TSTP Solution File: REL009+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : REL009+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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   : Theorem 22.43s 22.61s
% Output   : Refutation 22.43s
% 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    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(join(skc4,skc5),skc5),
    file('REL009+1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(converse(converse(u)),u),
    file('REL009+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(join(converse(u),converse(v)),converse(join(u,v))),
    file('REL009+1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(composition(converse(u),converse(v)),converse(composition(v,u))),
    file('REL009+1.p',unknown),
    [] ).

cnf(12,axiom,
    equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
    file('REL009+1.p',unknown),
    [] ).

cnf(15,axiom,
    ( ~ equal(join(composition(skc4,skc6),composition(skc5,skc6)),composition(skc5,skc6))
    | ~ equal(join(composition(skc7,skc4),composition(skc7,skc5)),composition(skc7,skc5)) ),
    file('REL009+1.p',unknown),
    [] ).

cnf(18,plain,
    ( ~ equal(composition(skc5,skc6),composition(skc5,skc6))
    | ~ equal(join(composition(skc7,skc4),composition(skc7,skc5)),composition(skc7,skc5)) ),
    inference(rew,[status(thm),theory(equality)],[1,15,12]),
    [iquote('0:Rew:1.0,15.0,12.0,15.0')] ).

cnf(19,plain,
    ~ equal(join(composition(skc7,skc4),composition(skc7,skc5)),composition(skc7,skc5)),
    inference(obv,[status(thm),theory(equality)],[18]),
    [iquote('0:Obv:18.0')] ).

cnf(32,plain,
    equal(converse(composition(u,converse(v))),composition(v,converse(u))),
    inference(spr,[status(thm),theory(equality)],[3,9]),
    [iquote('0:SpR:3.0,9.0')] ).

cnf(36,plain,
    equal(converse(join(u,converse(v))),join(converse(u),v)),
    inference(spr,[status(thm),theory(equality)],[3,8]),
    [iquote('0:SpR:3.0,8.0')] ).

cnf(323,plain,
    equal(join(converse(composition(u,v)),composition(w,converse(u))),composition(join(converse(v),w),converse(u))),
    inference(spr,[status(thm),theory(equality)],[9,12]),
    [iquote('0:SpR:9.0,12.0')] ).

cnf(582,plain,
    equal(join(converse(u),composition(v,converse(w))),converse(join(u,composition(w,converse(v))))),
    inference(spr,[status(thm),theory(equality)],[32,8]),
    [iquote('0:SpR:32.0,8.0')] ).

cnf(603,plain,
    equal(converse(join(composition(u,v),composition(u,converse(w)))),composition(join(converse(v),w),converse(u))),
    inference(rew,[status(thm),theory(equality)],[582,323]),
    [iquote('0:Rew:582.0,323.0')] ).

cnf(660,plain,
    equal(composition(join(converse(u),v),converse(w)),converse(composition(w,join(u,converse(v))))),
    inference(spr,[status(thm),theory(equality)],[36,9]),
    [iquote('0:SpR:36.0,9.0')] ).

cnf(696,plain,
    equal(converse(join(composition(u,v),composition(u,converse(w)))),converse(composition(u,join(v,converse(w))))),
    inference(rew,[status(thm),theory(equality)],[660,603]),
    [iquote('0:Rew:660.0,603.0')] ).

cnf(4526,plain,
    equal(converse(join(composition(u,v),composition(u,w))),converse(composition(u,join(v,w)))),
    inference(spr,[status(thm),theory(equality)],[3,696]),
    [iquote('0:SpR:3.0,696.0')] ).

cnf(61655,plain,
    equal(join(composition(u,v),composition(u,w)),converse(converse(composition(u,join(v,w))))),
    inference(spr,[status(thm),theory(equality)],[4526,3]),
    [iquote('0:SpR:4526.0,3.0')] ).

cnf(61872,plain,
    equal(join(composition(u,v),composition(u,w)),composition(u,join(v,w))),
    inference(rew,[status(thm),theory(equality)],[3,61655]),
    [iquote('0:Rew:3.0,61655.0')] ).

cnf(61875,plain,
    ~ equal(composition(skc7,join(skc4,skc5)),composition(skc7,skc5)),
    inference(rew,[status(thm),theory(equality)],[61872,19]),
    [iquote('0:Rew:61872.0,19.0')] ).

cnf(61879,plain,
    ~ equal(composition(skc7,skc5),composition(skc7,skc5)),
    inference(rew,[status(thm),theory(equality)],[1,61875]),
    [iquote('0:Rew:1.0,61875.0')] ).

cnf(61880,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[61879]),
    [iquote('0:Obv:61879.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : REL009+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n026.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Fri Jul  8 11:09:25 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 22.43/22.61  
% 22.43/22.61  SPASS V 3.9 
% 22.43/22.61  SPASS beiseite: Proof found.
% 22.43/22.61  % SZS status Theorem
% 22.43/22.61  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 22.43/22.61  SPASS derived 36835 clauses, backtracked 0 clauses, performed 0 splits and kept 3977 clauses.
% 22.43/22.61  SPASS allocated 138079 KBytes.
% 22.43/22.61  SPASS spent	0:0:21.24 on the problem.
% 22.43/22.61  		0:00:00.04 for the input.
% 22.43/22.61  		0:00:00.03 for the FLOTTER CNF translation.
% 22.43/22.61  		0:00:00.28 for inferences.
% 22.43/22.61  		0:00:00.00 for the backtracking.
% 22.43/22.61  		0:0:20.84 for the reduction.
% 22.43/22.61  
% 22.43/22.61  
% 22.43/22.61  Here is a proof with depth 3, length 21 :
% 22.43/22.61  % SZS output start Refutation
% See solution above
% 22.43/22.61  Formulae used in the proof : goals converse_idempotence converse_additivity converse_multiplicativity composition_distributivity
% 22.43/22.61  
%------------------------------------------------------------------------------