TSTP Solution File: GRP756-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP756-1 : TPTP v8.1.0. Released v4.0.0.
% 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 11:49:17 EDT 2022

% Result   : Unsatisfiable 1.38s 1.63s
% Output   : Refutation 1.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   31 (  31 unt;   0 nHn;  31 RR)
%            Number of literals    :   31 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    8 (   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(mult(u,ld(u,v)),v),
    file('GRP756-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(ld(u,mult(u,v)),v),
    file('GRP756-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(mult(rd(u,v),v),u),
    file('GRP756-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(rd(mult(u,v),v),u),
    file('GRP756-1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(mult(mult(u,v),mult(v,w)),mult(u,mult(mult(v,v),w))),
    file('GRP756-1.p',unknown),
    [] ).

cnf(6,axiom,
    ~ equal(mult(mult(a,b),c),mult(a,mult(b,c))),
    file('GRP756-1.p',unknown),
    [] ).

cnf(25,plain,
    equal(rd(mult(u,mult(mult(v,v),w)),mult(v,w)),mult(u,v)),
    inference(spr,[status(thm),theory(equality)],[5,4]),
    [iquote('0:SpR:5.0,4.0')] ).

cnf(26,plain,
    equal(ld(mult(u,v),mult(u,mult(mult(v,v),w))),mult(v,w)),
    inference(spr,[status(thm),theory(equality)],[5,2]),
    [iquote('0:SpR:5.0,2.0')] ).

cnf(28,plain,
    equal(mult(mult(u,mult(v,w)),mult(v,mult(mult(w,w),x))),mult(u,mult(mult(mult(v,w),mult(v,w)),mult(w,x)))),
    inference(spr,[status(thm),theory(equality)],[5]),
    [iquote('0:SpR:5.0,5.0')] ).

cnf(31,plain,
    equal(mult(u,mult(mult(v,v),ld(v,w))),mult(mult(u,v),w)),
    inference(spr,[status(thm),theory(equality)],[1,5]),
    [iquote('0:SpR:1.0,5.0')] ).

cnf(32,plain,
    equal(mult(rd(u,v),mult(mult(v,v),w)),mult(u,mult(v,w))),
    inference(spr,[status(thm),theory(equality)],[3,5]),
    [iquote('0:SpR:3.0,5.0')] ).

cnf(43,plain,
    equal(mult(rd(u,mult(mult(v,v),w)),v),rd(u,mult(v,w))),
    inference(spr,[status(thm),theory(equality)],[3,25]),
    [iquote('0:SpR:3.0,25.0')] ).

cnf(52,plain,
    equal(ld(mult(u,v),mult(u,w)),mult(v,ld(mult(v,v),w))),
    inference(spr,[status(thm),theory(equality)],[1,26]),
    [iquote('0:SpR:1.0,26.0')] ).

cnf(97,plain,
    equal(rd(mult(u,mult(v,w)),mult(mult(v,v),w)),rd(u,v)),
    inference(spr,[status(thm),theory(equality)],[32,4]),
    [iquote('0:SpR:32.0,4.0')] ).

cnf(109,plain,
    equal(mult(u,mult(v,ld(mult(v,v),w))),mult(rd(u,v),w)),
    inference(spr,[status(thm),theory(equality)],[1,32]),
    [iquote('0:SpR:1.0,32.0')] ).

cnf(234,plain,
    equal(ld(mult(rd(u,v),w),u),mult(w,ld(mult(w,w),v))),
    inference(spr,[status(thm),theory(equality)],[3,52]),
    [iquote('0:SpR:3.0,52.0')] ).

cnf(389,plain,
    equal(rd(mult(u,mult(v,mult(v,w))),mult(v,mult(mult(v,v),w))),rd(u,v)),
    inference(spr,[status(thm),theory(equality)],[5,97]),
    [iquote('0:SpR:5.0,97.0')] ).

cnf(585,plain,
    equal(mult(u,ld(mult(v,w),mult(v,x))),mult(rd(u,w),x)),
    inference(spr,[status(thm),theory(equality)],[52,109]),
    [iquote('0:SpR:52.0,109.0')] ).

cnf(1446,plain,
    equal(ld(u,u),mult(v,ld(mult(v,v),v))),
    inference(spr,[status(thm),theory(equality)],[3,234]),
    [iquote('0:SpR:3.0,234.0')] ).

cnf(1547,plain,
    equal(mult(u,mult(mult(v,v),mult(w,ld(mult(w,w),w)))),mult(mult(u,v),v)),
    inference(spr,[status(thm),theory(equality)],[1446,31]),
    [iquote('0:SpR:1446.0,31.0')] ).

cnf(1594,plain,
    equal(ld(u,u),mult(mult(mult(v,v),mult(mult(v,v),v)),ld(mult(mult(v,v),mult(mult(mult(mult(v,v),v),mult(mult(v,v),v)),mult(v,v))),mult(mult(v,v),mult(mult(v,v),v))))),
    inference(spr,[status(thm),theory(equality)],[28,1446]),
    [iquote('0:SpR:28.0,1446.0')] ).

cnf(1601,plain,
    equal(mult(mult(u,v),v),mult(u,mult(v,v))),
    inference(rew,[status(thm),theory(equality)],[3,1547,109]),
    [iquote('0:Rew:3.0,1547.0,109.0,1547.0')] ).

cnf(1727,plain,
    equal(ld(u,u),mult(rd(mult(mult(v,v),mult(v,mult(v,v))),mult(mult(mult(v,mult(v,v)),mult(v,mult(v,v))),mult(v,v))),mult(v,mult(v,v)))),
    inference(rew,[status(thm),theory(equality)],[585,1594,1601]),
    [iquote('0:Rew:585.0,1594.0,1601.0,1594.0')] ).

cnf(1728,plain,
    equal(ld(u,u),rd(mult(v,mult(v,mult(mult(v,v),v))),mult(mult(v,mult(v,v)),mult(v,v)))),
    inference(rew,[status(thm),theory(equality)],[43,1727,5]),
    [iquote('0:Rew:43.0,1727.0,5.0,1727.0,5.0,1727.0')] ).

cnf(1729,plain,
    equal(ld(u,u),rd(v,v)),
    inference(rew,[status(thm),theory(equality)],[389,1728,1601]),
    [iquote('0:Rew:389.0,1728.0,1601.0,1728.0,1601.0,1728.0')] ).

cnf(2162,plain,
    equal(mult(ld(u,u),v),v),
    inference(spr,[status(thm),theory(equality)],[1729,3]),
    [iquote('0:SpR:1729.0,3.0')] ).

cnf(2164,plain,
    equal(mult(ld(u,u),mult(mult(v,v),w)),mult(v,mult(v,w))),
    inference(spr,[status(thm),theory(equality)],[1729,32]),
    [iquote('0:SpR:1729.0,32.0')] ).

cnf(2189,plain,
    equal(mult(mult(u,u),v),mult(u,mult(u,v))),
    inference(rew,[status(thm),theory(equality)],[2162,2164]),
    [iquote('0:Rew:2162.0,2164.0')] ).

cnf(2192,plain,
    equal(mult(u,mult(v,mult(v,ld(v,w)))),mult(mult(u,v),w)),
    inference(rew,[status(thm),theory(equality)],[2189,31]),
    [iquote('0:Rew:2189.0,31.0')] ).

cnf(2619,plain,
    equal(mult(mult(u,v),w),mult(u,mult(v,w))),
    inference(rew,[status(thm),theory(equality)],[1,2192]),
    [iquote('0:Rew:1.0,2192.0')] ).

cnf(2620,plain,
    $false,
    inference(unc,[status(thm)],[2619,6]),
    [iquote('0:UnC:2619.0,6.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : GRP756-1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n006.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Tue Jun 14 08:57:11 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 1.38/1.63  
% 1.38/1.63  SPASS V 3.9 
% 1.38/1.63  SPASS beiseite: Proof found.
% 1.38/1.63  % SZS status Theorem
% 1.38/1.63  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 1.38/1.63  SPASS derived 1726 clauses, backtracked 0 clauses, performed 0 splits and kept 790 clauses.
% 1.38/1.63  SPASS allocated 71784 KBytes.
% 1.38/1.63  SPASS spent	0:00:01.23 on the problem.
% 1.38/1.63  		0:00:00.03 for the input.
% 1.38/1.63  		0:00:00.00 for the FLOTTER CNF translation.
% 1.38/1.63  		0:00:00.02 for inferences.
% 1.38/1.63  		0:00:00.00 for the backtracking.
% 1.38/1.63  		0:00:01.15 for the reduction.
% 1.38/1.63  
% 1.38/1.63  
% 1.38/1.63  Here is a proof with depth 6, length 31 :
% 1.38/1.63  % SZS output start Refutation
% See solution above
% 1.38/1.63  Formulae used in the proof : f01 f02 f03 f04 f05 goals
% 1.38/1.63  
%------------------------------------------------------------------------------