TSTP Solution File: GRP435-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP435-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n018.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 : Sat Jul 16 11:47:28 EDT 2022

% Result   : Unsatisfiable 3.47s 3.65s
% Output   : Refutation 3.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   60 (  60 unt;   0 nHn;  60 RR)
%            Number of literals    :   60 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   12 (   3 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(u,v),w)),u),v),multiply(x,inverse(x)))),w),
    file('GRP435-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
    file('GRP435-1.p',unknown),
    [] ).

cnf(4,plain,
    equal(inverse(multiply(multiply(multiply(u,multiply(inverse(multiply(multiply(v,w),u)),v)),w),multiply(x,inverse(x)))),multiply(y,inverse(y))),
    inference(spr,[status(thm),theory(equality)],[1]),
    [iquote('0:SpR:1.0,1.0')] ).

cnf(10,plain,
    equal(multiply(u,inverse(u)),multiply(v,inverse(v))),
    inference(spr,[status(thm),theory(equality)],[4]),
    [iquote('0:SpR:4.0,4.0')] ).

cnf(35,plain,
    equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(u,inverse(u)),v)),w),inverse(w)),multiply(x,inverse(x)))),v),
    inference(spr,[status(thm),theory(equality)],[10,1]),
    [iquote('0:SpR:10.0,1.0')] ).

cnf(37,plain,
    equal(inverse(multiply(multiply(multiply(inverse(multiply(u,inverse(u))),v),w),multiply(x,inverse(x)))),inverse(multiply(v,w))),
    inference(spr,[status(thm),theory(equality)],[10,1]),
    [iquote('0:SpR:10.0,1.0')] ).

cnf(105,plain,
    equal(inverse(multiply(multiply(multiply(u,inverse(u)),v),multiply(w,inverse(w)))),inverse(multiply(inverse(inverse(multiply(x,inverse(x)))),v))),
    inference(spr,[status(thm),theory(equality)],[10,37]),
    [iquote('0:SpR:10.0,37.0')] ).

cnf(117,plain,
    equal(inverse(multiply(u,inverse(u))),inverse(multiply(v,inverse(v)))),
    inference(spr,[status(thm),theory(equality)],[35,37]),
    [iquote('0:SpR:35.0,37.0')] ).

cnf(168,plain,
    equal(multiply(u,inverse(u)),multiply(multiply(v,inverse(v)),inverse(multiply(w,inverse(w))))),
    inference(spr,[status(thm),theory(equality)],[117,10]),
    [iquote('0:SpR:117.0,10.0')] ).

cnf(196,plain,
    equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(u,inverse(u)),v)),multiply(w,inverse(w))),inverse(multiply(x,inverse(x)))),multiply(y,inverse(y)))),v),
    inference(spr,[status(thm),theory(equality)],[117,35]),
    [iquote('0:SpR:117.0,35.0')] ).

cnf(239,plain,
    equal(inverse(multiply(multiply(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(v)))),inverse(inverse(inverse(multiply(multiply(w,inverse(w)),x))))),multiply(y,inverse(y)))),x),
    inference(spr,[status(thm),theory(equality)],[168,35]),
    [iquote('0:SpR:168.0,35.0')] ).

cnf(240,plain,
    equal(inverse(multiply(multiply(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(v)))),w),multiply(x,inverse(x)))),inverse(multiply(inverse(inverse(multiply(y,inverse(y)))),w))),
    inference(spr,[status(thm),theory(equality)],[168,37]),
    [iquote('0:SpR:168.0,37.0')] ).

cnf(263,plain,
    equal(inverse(multiply(multiply(multiply(inverse(multiply(u,inverse(u))),multiply(inverse(multiply(v,inverse(v))),w)),inverse(w)),multiply(x,inverse(x)))),multiply(y,inverse(y))),
    inference(spr,[status(thm),theory(equality)],[168,4]),
    [iquote('0:SpR:168.0,4.0')] ).

cnf(300,plain,
    equal(inverse(multiply(multiply(inverse(multiply(u,inverse(u))),v),inverse(v))),multiply(w,inverse(w))),
    inference(rew,[status(thm),theory(equality)],[37,263]),
    [iquote('0:Rew:37.0,263.0')] ).

cnf(414,plain,
    equal(inverse(multiply(multiply(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(v)))),w),multiply(x,inverse(x)))),inverse(w)),
    inference(spr,[status(thm),theory(equality)],[300,1]),
    [iquote('0:SpR:300.0,1.0')] ).

cnf(512,plain,
    equal(inverse(inverse(inverse(inverse(multiply(multiply(u,inverse(u)),v))))),v),
    inference(rew,[status(thm),theory(equality)],[414,239]),
    [iquote('0:Rew:414.0,239.0')] ).

cnf(513,plain,
    equal(inverse(multiply(inverse(inverse(multiply(u,inverse(u)))),v)),inverse(v)),
    inference(rew,[status(thm),theory(equality)],[414,240]),
    [iquote('0:Rew:414.0,240.0')] ).

cnf(517,plain,
    equal(inverse(multiply(multiply(multiply(u,inverse(u)),v),multiply(w,inverse(w)))),inverse(v)),
    inference(rew,[status(thm),theory(equality)],[513,105]),
    [iquote('0:Rew:513.0,105.0')] ).

cnf(560,plain,
    equal(inverse(inverse(inverse(inverse(multiply(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(v)))),w))))),w),
    inference(spr,[status(thm),theory(equality)],[117,512]),
    [iquote('0:SpR:117.0,512.0')] ).

cnf(565,plain,
    equal(inverse(inverse(inverse(inverse(multiply(inverse(multiply(multiply(inverse(multiply(u,inverse(u))),v),inverse(v))),w))))),w),
    inference(spr,[status(thm),theory(equality)],[300,512]),
    [iquote('0:SpR:300.0,512.0')] ).

cnf(589,plain,
    equal(inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(u,inverse(u))))))),v)),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[513]),
    [iquote('0:SpR:513.0,513.0')] ).

cnf(1098,plain,
    equal(inverse(inverse(inverse(inverse(inverse(multiply(u,inverse(u))))))),multiply(v,inverse(v))),
    inference(spr,[status(thm),theory(equality)],[517,512]),
    [iquote('0:SpR:517.0,512.0')] ).

cnf(1151,plain,
    equal(inverse(multiply(multiply(multiply(u,inverse(u)),v),multiply(multiply(w,inverse(w)),inverse(multiply(x,inverse(x)))))),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[168,517]),
    [iquote('0:SpR:168.0,517.0')] ).

cnf(1617,plain,
    equal(inverse(multiply(multiply(u,inverse(u)),v)),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[1098,589]),
    [iquote('0:SpR:1098.0,589.0')] ).

cnf(1744,plain,
    equal(inverse(multiply(multiply(multiply(inverse(u),v),inverse(v)),multiply(w,inverse(w)))),u),
    inference(rew,[status(thm),theory(equality)],[1617,35]),
    [iquote('0:Rew:1617.0,35.0')] ).

cnf(1745,plain,
    equal(inverse(inverse(inverse(inverse(u)))),u),
    inference(rew,[status(thm),theory(equality)],[1617,512]),
    [iquote('0:Rew:1617.0,512.0')] ).

cnf(1868,plain,
    equal(inverse(multiply(multiply(multiply(inverse(u),multiply(v,inverse(v))),inverse(multiply(w,inverse(w)))),multiply(x,inverse(x)))),u),
    inference(rew,[status(thm),theory(equality)],[1617,196]),
    [iquote('0:Rew:1617.0,196.0')] ).

cnf(1990,plain,
    equal(multiply(inverse(multiply(multiply(inverse(multiply(u,inverse(u))),v),inverse(v))),w),w),
    inference(rew,[status(thm),theory(equality)],[1745,565]),
    [iquote('0:Rew:1745.0,565.0')] ).

cnf(1994,plain,
    equal(multiply(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(v)))),w),w),
    inference(rew,[status(thm),theory(equality)],[1745,560]),
    [iquote('0:Rew:1745.0,560.0')] ).

cnf(2093,plain,
    equal(inverse(multiply(u,multiply(v,inverse(v)))),inverse(u)),
    inference(rew,[status(thm),theory(equality)],[1994,414]),
    [iquote('0:Rew:1994.0,414.0')] ).

cnf(2101,plain,
    equal(inverse(multiply(multiply(u,multiply(inverse(multiply(multiply(v,w),u)),v)),w)),multiply(x,inverse(x))),
    inference(rew,[status(thm),theory(equality)],[2093,4]),
    [iquote('0:Rew:2093.0,4.0')] ).

cnf(2103,plain,
    equal(inverse(multiply(multiply(inverse(multiply(multiply(u,v),w)),u),v)),w),
    inference(rew,[status(thm),theory(equality)],[2093,1]),
    [iquote('0:Rew:2093.0,1.0')] ).

cnf(2432,plain,
    equal(inverse(multiply(multiply(inverse(u),v),inverse(v))),u),
    inference(rew,[status(thm),theory(equality)],[2093,1744]),
    [iquote('0:Rew:2093.0,1744.0')] ).

cnf(2481,plain,
    equal(multiply(multiply(u,inverse(u)),v),v),
    inference(rew,[status(thm),theory(equality)],[2432,1990]),
    [iquote('0:Rew:2432.0,1990.0')] ).

cnf(2500,plain,
    equal(inverse(multiply(multiply(multiply(u,inverse(u)),v),inverse(multiply(w,inverse(w))))),inverse(v)),
    inference(rew,[status(thm),theory(equality)],[2481,1151]),
    [iquote('0:Rew:2481.0,1151.0')] ).

cnf(2660,plain,
    equal(inverse(multiply(u,inverse(multiply(v,inverse(v))))),inverse(u)),
    inference(rew,[status(thm),theory(equality)],[2481,2500]),
    [iquote('0:Rew:2481.0,2500.0')] ).

cnf(2813,plain,
    equal(inverse(inverse(u)),u),
    inference(rew,[status(thm),theory(equality)],[2093,1868,2660]),
    [iquote('0:Rew:2093.0,1868.0,2660.0,1868.0,2093.0,1868.0')] ).

cnf(3645,plain,
    equal(inverse(multiply(multiply(u,inverse(multiply(multiply(v,w),u))),v)),w),
    inference(spr,[status(thm),theory(equality)],[2103]),
    [iquote('0:SpR:2103.0,2103.0')] ).

cnf(3861,plain,
    equal(multiply(multiply(u,inverse(multiply(multiply(v,w),u))),v),inverse(w)),
    inference(spr,[status(thm),theory(equality)],[3645,2813]),
    [iquote('0:SpR:3645.0,2813.0')] ).

cnf(3868,plain,
    equal(inverse(multiply(multiply(u,inverse(multiply(v,u))),multiply(w,inverse(w)))),v),
    inference(spr,[status(thm),theory(equality)],[2481,3645]),
    [iquote('0:SpR:2481.0,3645.0')] ).

cnf(3889,plain,
    equal(inverse(multiply(u,inverse(multiply(v,u)))),v),
    inference(rew,[status(thm),theory(equality)],[2093,3868]),
    [iquote('0:Rew:2093.0,3868.0')] ).

cnf(3924,plain,
    equal(multiply(u,inverse(multiply(v,u))),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[3889,2813]),
    [iquote('0:SpR:3889.0,2813.0')] ).

cnf(3945,plain,
    equal(multiply(inverse(multiply(u,v)),u),inverse(v)),
    inference(rew,[status(thm),theory(equality)],[3924,3861]),
    [iquote('0:Rew:3924.0,3861.0')] ).

cnf(4177,plain,
    equal(inverse(multiply(multiply(u,multiply(multiply(v,inverse(v)),w)),multiply(inverse(multiply(multiply(x,u),w)),x))),multiply(y,inverse(y))),
    inference(spr,[status(thm),theory(equality)],[2101]),
    [iquote('0:SpR:2101.0,2101.0')] ).

cnf(4328,plain,
    equal(inverse(multiply(multiply(u,v),multiply(inverse(multiply(multiply(w,u),v)),w))),multiply(x,inverse(x))),
    inference(rew,[status(thm),theory(equality)],[2481,4177]),
    [iquote('0:Rew:2481.0,4177.0')] ).

cnf(4647,plain,
    equal(inverse(multiply(multiply(u,v),multiply(inverse(multiply(inverse(w),v)),inverse(multiply(u,w))))),multiply(x,inverse(x))),
    inference(spr,[status(thm),theory(equality)],[3945,4328]),
    [iquote('0:SpR:3945.0,4328.0')] ).

cnf(4855,plain,
    equal(inverse(multiply(inverse(u),v)),multiply(inverse(v),u)),
    inference(spr,[status(thm),theory(equality)],[2432,3924]),
    [iquote('0:SpR:2432.0,3924.0')] ).

cnf(4856,plain,
    equal(multiply(u,multiply(inverse(u),v)),inverse(inverse(v))),
    inference(spr,[status(thm),theory(equality)],[2432,3945]),
    [iquote('0:SpR:2432.0,3945.0')] ).

cnf(4908,plain,
    equal(inverse(multiply(multiply(u,v),multiply(multiply(inverse(v),w),inverse(multiply(u,w))))),multiply(x,inverse(x))),
    inference(rew,[status(thm),theory(equality)],[4855,4647]),
    [iquote('0:Rew:4855.0,4647.0')] ).

cnf(4921,plain,
    equal(multiply(u,multiply(inverse(u),v)),v),
    inference(rew,[status(thm),theory(equality)],[2813,4856]),
    [iquote('0:Rew:2813.0,4856.0')] ).

cnf(5004,plain,
    equal(multiply(inverse(u),multiply(u,v)),v),
    inference(spr,[status(thm),theory(equality)],[2813,4921]),
    [iquote('0:SpR:2813.0,4921.0')] ).

cnf(5009,plain,
    equal(inverse(multiply(u,inverse(v))),multiply(v,inverse(u))),
    inference(spr,[status(thm),theory(equality)],[3924,4921]),
    [iquote('0:SpR:3924.0,4921.0')] ).

cnf(5014,plain,
    equal(multiply(multiply(u,v),inverse(v)),u),
    inference(spr,[status(thm),theory(equality)],[3945,4921]),
    [iquote('0:SpR:3945.0,4921.0')] ).

cnf(5043,plain,
    equal(multiply(inverse(u),inverse(v)),inverse(multiply(v,u))),
    inference(spr,[status(thm),theory(equality)],[5004,3945]),
    [iquote('0:SpR:5004.0,3945.0')] ).

cnf(5080,plain,
    equal(multiply(multiply(u,inverse(v)),v),u),
    inference(spr,[status(thm),theory(equality)],[2813,5014]),
    [iquote('0:SpR:2813.0,5014.0')] ).

cnf(5165,plain,
    equal(inverse(multiply(multiply(u,multiply(v,w)),multiply(inverse(w),inverse(multiply(u,v))))),multiply(x,inverse(x))),
    inference(spr,[status(thm),theory(equality)],[3945,4908]),
    [iquote('0:SpR:3945.0,4908.0')] ).

cnf(5224,plain,
    equal(multiply(multiply(multiply(u,v),w),inverse(multiply(u,multiply(v,w)))),multiply(x,inverse(x))),
    inference(rew,[status(thm),theory(equality)],[5009,5165,5043]),
    [iquote('0:Rew:5009.0,5165.0,5043.0,5165.0')] ).

cnf(5534,plain,
    equal(multiply(multiply(u,inverse(u)),multiply(v,multiply(w,x))),multiply(multiply(v,w),x)),
    inference(spr,[status(thm),theory(equality)],[5224,5080]),
    [iquote('0:SpR:5224.0,5080.0')] ).

cnf(5632,plain,
    equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
    inference(rew,[status(thm),theory(equality)],[2481,5534]),
    [iquote('0:Rew:2481.0,5534.0')] ).

cnf(5633,plain,
    $false,
    inference(unc,[status(thm)],[5632,2]),
    [iquote('0:UnC:5632.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP435-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n018.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 : Mon Jun 13 21:54:13 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 3.47/3.65  
% 3.47/3.65  SPASS V 3.9 
% 3.47/3.65  SPASS beiseite: Proof found.
% 3.47/3.65  % SZS status Theorem
% 3.47/3.65  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 3.47/3.65  SPASS derived 3820 clauses, backtracked 0 clauses, performed 0 splits and kept 1235 clauses.
% 3.47/3.65  SPASS allocated 73061 KBytes.
% 3.47/3.65  SPASS spent	0:00:03.31 on the problem.
% 3.47/3.65  		0:00:00.03 for the input.
% 3.47/3.65  		0:00:00.00 for the FLOTTER CNF translation.
% 3.47/3.65  		0:00:00.03 for inferences.
% 3.47/3.65  		0:00:00.00 for the backtracking.
% 3.47/3.65  		0:00:03.22 for the reduction.
% 3.47/3.65  
% 3.47/3.65  
% 3.47/3.65  Here is a proof with depth 10, length 60 :
% 3.47/3.65  % SZS output start Refutation
% See solution above
% 3.47/3.65  Formulae used in the proof : single_axiom prove_these_axioms_3
% 3.47/3.69  
%------------------------------------------------------------------------------