TSTP Solution File: COL003-15 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : COL003-15 : TPTP v8.1.0. Released v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 : Fri Jul 15 00:42:21 EDT 2022

% Result   : Unsatisfiable 3.00s 3.18s
% Output   : Refutation 3.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   14 (  14 unt;   0 nHn;  14 RR)
%            Number of literals    :   14 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(apply(apply(apply(b,u),v),w),apply(u,apply(v,w))),
    file('COL003-15.p',unknown),
    [] ).

cnf(2,axiom,
    equal(apply(apply(w__dfg,u),v),apply(apply(u,v),v)),
    file('COL003-15.p',unknown),
    [] ).

cnf(3,axiom,
    equal(apply(apply(b,apply(apply(b,apply(w__dfg,w__dfg)),w__dfg)),apply(apply(b,b),b)),strong_fixed_point),
    file('COL003-15.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),apply(strong_fixed_point,fixed_pt)),
    file('COL003-15.p',unknown),
    [] ).

cnf(6,plain,
    equal(apply(apply(w__dfg,w__dfg),u),apply(apply(u,u),u)),
    inference(spr,[status(thm),theory(equality)],[2]),
    [iquote('0:SpR:2.0,2.0')] ).

cnf(26,plain,
    equal(apply(apply(w__dfg,apply(b,u)),v),apply(u,apply(v,v))),
    inference(spr,[status(thm),theory(equality)],[1,2]),
    [iquote('0:SpR:1.0,2.0')] ).

cnf(35,plain,
    equal(apply(apply(apply(b,apply(w__dfg,w__dfg)),w__dfg),apply(apply(apply(b,b),b),u)),apply(strong_fixed_point,u)),
    inference(spr,[status(thm),theory(equality)],[3,1]),
    [iquote('0:SpR:3.0,1.0')] ).

cnf(36,plain,
    equal(apply(apply(w__dfg,w__dfg),apply(w__dfg,apply(b,apply(b,u)))),apply(strong_fixed_point,u)),
    inference(rew,[status(thm),theory(equality)],[1,35]),
    [iquote('0:Rew:1.0,35.0,1.0,35.0')] ).

cnf(38,plain,
    equal(apply(apply(w__dfg,apply(w__dfg,apply(b,u))),v),apply(apply(u,apply(v,v)),v)),
    inference(spr,[status(thm),theory(equality)],[26,2]),
    [iquote('0:SpR:26.0,2.0')] ).

cnf(485,plain,
    equal(apply(apply(w__dfg,apply(w__dfg,apply(b,apply(b,u)))),v),apply(u,apply(apply(v,v),v))),
    inference(spr,[status(thm),theory(equality)],[38,1]),
    [iquote('0:SpR:38.0,1.0')] ).

cnf(3790,plain,
    equal(apply(apply(w__dfg,apply(w__dfg,apply(b,apply(b,u)))),v),apply(u,apply(apply(w__dfg,w__dfg),v))),
    inference(spr,[status(thm),theory(equality)],[6,485]),
    [iquote('0:SpR:6.0,485.0')] ).

cnf(5511,plain,
    equal(apply(u,apply(apply(w__dfg,w__dfg),apply(w__dfg,apply(b,apply(b,u))))),apply(apply(w__dfg,w__dfg),apply(w__dfg,apply(b,apply(b,u))))),
    inference(spr,[status(thm),theory(equality)],[3790,2]),
    [iquote('0:SpR:3790.0,2.0')] ).

cnf(5562,plain,
    equal(apply(u,apply(strong_fixed_point,u)),apply(strong_fixed_point,u)),
    inference(rew,[status(thm),theory(equality)],[36,5511]),
    [iquote('0:Rew:36.0,5511.0')] ).

cnf(5563,plain,
    $false,
    inference(unc,[status(thm)],[5562,4]),
    [iquote('0:UnC:5562.0,4.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : COL003-15 : TPTP v8.1.0. Released v2.1.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n029.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 : Tue May 31 06:02:59 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 3.00/3.18  
% 3.00/3.18  SPASS V 3.9 
% 3.00/3.18  SPASS beiseite: Proof found.
% 3.00/3.18  % SZS status Theorem
% 3.00/3.18  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 3.00/3.18  SPASS derived 3022 clauses, backtracked 0 clauses, performed 0 splits and kept 1124 clauses.
% 3.00/3.18  SPASS allocated 73713 KBytes.
% 3.00/3.18  SPASS spent	0:00:02.79 on the problem.
% 3.00/3.18  		0:00:00.03 for the input.
% 3.00/3.18  		0:00:00.00 for the FLOTTER CNF translation.
% 3.00/3.18  		0:00:00.06 for inferences.
% 3.00/3.18  		0:00:00.00 for the backtracking.
% 3.00/3.18  		0:00:02.67 for the reduction.
% 3.00/3.18  
% 3.00/3.18  
% 3.00/3.18  Here is a proof with depth 5, length 14 :
% 3.00/3.18  % SZS output start Refutation
% See solution above
% 3.00/3.18  Formulae used in the proof : b_definition w_definition strong_fixed_point prove_strong_fixed_point
% 3.00/3.18  
%------------------------------------------------------------------------------