TSTP Solution File: BOO072-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : BOO072-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n019.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 : Thu Jul 14 23:49:33 EDT 2022

% Result   : Unsatisfiable 7.12s 7.30s
% Output   : Refutation 7.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   53 (  53 unt;   0 nHn;  53 RR)
%            Number of literals    :   53 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   21 (   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(add(inverse(add(inverse(add(u,v)),w)),inverse(add(u,inverse(add(inverse(w),inverse(add(w,x)))))))),w),
    file('BOO072-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(add(a,b),add(b,a)),
    file('BOO072-1.p',unknown),
    [] ).

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

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

cnf(7,plain,
    equal(inverse(add(u,inverse(add(inverse(add(v,w)),inverse(add(inverse(inverse(add(v,inverse(add(inverse(u),inverse(add(u,x))))))),inverse(add(inverse(add(v,inverse(add(inverse(u),inverse(add(u,x)))))),y)))))))),inverse(add(v,inverse(add(inverse(u),inverse(add(u,x))))))),
    inference(spr,[status(thm),theory(equality)],[1]),
    [iquote('0:SpR:1.0,1.0')] ).

cnf(18,plain,
    equal(inverse(add(inverse(add(u,inverse(u))),u)),inverse(u)),
    inference(spr,[status(thm),theory(equality)],[1,4]),
    [iquote('0:SpR:1.0,4.0')] ).

cnf(22,plain,
    equal(inverse(add(inverse(u),inverse(add(u,inverse(add(inverse(u),inverse(add(u,v)))))))),u),
    inference(spr,[status(thm),theory(equality)],[18,1]),
    [iquote('0:SpR:18.0,1.0')] ).

cnf(48,plain,
    equal(inverse(add(inverse(add(u,v)),inverse(add(inverse(add(w,u)),inverse(add(inverse(v),inverse(add(v,x)))))))),v),
    inference(spr,[status(thm),theory(equality)],[1,6]),
    [iquote('0:SpR:1.0,6.0')] ).

cnf(61,plain,
    equal(inverse(add(inverse(add(inverse(add(u,v)),w)),inverse(add(u,w)))),w),
    inference(spr,[status(thm),theory(equality)],[22,1]),
    [iquote('0:SpR:22.0,1.0')] ).

cnf(67,plain,
    equal(inverse(add(inverse(u),inverse(add(u,u)))),u),
    inference(spr,[status(thm),theory(equality)],[22]),
    [iquote('0:SpR:22.0,22.0')] ).

cnf(86,plain,
    equal(inverse(add(add(u,v),inverse(add(u,inverse(add(inverse(inverse(add(add(u,v),add(u,v)))),inverse(add(inverse(add(add(u,v),add(u,v))),w)))))))),inverse(add(add(u,v),add(u,v)))),
    inference(spr,[status(thm),theory(equality)],[67,1]),
    [iquote('0:SpR:67.0,1.0')] ).

cnf(123,plain,
    equal(inverse(add(inverse(add(u,v)),inverse(add(inverse(u),v)))),v),
    inference(spr,[status(thm),theory(equality)],[22,61]),
    [iquote('0:SpR:22.0,61.0')] ).

cnf(128,plain,
    equal(inverse(add(add(u,v),inverse(add(u,inverse(add(add(u,v),inverse(add(inverse(add(u,v)),inverse(add(add(u,v),w)))))))))),inverse(add(add(u,v),inverse(add(inverse(add(u,v)),inverse(add(add(u,v),w))))))),
    inference(spr,[status(thm),theory(equality)],[22,61]),
    [iquote('0:SpR:22.0,61.0')] ).

cnf(133,plain,
    equal(inverse(add(inverse(add(u,v)),inverse(add(inverse(add(w,u)),v)))),v),
    inference(spr,[status(thm),theory(equality)],[123,61]),
    [iquote('0:SpR:123.0,61.0')] ).

cnf(138,plain,
    equal(inverse(add(u,inverse(add(v,inverse(add(inverse(v),u)))))),inverse(add(inverse(v),u))),
    inference(spr,[status(thm),theory(equality)],[123,61]),
    [iquote('0:SpR:123.0,61.0')] ).

cnf(157,plain,
    equal(inverse(add(inverse(add(add(u,inverse(u)),u)),inverse(u))),u),
    inference(spr,[status(thm),theory(equality)],[18,123]),
    [iquote('0:SpR:18.0,123.0')] ).

cnf(238,plain,
    equal(inverse(add(u,inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(inverse(add(inverse(u),inverse(add(u,v)))))),w)),inverse(add(inverse(u),inverse(add(u,v)))))),x)),inverse(inverse(add(inverse(u),inverse(add(u,v))))))),y)),inverse(add(inverse(inverse(inverse(add(inverse(u),inverse(add(u,v)))))),inverse(add(inverse(inverse(add(inverse(u),inverse(add(u,v))))),z)))))))),inverse(inverse(add(inverse(u),inverse(add(u,v)))))),
    inference(spr,[status(thm),theory(equality)],[4,7]),
    [iquote('0:SpR:4.0,7.0')] ).

cnf(264,plain,
    equal(inverse(add(u,inverse(add(add(u,inverse(u)),inverse(u))))),inverse(u)),
    inference(spr,[status(thm),theory(equality)],[157,61]),
    [iquote('0:SpR:157.0,61.0')] ).

cnf(295,plain,
    equal(inverse(add(inverse(add(inverse(u),v)),inverse(add(u,v)))),v),
    inference(spr,[status(thm),theory(equality)],[264,61]),
    [iquote('0:SpR:264.0,61.0')] ).

cnf(296,plain,
    equal(inverse(add(inverse(u),inverse(add(u,inverse(add(inverse(u),inverse(u))))))),u),
    inference(spr,[status(thm),theory(equality)],[264,22]),
    [iquote('0:SpR:264.0,22.0')] ).

cnf(335,plain,
    equal(inverse(add(inverse(u),inverse(u))),u),
    inference(rew,[status(thm),theory(equality)],[138,296]),
    [iquote('0:Rew:138.0,296.0')] ).

cnf(347,plain,
    equal(inverse(add(inverse(add(inverse(add(inverse(u),v)),inverse(u))),u)),inverse(u)),
    inference(spr,[status(thm),theory(equality)],[335,61]),
    [iquote('0:SpR:335.0,61.0')] ).

cnf(366,plain,
    equal(add(inverse(u),inverse(u)),inverse(add(u,u))),
    inference(spr,[status(thm),theory(equality)],[335]),
    [iquote('0:SpR:335.0,335.0')] ).

cnf(372,plain,
    equal(add(inverse(add(inverse(add(u,v)),w)),inverse(add(u,w))),inverse(add(w,w))),
    inference(spr,[status(thm),theory(equality)],[61,335]),
    [iquote('0:SpR:61.0,335.0')] ).

cnf(373,plain,
    equal(add(inverse(add(u,inverse(u))),u),inverse(add(inverse(u),inverse(u)))),
    inference(spr,[status(thm),theory(equality)],[18,335]),
    [iquote('0:SpR:18.0,335.0')] ).

cnf(375,plain,
    equal(add(inverse(u),inverse(add(u,inverse(add(inverse(u),inverse(add(u,v))))))),inverse(add(u,u))),
    inference(spr,[status(thm),theory(equality)],[22,335]),
    [iquote('0:SpR:22.0,335.0')] ).

cnf(391,plain,
    equal(inverse(inverse(add(u,u))),u),
    inference(rew,[status(thm),theory(equality)],[366,335]),
    [iquote('0:Rew:366.0,335.0')] ).

cnf(392,plain,
    equal(inverse(add(add(u,v),inverse(add(u,inverse(add(add(u,v),inverse(add(inverse(add(add(u,v),add(u,v))),w)))))))),inverse(add(add(u,v),add(u,v)))),
    inference(rew,[status(thm),theory(equality)],[391,86]),
    [iquote('0:Rew:391.0,86.0')] ).

cnf(403,plain,
    equal(add(inverse(add(u,inverse(u))),u),u),
    inference(rew,[status(thm),theory(equality)],[391,373,366]),
    [iquote('0:Rew:391.0,373.0,366.0,373.0')] ).

cnf(857,plain,
    equal(inverse(add(inverse(add(inverse(add(u,v)),u)),inverse(add(u,v)))),u),
    inference(spr,[status(thm),theory(equality)],[295,48]),
    [iquote('0:SpR:295.0,48.0')] ).

cnf(1853,plain,
    equal(inverse(add(inverse(add(inverse(u),u)),inverse(u))),u),
    inference(spr,[status(thm),theory(equality)],[403,133]),
    [iquote('0:SpR:403.0,133.0')] ).

cnf(2109,plain,
    equal(inverse(add(u,u)),inverse(u)),
    inference(spr,[status(thm),theory(equality)],[1853,347]),
    [iquote('0:SpR:1853.0,347.0')] ).

cnf(2180,plain,
    equal(inverse(inverse(u)),u),
    inference(rew,[status(thm),theory(equality)],[2109,391]),
    [iquote('0:Rew:2109.0,391.0')] ).

cnf(2202,plain,
    equal(inverse(add(add(u,v),inverse(add(u,inverse(add(add(u,v),inverse(add(inverse(add(u,v)),w)))))))),inverse(add(u,v))),
    inference(rew,[status(thm),theory(equality)],[2109,392]),
    [iquote('0:Rew:2109.0,392.0')] ).

cnf(2210,plain,
    equal(add(inverse(u),inverse(add(u,inverse(add(inverse(u),inverse(add(u,v))))))),inverse(u)),
    inference(rew,[status(thm),theory(equality)],[2109,375]),
    [iquote('0:Rew:2109.0,375.0')] ).

cnf(2226,plain,
    equal(add(inverse(add(inverse(add(u,v)),w)),inverse(add(u,w))),inverse(w)),
    inference(rew,[status(thm),theory(equality)],[2109,372]),
    [iquote('0:Rew:2109.0,372.0')] ).

cnf(2369,plain,
    equal(inverse(add(u,inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(u),inverse(add(u,v)))),w)),inverse(add(inverse(u),inverse(add(u,v)))))),x)),inverse(inverse(add(inverse(u),inverse(add(u,v))))))),y)),inverse(add(inverse(add(inverse(u),inverse(add(u,v)))),inverse(add(inverse(inverse(add(inverse(u),inverse(add(u,v))))),z)))))))),inverse(inverse(add(inverse(u),inverse(add(u,v)))))),
    inference(rew,[status(thm),theory(equality)],[2180,238]),
    [iquote('0:Rew:2180.0,238.0')] ).

cnf(2770,plain,
    equal(inverse(add(add(u,v),inverse(add(inverse(add(u,v)),inverse(add(add(u,v),w)))))),inverse(add(u,v))),
    inference(rew,[status(thm),theory(equality)],[2202,128]),
    [iquote('0:Rew:2202.0,128.0')] ).

cnf(2976,plain,
    equal(inverse(add(u,inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(u),inverse(add(u,v)))),w)),inverse(add(inverse(u),inverse(add(u,v)))))),x)),add(inverse(u),inverse(add(u,v))))),y)),inverse(add(inverse(add(inverse(u),inverse(add(u,v)))),inverse(add(add(inverse(u),inverse(add(u,v))),z)))))))),add(inverse(u),inverse(add(u,v)))),
    inference(rew,[status(thm),theory(equality)],[2180,2369]),
    [iquote('0:Rew:2180.0,2369.0')] ).

cnf(3018,plain,
    equal(add(inverse(add(inverse(u),v)),inverse(add(u,v))),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[295,2180]),
    [iquote('0:SpR:295.0,2180.0')] ).

cnf(3019,plain,
    equal(add(inverse(add(inverse(add(inverse(u),v)),inverse(u))),u),inverse(inverse(u))),
    inference(spr,[status(thm),theory(equality)],[347,2180]),
    [iquote('0:SpR:347.0,2180.0')] ).

cnf(3105,plain,
    equal(add(inverse(add(inverse(add(inverse(u),v)),inverse(u))),u),u),
    inference(rew,[status(thm),theory(equality)],[2180,3019]),
    [iquote('0:Rew:2180.0,3019.0')] ).

cnf(4607,plain,
    equal(add(u,add(u,v)),add(u,v)),
    inference(spr,[status(thm),theory(equality)],[857,3105]),
    [iquote('0:SpR:857.0,3105.0')] ).

cnf(6468,plain,
    equal(add(inverse(inverse(u)),inverse(add(inverse(v),inverse(add(v,u))))),inverse(inverse(add(v,u)))),
    inference(spr,[status(thm),theory(equality)],[3018,2226]),
    [iquote('0:SpR:3018.0,2226.0')] ).

cnf(6501,plain,
    equal(add(u,inverse(add(inverse(v),inverse(add(v,u))))),add(v,u)),
    inference(rew,[status(thm),theory(equality)],[2180,6468]),
    [iquote('0:Rew:2180.0,6468.0,2180.0,6468.0')] ).

cnf(7576,plain,
    equal(inverse(add(u,inverse(add(inverse(inverse(add(inverse(u),inverse(add(u,v))))),inverse(add(inverse(add(inverse(u),inverse(add(u,v)))),inverse(add(add(inverse(u),inverse(add(u,v))),w)))))))),add(inverse(u),inverse(add(u,v)))),
    inference(spr,[status(thm),theory(equality)],[2226,2976]),
    [iquote('0:SpR:2226.0,2976.0')] ).

cnf(7607,plain,
    equal(inverse(add(u,inverse(add(add(inverse(u),inverse(add(u,v))),inverse(add(inverse(add(inverse(u),inverse(add(u,v)))),inverse(add(add(inverse(u),inverse(add(u,v))),w)))))))),add(inverse(u),inverse(add(u,v)))),
    inference(rew,[status(thm),theory(equality)],[2180,7576]),
    [iquote('0:Rew:2180.0,7576.0')] ).

cnf(7608,plain,
    equal(inverse(add(u,inverse(add(inverse(u),inverse(add(u,v)))))),add(inverse(u),inverse(add(u,v)))),
    inference(rew,[status(thm),theory(equality)],[2770,7607]),
    [iquote('0:Rew:2770.0,7607.0')] ).

cnf(7613,plain,
    equal(add(inverse(u),add(inverse(u),inverse(add(u,v)))),inverse(u)),
    inference(rew,[status(thm),theory(equality)],[7608,2210]),
    [iquote('0:Rew:7608.0,2210.0')] ).

cnf(7616,plain,
    equal(add(inverse(u),inverse(add(u,v))),inverse(u)),
    inference(rew,[status(thm),theory(equality)],[4607,7613]),
    [iquote('0:Rew:4607.0,7613.0')] ).

cnf(7619,plain,
    equal(add(u,inverse(inverse(v))),add(v,u)),
    inference(rew,[status(thm),theory(equality)],[7616,6501]),
    [iquote('0:Rew:7616.0,6501.0')] ).

cnf(7827,plain,
    equal(add(u,v),add(v,u)),
    inference(rew,[status(thm),theory(equality)],[2180,7619]),
    [iquote('0:Rew:2180.0,7619.0')] ).

cnf(7828,plain,
    $false,
    inference(unc,[status(thm)],[7827,2]),
    [iquote('0:UnC:7827.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : BOO072-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n019.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Wed Jun  1 20:23:40 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 7.12/7.30  
% 7.12/7.30  SPASS V 3.9 
% 7.12/7.30  SPASS beiseite: Proof found.
% 7.12/7.30  % SZS status Theorem
% 7.12/7.30  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 7.12/7.30  SPASS derived 5520 clauses, backtracked 0 clauses, performed 0 splits and kept 1642 clauses.
% 7.12/7.30  SPASS allocated 95379 KBytes.
% 7.12/7.30  SPASS spent	0:00:06.76 on the problem.
% 7.12/7.30  		0:00:00.03 for the input.
% 7.12/7.30  		0:00:00.00 for the FLOTTER CNF translation.
% 7.12/7.30  		0:00:00.07 for inferences.
% 7.12/7.30  		0:00:00.00 for the backtracking.
% 7.12/7.30  		0:00:06.63 for the reduction.
% 7.12/7.30  
% 7.12/7.30  
% 7.12/7.30  Here is a proof with depth 11, length 53 :
% 7.12/7.30  % SZS output start Refutation
% See solution above
% 7.12/7.30  Formulae used in the proof : dn1 huntinton_1
% 7.12/7.30  
%------------------------------------------------------------------------------