TSTP Solution File: REL009-2 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : REL009-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n014.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 20:01:34 EDT 2022

% Result   : Unsatisfiable 61.08s 61.28s
% Output   : Refutation 61.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   21 (  19 unt;   0 nHn;  21 RR)
%            Number of literals    :   23 (   0 equ;   7 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(join(sk1,sk2),sk2),
    file('REL009-2.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ equal(join(composition(sk1,sk3),composition(sk2,sk3)),composition(sk2,sk3))
    | ~ equal(join(composition(sk3,sk1),composition(sk3,sk2)),composition(sk3,sk2)) ),
    file('REL009-2.p',unknown),
    [] ).

cnf(9,axiom,
    equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
    file('REL009-2.p',unknown),
    [] ).

cnf(10,axiom,
    equal(converse(converse(u)),u),
    file('REL009-2.p',unknown),
    [] ).

cnf(11,axiom,
    equal(join(converse(u),converse(v)),converse(join(u,v))),
    file('REL009-2.p',unknown),
    [] ).

cnf(12,axiom,
    equal(composition(converse(u),converse(v)),converse(composition(v,u))),
    file('REL009-2.p',unknown),
    [] ).

cnf(21,plain,
    ( ~ equal(composition(sk2,sk3),composition(sk2,sk3))
    | ~ equal(join(composition(sk3,sk1),composition(sk3,sk2)),composition(sk3,sk2)) ),
    inference(rew,[status(thm),theory(equality)],[1,2,9]),
    [iquote('0:Rew:1.0,2.0,9.0,2.0')] ).

cnf(22,plain,
    ~ equal(join(composition(sk3,sk1),composition(sk3,sk2)),composition(sk3,sk2)),
    inference(obv,[status(thm),theory(equality)],[21]),
    [iquote('0:Obv:21.0')] ).

cnf(35,plain,
    equal(converse(composition(u,converse(v))),composition(v,converse(u))),
    inference(spr,[status(thm),theory(equality)],[10,12]),
    [iquote('0:SpR:10.0,12.0')] ).

cnf(39,plain,
    equal(converse(join(u,converse(v))),join(converse(u),v)),
    inference(spr,[status(thm),theory(equality)],[10,11]),
    [iquote('0:SpR:10.0,11.0')] ).

cnf(329,plain,
    equal(join(converse(composition(u,v)),composition(w,converse(u))),composition(join(converse(v),w),converse(u))),
    inference(spr,[status(thm),theory(equality)],[12,9]),
    [iquote('0:SpR:12.0,9.0')] ).

cnf(762,plain,
    equal(join(converse(u),composition(v,converse(w))),converse(join(u,composition(w,converse(v))))),
    inference(spr,[status(thm),theory(equality)],[35,11]),
    [iquote('0:SpR:35.0,11.0')] ).

cnf(785,plain,
    equal(converse(join(composition(u,v),composition(u,converse(w)))),composition(join(converse(v),w),converse(u))),
    inference(rew,[status(thm),theory(equality)],[762,329]),
    [iquote('0:Rew:762.0,329.0')] ).

cnf(935,plain,
    equal(composition(join(converse(u),v),converse(w)),converse(composition(w,join(u,converse(v))))),
    inference(spr,[status(thm),theory(equality)],[39,12]),
    [iquote('0:SpR:39.0,12.0')] ).

cnf(969,plain,
    equal(converse(join(composition(u,v),composition(u,converse(w)))),converse(composition(u,join(v,converse(w))))),
    inference(rew,[status(thm),theory(equality)],[935,785]),
    [iquote('0:Rew:935.0,785.0')] ).

cnf(5668,plain,
    equal(converse(join(composition(u,v),composition(u,w))),converse(composition(u,join(v,w)))),
    inference(spr,[status(thm),theory(equality)],[10,969]),
    [iquote('0:SpR:10.0,969.0')] ).

cnf(86671,plain,
    equal(join(composition(u,v),composition(u,w)),converse(converse(composition(u,join(v,w))))),
    inference(spr,[status(thm),theory(equality)],[5668,10]),
    [iquote('0:SpR:5668.0,10.0')] ).

cnf(86920,plain,
    equal(join(composition(u,v),composition(u,w)),composition(u,join(v,w))),
    inference(rew,[status(thm),theory(equality)],[10,86671]),
    [iquote('0:Rew:10.0,86671.0')] ).

cnf(86924,plain,
    ~ equal(composition(sk3,join(sk1,sk2)),composition(sk3,sk2)),
    inference(rew,[status(thm),theory(equality)],[86920,22]),
    [iquote('0:Rew:86920.0,22.0')] ).

cnf(86950,plain,
    ~ equal(composition(sk3,sk2),composition(sk3,sk2)),
    inference(rew,[status(thm),theory(equality)],[1,86924]),
    [iquote('0:Rew:1.0,86924.0')] ).

cnf(86951,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[86950]),
    [iquote('0:Obv:86950.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : REL009-2 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n014.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 : Fri Jul  8 07:55:51 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 61.08/61.28  
% 61.08/61.28  SPASS V 3.9 
% 61.08/61.28  SPASS beiseite: Proof found.
% 61.08/61.28  % SZS status Theorem
% 61.08/61.28  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 61.08/61.28  SPASS derived 52295 clauses, backtracked 0 clauses, performed 0 splits and kept 7255 clauses.
% 61.08/61.28  SPASS allocated 159739 KBytes.
% 61.08/61.28  SPASS spent	0:0:59.02 on the problem.
% 61.08/61.28  		0:00:00.04 for the input.
% 61.08/61.28  		0:00:00.00 for the FLOTTER CNF translation.
% 61.08/61.28  		0:00:00.46 for inferences.
% 61.08/61.28  		0:00:00.00 for the backtracking.
% 61.08/61.28  		0:0:58.39 for the reduction.
% 61.08/61.28  
% 61.08/61.28  
% 61.08/61.28  Here is a proof with depth 3, length 21 :
% 61.08/61.28  % SZS output start Refutation
% See solution above
% 61.08/61.28  Formulae used in the proof : goals_17 goals_18 composition_distributivity_7 converse_idempotence_8 converse_additivity_9 converse_multiplicativity_10
% 61.08/61.28  
%------------------------------------------------------------------------------