TSTP Solution File: GRP410-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP410-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n006.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 11:47:15 EDT 2022

% Result   : Unsatisfiable 1.07s 1.23s
% Output   : Refutation 1.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   31 (  31 unt;   0 nHn;  31 RR)
%            Number of literals    :   31 (   0 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   10 (   3 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(multiply(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(w))),inverse(multiply(inverse(w),w))),v),
    file('GRP410-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
    file('GRP410-1.p',unknown),
    [] ).

cnf(3,plain,
    equal(multiply(multiply(inverse(multiply(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(w))),inverse(multiply(x,multiply(inverse(w),w))))),v),inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w)))),x),
    inference(spr,[status(thm),theory(equality)],[1]),
    [iquote('0:SpR:1.0,1.0')] ).

cnf(6,plain,
    equal(multiply(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(w),w))))),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))),multiply(inverse(multiply(x,inverse(multiply(v,w)))),multiply(x,inverse(w)))),
    inference(spr,[status(thm),theory(equality)],[1]),
    [iquote('0:SpR:1.0,1.0')] ).

cnf(60,plain,
    equal(multiply(inverse(multiply(u,inverse(multiply(multiply(v,inverse(multiply(inverse(w),w))),w)))),multiply(u,inverse(w))),v),
    inference(spr,[status(thm),theory(equality)],[6,1]),
    [iquote('0:SpR:6.0,1.0')] ).

cnf(61,plain,
    equal(multiply(inverse(multiply(u,inverse(multiply(v,w)))),multiply(u,inverse(w))),multiply(inverse(multiply(x,inverse(multiply(v,w)))),multiply(x,inverse(w)))),
    inference(spr,[status(thm),theory(equality)],[6]),
    [iquote('0:SpR:6.0,6.0')] ).

cnf(73,plain,
    equal(multiply(multiply(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(w),w))))),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))),inverse(multiply(inverse(w),w))),v),
    inference(spr,[status(thm),theory(equality)],[6,1]),
    [iquote('0:SpR:6.0,1.0')] ).

cnf(108,plain,
    equal(multiply(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(w,inverse(x))))),inverse(multiply(inverse(multiply(w,inverse(x))),multiply(w,inverse(x))))),inverse(multiply(w,inverse(multiply(multiply(v,inverse(multiply(inverse(x),x))),x))))),
    inference(spr,[status(thm),theory(equality)],[60,1]),
    [iquote('0:SpR:60.0,1.0')] ).

cnf(183,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(w,inverse(x))))),multiply(inverse(multiply(y,inverse(v))),multiply(y,inverse(multiply(w,inverse(x)))))),
    inference(spr,[status(thm),theory(equality)],[60,61]),
    [iquote('0:SpR:60.0,61.0')] ).

cnf(268,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),multiply(inverse(multiply(x,inverse(v))),multiply(x,inverse(w)))),
    inference(spr,[status(thm),theory(equality)],[3,183]),
    [iquote('0:SpR:3.0,183.0')] ).

cnf(360,plain,
    equal(multiply(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(v,inverse(w))),multiply(v,inverse(x)))))),multiply(u,inverse(multiply(y,inverse(x))))),inverse(multiply(inverse(multiply(y,inverse(x))),multiply(y,inverse(x))))),inverse(multiply(y,inverse(w)))),
    inference(spr,[status(thm),theory(equality)],[268,1]),
    [iquote('0:SpR:268.0,1.0')] ).

cnf(390,plain,
    equal(inverse(multiply(u,inverse(multiply(multiply(multiply(inverse(multiply(v,inverse(w))),multiply(v,inverse(x))),inverse(multiply(inverse(x),x))),x)))),inverse(multiply(u,inverse(w)))),
    inference(rew,[status(thm),theory(equality)],[108,360]),
    [iquote('0:Rew:108.0,360.0')] ).

cnf(422,plain,
    equal(multiply(multiply(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(w),w))))),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))),inverse(multiply(inverse(w),w))),multiply(multiply(multiply(inverse(multiply(x,inverse(v))),multiply(x,inverse(y))),inverse(multiply(inverse(y),y))),y)),
    inference(spr,[status(thm),theory(equality)],[390,73]),
    [iquote('0:SpR:390.0,73.0')] ).

cnf(463,plain,
    equal(multiply(multiply(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),inverse(multiply(inverse(w),w))),w),v),
    inference(rew,[status(thm),theory(equality)],[73,422]),
    [iquote('0:Rew:73.0,422.0')] ).

cnf(529,plain,
    equal(multiply(multiply(multiply(inverse(u),multiply(multiply(inverse(multiply(v,inverse(multiply(u,w)))),multiply(v,inverse(w))),inverse(x))),inverse(multiply(inverse(x),x))),x),multiply(inverse(w),w)),
    inference(spr,[status(thm),theory(equality)],[1,463]),
    [iquote('0:SpR:1.0,463.0')] ).

cnf(615,plain,
    equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(inverse(v),v)),multiply(inverse(v),v)))),multiply(inverse(v),v)),multiply(inverse(v),v)),
    inference(spr,[status(thm),theory(equality)],[1,529]),
    [iquote('0:SpR:1.0,529.0')] ).

cnf(688,plain,
    equal(multiply(inverse(multiply(u,inverse(multiply(inverse(v),v)))),multiply(u,inverse(multiply(inverse(v),v)))),multiply(inverse(w),w)),
    inference(spr,[status(thm),theory(equality)],[615,60]),
    [iquote('0:SpR:615.0,60.0')] ).

cnf(715,plain,
    equal(multiply(inverse(u),u),multiply(inverse(v),v)),
    inference(spr,[status(thm),theory(equality)],[688]),
    [iquote('0:SpR:688.0,688.0')] ).

cnf(826,plain,
    equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),v),v),
    inference(spr,[status(thm),theory(equality)],[715,463]),
    [iquote('0:SpR:715.0,463.0')] ).

cnf(870,plain,
    equal(multiply(inverse(multiply(u,inverse(multiply(multiply(v,inverse(multiply(inverse(w),w))),x)))),multiply(u,inverse(x))),v),
    inference(spr,[status(thm),theory(equality)],[715,60]),
    [iquote('0:SpR:715.0,60.0')] ).

cnf(890,plain,
    equal(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(inverse(multiply(multiply(v,inverse(multiply(inverse(w),w))),w))),inverse(w))),v),
    inference(spr,[status(thm),theory(equality)],[715,60]),
    [iquote('0:SpR:715.0,60.0')] ).

cnf(916,plain,
    ~ equal(multiply(multiply(inverse(u),u),a2),a2),
    inference(spl,[status(thm),theory(equality)],[715,2]),
    [iquote('0:SpL:715.0,2.0')] ).

cnf(1015,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),multiply(inverse(inverse(v)),multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(inverse(v)),inverse(v)))),inverse(w)))),
    inference(spr,[status(thm),theory(equality)],[826,268]),
    [iquote('0:SpR:826.0,268.0')] ).

cnf(1019,plain,
    equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),w),w),
    inference(spr,[status(thm),theory(equality)],[715,826]),
    [iquote('0:SpR:715.0,826.0')] ).

cnf(1025,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),multiply(inverse(inverse(v)),inverse(w))),
    inference(rew,[status(thm),theory(equality)],[1019,1015]),
    [iquote('0:Rew:1019.0,1015.0')] ).

cnf(1081,plain,
    equal(multiply(inverse(inverse(multiply(multiply(u,inverse(multiply(inverse(v),v))),w))),inverse(w)),u),
    inference(rew,[status(thm),theory(equality)],[1025,870]),
    [iquote('0:Rew:1025.0,870.0')] ).

cnf(1227,plain,
    equal(multiply(inverse(multiply(inverse(u),u)),v),v),
    inference(rew,[status(thm),theory(equality)],[1081,890]),
    [iquote('0:Rew:1081.0,890.0')] ).

cnf(1509,plain,
    equal(multiply(inverse(inverse(multiply(inverse(multiply(inverse(u),u)),v))),inverse(v)),inverse(multiply(inverse(w),w))),
    inference(spr,[status(thm),theory(equality)],[1227,1081]),
    [iquote('0:SpR:1227.0,1081.0')] ).

cnf(1514,plain,
    equal(multiply(inverse(inverse(u)),inverse(u)),inverse(multiply(inverse(v),v))),
    inference(rew,[status(thm),theory(equality)],[1227,1509]),
    [iquote('0:Rew:1227.0,1509.0')] ).

cnf(1540,plain,
    equal(multiply(multiply(inverse(inverse(u)),inverse(u)),v),v),
    inference(spr,[status(thm),theory(equality)],[1514,1227]),
    [iquote('0:SpR:1514.0,1227.0')] ).

cnf(1575,plain,
    $false,
    inference(unc,[status(thm)],[1540,916]),
    [iquote('0:UnC:1540.0,916.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP410-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n006.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 05:03:12 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.07/1.23  
% 1.07/1.23  SPASS V 3.9 
% 1.07/1.23  SPASS beiseite: Proof found.
% 1.07/1.23  % SZS status Theorem
% 1.07/1.23  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 1.07/1.23  SPASS derived 1296 clauses, backtracked 0 clauses, performed 0 splits and kept 582 clauses.
% 1.07/1.23  SPASS allocated 70422 KBytes.
% 1.07/1.23  SPASS spent	0:00:00.86 on the problem.
% 1.07/1.23  		0:00:00.04 for the input.
% 1.07/1.23  		0:00:00.00 for the FLOTTER CNF translation.
% 1.07/1.23  		0:00:00.02 for inferences.
% 1.07/1.23  		0:00:00.00 for the backtracking.
% 1.07/1.23  		0:00:00.78 for the reduction.
% 1.07/1.23  
% 1.07/1.23  
% 1.07/1.23  Here is a proof with depth 13, length 31 :
% 1.07/1.23  % SZS output start Refutation
% See solution above
% 1.07/1.23  Formulae used in the proof : single_axiom prove_these_axioms_2
% 1.07/1.23  
%------------------------------------------------------------------------------