TSTP Solution File: ANA043-2 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : ANA043-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n012.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 12:46:48 EDT 2022

% Result   : Unsatisfiable 1.66s 1.82s
% Output   : Refutation 1.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   17 (  11 unt;   0 nHn;  11 RR)
%            Number of literals    :   25 (   2 equ;  10 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   3 con; 0-3 aty)
%            Number of variables   :   22 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ c_lesse_quals(c_times(c_HOL_Oabs(v_l(v_x(A),v_xa(A)),t_b),c_HOL_Oabs(v_f(v_k(v_x(A),v_xa(A))),t_b),t_b),c_times(A,c_times(c_HOL_Oabs(v_l(v_x(A),v_xa(A)),t_b),c_HOL_Oabs(v_h(v_k(v_x(A),v_xa(A))),t_b),t_b),t_b),t_b),
    file('ANA043-2.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
    | c_lesse_quals(c_0,c_HOL_Oabs(B,A),A) ),
    file('ANA043-2.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__mult(A)
    | c_times(B,c_times(C,D,A),A) = c_times(C,c_times(B,D,A),A) ),
    file('ANA043-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(A)
    | ~ c_lesse_quals(B,C,A)
    | ~ c_lesse_quals(c_0,D,A)
    | c_lesse_quals(c_times(D,B,A),c_times(D,C,A),A) ),
    file('ANA043-2.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(A)
    | class_OrderedGroup_Oab__semigroup__mult(A) ),
    file('ANA043-2.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(A)
    | class_Ring__and__Field_Opordered__semiring(A) ),
    file('ANA043-2.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(A)
    | class_OrderedGroup_Olordered__ab__group__abs(A) ),
    file('ANA043-2.p',unknown),
    [] ).

cnf(9,axiom,
    c_lesse_quals(c_HOL_Oabs(v_f(A),t_b),c_times(v_c,c_HOL_Oabs(v_h(A),t_b),t_b),t_b),
    file('ANA043-2.p',unknown),
    [] ).

cnf(10,axiom,
    class_Ring__and__Field_Oordered__idom(t_b),
    file('ANA043-2.p',unknown),
    [] ).

cnf(11,plain,
    class_OrderedGroup_Olordered__ab__group__abs(t_b),
    inference(hyper,[status(thm)],[10,7]),
    [iquote('hyper,10,7')] ).

cnf(12,plain,
    class_Ring__and__Field_Opordered__semiring(t_b),
    inference(hyper,[status(thm)],[10,6]),
    [iquote('hyper,10,6')] ).

cnf(13,plain,
    class_OrderedGroup_Oab__semigroup__mult(t_b),
    inference(hyper,[status(thm)],[10,5]),
    [iquote('hyper,10,5')] ).

cnf(14,plain,
    c_lesse_quals(c_0,c_HOL_Oabs(A,t_b),t_b),
    inference(hyper,[status(thm)],[11,2]),
    [iquote('hyper,11,2')] ).

cnf(15,plain,
    c_times(A,c_times(B,C,t_b),t_b) = c_times(B,c_times(A,C,t_b),t_b),
    inference(hyper,[status(thm)],[13,3]),
    [iquote('hyper,13,3')] ).

cnf(17,plain,
    c_lesse_quals(c_times(c_HOL_Oabs(A,t_b),c_HOL_Oabs(v_f(B),t_b),t_b),c_times(c_HOL_Oabs(A,t_b),c_times(v_c,c_HOL_Oabs(v_h(B),t_b),t_b),t_b),t_b),
    inference(hyper,[status(thm)],[14,4,12,9]),
    [iquote('hyper,14,4,12,9')] ).

cnf(22,plain,
    ~ c_lesse_quals(c_times(c_HOL_Oabs(v_l(v_x(A),v_xa(A)),t_b),c_HOL_Oabs(v_f(v_k(v_x(A),v_xa(A))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(A),v_xa(A)),t_b),c_times(A,c_HOL_Oabs(v_h(v_k(v_x(A),v_xa(A))),t_b),t_b),t_b),t_b),
    inference(para_from,[status(thm),theory(equality)],[15,1]),
    [iquote('para_from,15.1.1,1.1.2')] ).

cnf(23,plain,
    $false,
    inference(binary,[status(thm)],[22,17]),
    [iquote('binary,22.1,17.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : ANA043-2 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13  % Command  : otter-tptp-script %s
% 0.13/0.34  % Computer : n012.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  : 300
% 0.13/0.34  % DateTime : Wed Jul 27 10:04:20 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.66/1.82  ----- Otter 3.3f, August 2004 -----
% 1.66/1.82  The process was started by sandbox on n012.cluster.edu,
% 1.66/1.82  Wed Jul 27 10:04:20 2022
% 1.66/1.82  The command was "./otter".  The process ID is 28565.
% 1.66/1.82  
% 1.66/1.82  set(prolog_style_variables).
% 1.66/1.82  set(auto).
% 1.66/1.82     dependent: set(auto1).
% 1.66/1.82     dependent: set(process_input).
% 1.66/1.82     dependent: clear(print_kept).
% 1.66/1.82     dependent: clear(print_new_demod).
% 1.66/1.82     dependent: clear(print_back_demod).
% 1.66/1.82     dependent: clear(print_back_sub).
% 1.66/1.82     dependent: set(control_memory).
% 1.66/1.82     dependent: assign(max_mem, 12000).
% 1.66/1.82     dependent: assign(pick_given_ratio, 4).
% 1.66/1.82     dependent: assign(stats_level, 1).
% 1.66/1.82     dependent: assign(max_seconds, 10800).
% 1.66/1.82  clear(print_given).
% 1.66/1.82  
% 1.66/1.82  list(usable).
% 1.66/1.82  0 [] A=A.
% 1.66/1.82  0 [] c_lesse_quals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b).
% 1.66/1.82  0 [] -c_lesse_quals(c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_f(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_h(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),t_b),t_b).
% 1.66/1.82  0 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.66/1.82  0 [] -class_OrderedGroup_Olordered__ab__group__abs(T_a)|c_lesse_quals(c_0,c_HOL_Oabs(V_a,T_a),T_a).
% 1.66/1.82  0 [] -class_OrderedGroup_Oab__semigroup__mult(T_a)|c_times(V_a,c_times(V_b,V_c,T_a),T_a)=c_times(V_b,c_times(V_a,V_c,T_a),T_a).
% 1.66/1.82  0 [] -class_Ring__and__Field_Opordered__semiring(T_a)| -c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(c_0,V_c,T_a)|c_lesse_quals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a).
% 1.66/1.82  0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Oab__semigroup__mult(T).
% 1.66/1.82  0 [] -class_Ring__and__Field_Oordered__idom(T)|class_Ring__and__Field_Opordered__semiring(T).
% 1.66/1.82  0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Olordered__ab__group__abs(T).
% 1.66/1.82  end_of_list.
% 1.66/1.82  
% 1.66/1.82  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.66/1.82  
% 1.66/1.82  This is a Horn set with equality.  The strategy will be
% 1.66/1.82  Knuth-Bendix and hyper_res, with positive clauses in
% 1.66/1.82  sos and nonpositive clauses in usable.
% 1.66/1.82  
% 1.66/1.82     dependent: set(knuth_bendix).
% 1.66/1.82     dependent: set(anl_eq).
% 1.66/1.82     dependent: set(para_from).
% 1.66/1.82     dependent: set(para_into).
% 1.66/1.82     dependent: clear(para_from_right).
% 1.66/1.82     dependent: clear(para_into_right).
% 1.66/1.82     dependent: set(para_from_vars).
% 1.66/1.82     dependent: set(eq_units_both_ways).
% 1.66/1.82     dependent: set(dynamic_demod_all).
% 1.66/1.82     dependent: set(dynamic_demod).
% 1.66/1.82     dependent: set(order_eq).
% 1.66/1.82     dependent: set(back_demod).
% 1.66/1.82     dependent: set(lrpo).
% 1.66/1.82     dependent: set(hyper_res).
% 1.66/1.82     dependent: clear(order_hyper).
% 1.66/1.82  
% 1.66/1.82  ------------> process usable:
% 1.66/1.82  ** KEPT (pick-wt=39): 1 [] -c_lesse_quals(c_times(c_HOL_Oabs(v_l(v_x(A),v_xa(A)),t_b),c_HOL_Oabs(v_f(v_k(v_x(A),v_xa(A))),t_b),t_b),c_times(A,c_times(c_HOL_Oabs(v_l(v_x(A),v_xa(A)),t_b),c_HOL_Oabs(v_h(v_k(v_x(A),v_xa(A))),t_b),t_b),t_b),t_b).
% 1.66/1.82  ** KEPT (pick-wt=8): 2 [] -class_OrderedGroup_Olordered__ab__group__abs(A)|c_lesse_quals(c_0,c_HOL_Oabs(B,A),A).
% 1.66/1.82  ** KEPT (pick-wt=17): 3 [] -class_OrderedGroup_Oab__semigroup__mult(A)|c_times(B,c_times(C,D,A),A)=c_times(C,c_times(B,D,A),A).
% 1.66/1.82  ** KEPT (pick-wt=20): 4 [] -class_Ring__and__Field_Opordered__semiring(A)| -c_lesse_quals(B,C,A)| -c_lesse_quals(c_0,D,A)|c_lesse_quals(c_times(D,B,A),c_times(D,C,A),A).
% 1.66/1.82  ** KEPT (pick-wt=4): 5 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Oab__semigroup__mult(A).
% 1.66/1.82  ** KEPT (pick-wt=4): 6 [] -class_Ring__and__Field_Oordered__idom(A)|class_Ring__and__Field_Opordered__semiring(A).
% 1.66/1.82  ** KEPT (pick-wt=4): 7 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Olordered__ab__group__abs(A).
% 1.66/1.82  
% 1.66/1.82  ------------> process sos:
% 1.66/1.82  ** KEPT (pick-wt=3): 8 [] A=A.
% 1.66/1.82  ** KEPT (pick-wt=13): 9 [] c_lesse_quals(c_HOL_Oabs(v_f(A),t_b),c_times(v_c,c_HOL_Oabs(v_h(A),t_b),t_b),t_b).
% 1.66/1.82  ** KEPT (pick-wt=2): 10 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.66/1.82    Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] A=A.
% 1.66/1.82  
% 1.66/1.82  ======= end of input processing =======
% 1.66/1.82  
% 1.66/1.82  =========== start of search ===========
% 1.66/1.82  
% 1.66/1.82  -------- PROOF -------- 
% 1.66/1.82  
% 1.66/1.82  ----> UNIT CONFLICT at   0.00 sec ----> 23 [binary,22.1,17.1] $F.
% 1.66/1.82  
% 1.66/1.82  Length of proof is 7.  Level of proof is 3.
% 1.66/1.82  
% 1.66/1.82  ---------------- PROOF ----------------
% 1.66/1.82  % SZS status Unsatisfiable
% 1.66/1.82  % SZS output start Refutation
% See solution above
% 1.66/1.82  ------------ end of proof -------------
% 1.66/1.82  
% 1.66/1.82  
% 1.66/1.82  Search stopped by max_proofs option.
% 1.66/1.82  
% 1.66/1.82  
% 1.66/1.82  Search stopped by max_proofs option.
% 1.66/1.82  
% 1.66/1.82  ============ end of search ============
% 1.66/1.82  
% 1.66/1.82  -------------- statistics -------------
% 1.66/1.82  clauses given                  8
% 1.66/1.82  clauses generated             19
% 1.66/1.82  clauses kept                  22
% 1.66/1.82  clauses forward subsumed      11
% 1.66/1.82  clauses back subsumed          0
% 1.66/1.82  Kbytes malloced              976
% 1.66/1.82  
% 1.66/1.82  ----------- times (seconds) -----------
% 1.66/1.82  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.66/1.82  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.66/1.82  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.66/1.82  
% 1.66/1.82  That finishes the proof of the theorem.
% 1.66/1.82  
% 1.66/1.82  Process 28565 finished Wed Jul 27 10:04:22 2022
% 1.66/1.82  Otter interrupted
% 1.66/1.82  PROOF FOUND
%------------------------------------------------------------------------------