthogonal_lines(A,B)|unorthogonal_lines(A,C)|unorthogonal_lines(B,C).
% 1.75/1.96  ** KEPT (pick-wt=5): 21 [] -unorthogonal_lines(orthogonal_through_point(A,B),A).
% 1.75/1.96  ** KEPT (pick-wt=5): 22 [] -apart_point_and_line(A,orthogonal_through_point(B,A)).
% 1.75/1.96  ** KEPT (pick-wt=15): 23 [] -distinct_lines(A,B)|apart_point_and_line(C,A)|apart_point_and_line(C,B)|unorthogonal_lines(A,D)|unorthogonal_lines(B,D).
% 1.75/1.96  ** KEPT (pick-wt=3): 24 [] -convergent_lines($c3,$c1).
% 1.75/1.96  ** KEPT (pick-wt=3): 25 [] -unorthogonal_lines($c2,$c1).
% 1.75/1.96  
% 1.75/1.96  ------------> process sos:
% 1.75/1.96  ** KEPT (pick-wt=6): 26 [] convergent_lines(A,B)|unorthogonal_lines(A,B).
% 1.75/1.96  ** KEPT (pick-wt=3): 27 [] unorthogonal_lines($c3,$c2).
% 1.75/1.96  
% 1.75/1.96  ======= end of input processing =======
% 1.75/1.96  
% 1.75/1.96  =========== start of search ===========
% 1.75/1.96  
% 1.75/1.96  -------- PROOF -------- 
% 1.75/1.96  
% 1.75/1.96  ----> UNIT CONFLICT at   0.07 sec ----> 361 [binary,360.1,24.1] $F.
% 1.75/1.96  
% 1.75/1.96  Length of proof is 7.  Level of proof is 7.
% 1.75/1.96  
% 1.75/1.96  ---------------- PROOF ----------------
% 1.75/1.96  % SZS status Theorem
% 1.75/1.96  % SZS output start Refutation
% See solution above
% 1.75/1.96  ------------ end of proof -------------
% 1.75/1.96  
% 1.75/1.96  
% 1.75/1.96  Search stopped by max_proofs option.
% 1.75/1.96  
% 1.75/1.96  
% 1.75/1.96  Search stopped by max_proofs option.
% 1.75/1.96  
% 1.75/1.96  ============ end of search ============
% 1.75/1.96  
% 1.75/1.96  -------------- statistics -------------
% 1.75/1.96  clauses given                 45
% 1.75/1.96  clauses generated           1109
% 1.75/1.96  clauses kept                 360
% 1.75/1.96  clauses forward subsumed     777
% 1.75/1.96  clauses back subsumed         36
% 1.75/1.96  Kbytes malloced              976
% 1.75/1.96  
% 1.75/1.96  ----------- times (seconds) -----------
% 1.75/1.96  user CPU time          0.07          (0 hr, 0 min, 0 sec)
% 1.75/1.96  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.75/1.96  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.75/1.96  
% 1.75/1.96  That finishes the proof of the theorem.
% 1.75/1.96  
% 1.75/1.96  Process 13590 finished Wed Jul 27 07:06:43 2022
% 1.75/1.96  Otter interrupted
% 1.75/1.96  PROOF FOUND
%------------------------------------------------------------------------------