TSTP Solution File: GRP682+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP682+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n021.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 11:48:57 EDT 2022

% Result   : Theorem 0.52s 0.73s
% Output   : Refutation 0.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   47 (  45 unt;   0 nHn;  47 RR)
%            Number of literals    :   49 (   0 equ;   5 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;  10 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(ld(u,mult(u,u)),u),
    file('GRP682+1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(rd(mult(u,u),u),u),
    file('GRP682+1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(mult(u,ld(u,v)),ld(u,mult(u,v))),
    file('GRP682+1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(mult(rd(u,v),v),rd(mult(u,v),v)),
    file('GRP682+1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(rd(mult(rd(u,u),v),v),ld(u,mult(u,ld(v,v)))),
    file('GRP682+1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(ld(ld(u,v),mult(ld(u,v),mult(w,x))),mult(ld(u,mult(u,w)),x)),
    file('GRP682+1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(rd(mult(mult(u,v),rd(w,x)),rd(w,x)),mult(u,rd(mult(v,x),x))),
    file('GRP682+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ equal(ld(ld(skc6,skc7),mult(ld(skc6,skc7),skc8)),ld(skc6,mult(skc6,skc8)))
    | ~ equal(ld(rd(skc9,skc10),mult(rd(skc9,skc10),skc11)),ld(skc9,mult(skc9,skc11))) ),
    file('GRP682+1.p',unknown),
    [] ).

cnf(17,plain,
    equal(mult(ld(u,mult(u,ld(v,v))),v),rd(mult(mult(rd(u,u),v),v),v)),
    inference(spr,[status(thm),theory(equality)],[5,4]),
    [iquote('0:SpR:5.0,4.0')] ).

cnf(19,plain,
    equal(rd(rd(mult(u,u),u),u),ld(u,mult(u,ld(u,u)))),
    inference(spr,[status(thm),theory(equality)],[4,5]),
    [iquote('0:SpR:4.0,5.0')] ).

cnf(20,plain,
    equal(rd(u,u),ld(u,u)),
    inference(rew,[status(thm),theory(equality)],[2,19,1,3]),
    [iquote('0:Rew:2.0,19.0,1.0,19.0,3.0,19.0')] ).

cnf(23,plain,
    equal(mult(ld(u,mult(u,ld(v,v))),v),rd(mult(mult(ld(u,u),v),v),v)),
    inference(rew,[status(thm),theory(equality)],[20,17]),
    [iquote('0:Rew:20.0,17.0')] ).

cnf(25,plain,
    equal(mult(ld(u,u),u),rd(mult(u,u),u)),
    inference(spr,[status(thm),theory(equality)],[20,4]),
    [iquote('0:SpR:20.0,4.0')] ).

cnf(27,plain,
    equal(mult(ld(u,u),u),u),
    inference(rew,[status(thm),theory(equality)],[2,25]),
    [iquote('0:Rew:2.0,25.0')] ).

cnf(53,plain,
    equal(mult(u,rd(mult(v,w),w)),rd(mult(mult(u,v),w),w)),
    inference(spr,[status(thm),theory(equality)],[2,7]),
    [iquote('0:SpR:2.0,7.0')] ).

cnf(65,plain,
    equal(rd(mult(u,rd(v,w)),rd(v,w)),mult(ld(u,u),rd(mult(u,w),w))),
    inference(spr,[status(thm),theory(equality)],[27,7]),
    [iquote('0:SpR:27.0,7.0')] ).

cnf(72,plain,
    equal(rd(mult(u,rd(v,w)),rd(v,w)),rd(mult(mult(ld(u,u),u),w),w)),
    inference(rew,[status(thm),theory(equality)],[53,65]),
    [iquote('0:Rew:53.0,65.0')] ).

cnf(73,plain,
    equal(rd(mult(u,rd(v,w)),rd(v,w)),rd(mult(u,w),w)),
    inference(rew,[status(thm),theory(equality)],[27,72]),
    [iquote('0:Rew:27.0,72.0')] ).

cnf(102,plain,
    equal(rd(mult(mult(u,v),v),v),mult(u,v)),
    inference(spr,[status(thm),theory(equality)],[2,53]),
    [iquote('0:SpR:2.0,53.0')] ).

cnf(106,plain,
    equal(mult(ld(u,mult(u,ld(v,v))),v),mult(ld(u,u),v)),
    inference(rew,[status(thm),theory(equality)],[102,23]),
    [iquote('0:Rew:102.0,23.0')] ).

cnf(130,plain,
    equal(rd(mult(rd(u,v),v),v),rd(u,v)),
    inference(spr,[status(thm),theory(equality)],[73,2]),
    [iquote('0:SpR:73.0,2.0')] ).

cnf(135,plain,
    equal(rd(mult(mult(u,rd(v,w)),rd(v,w)),rd(v,w)),mult(rd(mult(u,w),w),rd(v,w))),
    inference(spr,[status(thm),theory(equality)],[73,4]),
    [iquote('0:SpR:73.0,4.0')] ).

cnf(145,plain,
    equal(rd(rd(mult(mult(u,v),w),w),rd(mult(v,w),w)),rd(mult(u,w),w)),
    inference(spr,[status(thm),theory(equality)],[53,73]),
    [iquote('0:SpR:53.0,73.0')] ).

cnf(148,plain,
    equal(rd(rd(mult(u,v),v),v),rd(u,v)),
    inference(rew,[status(thm),theory(equality)],[4,130]),
    [iquote('0:Rew:4.0,130.0')] ).

cnf(165,plain,
    equal(mult(rd(mult(u,v),v),rd(w,v)),mult(u,rd(w,v))),
    inference(rew,[status(thm),theory(equality)],[102,135]),
    [iquote('0:Rew:102.0,135.0')] ).

cnf(176,plain,
    equal(rd(rd(mult(u,v),v),rd(w,v)),rd(u,rd(w,v))),
    inference(spr,[status(thm),theory(equality)],[73,148]),
    [iquote('0:SpR:73.0,148.0')] ).

cnf(183,plain,
    equal(rd(mult(u,v),rd(mult(v,w),w)),rd(mult(u,w),w)),
    inference(rew,[status(thm),theory(equality)],[176,145]),
    [iquote('0:Rew:176.0,145.0')] ).

cnf(194,plain,
    equal(ld(ld(u,v),mult(ld(u,v),w)),mult(ld(u,mult(u,ld(w,w))),w)),
    inference(spr,[status(thm),theory(equality)],[27,6]),
    [iquote('0:SpR:27.0,6.0')] ).

cnf(195,plain,
    equal(mult(ld(u,mult(u,v)),w),ld(u,mult(u,mult(v,w)))),
    inference(spr,[status(thm),theory(equality)],[1,6]),
    [iquote('0:SpR:1.0,6.0')] ).

cnf(208,plain,
    equal(ld(u,mult(u,mult(ld(v,v),v))),mult(ld(u,u),v)),
    inference(rew,[status(thm),theory(equality)],[195,106]),
    [iquote('0:Rew:195.0,106.0')] ).

cnf(209,plain,
    equal(mult(ld(u,u),v),ld(u,mult(u,v))),
    inference(rew,[status(thm),theory(equality)],[27,208]),
    [iquote('0:Rew:27.0,208.0')] ).

cnf(215,plain,
    equal(ld(ld(u,v),mult(ld(u,v),w)),ld(u,mult(u,ld(w,mult(w,w))))),
    inference(rew,[status(thm),theory(equality)],[209,194,195]),
    [iquote('0:Rew:209.0,194.0,195.0,194.0')] ).

cnf(216,plain,
    equal(ld(ld(u,v),mult(ld(u,v),w)),ld(u,mult(u,w))),
    inference(rew,[status(thm),theory(equality)],[1,215]),
    [iquote('0:Rew:1.0,215.0')] ).

cnf(217,plain,
    ( ~ equal(ld(skc6,mult(skc6,skc8)),ld(skc6,mult(skc6,skc8)))
    | ~ equal(ld(rd(skc9,skc10),mult(rd(skc9,skc10),skc11)),ld(skc9,mult(skc9,skc11))) ),
    inference(rew,[status(thm),theory(equality)],[216,8]),
    [iquote('0:Rew:216.0,8.0')] ).

cnf(237,plain,
    ~ equal(ld(rd(skc9,skc10),mult(rd(skc9,skc10),skc11)),ld(skc9,mult(skc9,skc11))),
    inference(obv,[status(thm),theory(equality)],[217]),
    [iquote('0:Obv:217.0')] ).

cnf(657,plain,
    equal(ld(u,mult(u,mult(u,v))),mult(u,v)),
    inference(spr,[status(thm),theory(equality)],[1,195]),
    [iquote('0:SpR:1.0,195.0')] ).

cnf(969,plain,
    equal(rd(mult(u,rd(v,w)),rd(mult(rd(v,w),x),x)),rd(mult(rd(mult(u,w),w),x),x)),
    inference(spr,[status(thm),theory(equality)],[165,183]),
    [iquote('0:SpR:165.0,183.0')] ).

cnf(981,plain,
    equal(rd(mult(rd(mult(u,v),v),w),w),rd(mult(u,w),w)),
    inference(rew,[status(thm),theory(equality)],[183,969]),
    [iquote('0:Rew:183.0,969.0')] ).

cnf(1011,plain,
    equal(ld(mult(u,v),mult(mult(u,v),w)),ld(u,mult(u,w))),
    inference(spr,[status(thm),theory(equality)],[657,216]),
    [iquote('0:SpR:657.0,216.0')] ).

cnf(1677,plain,
    equal(rd(mult(mult(rd(mult(u,v),v),w),w),w),mult(rd(mult(u,w),w),w)),
    inference(spr,[status(thm),theory(equality)],[981,4]),
    [iquote('0:SpR:981.0,4.0')] ).

cnf(1749,plain,
    equal(mult(rd(mult(u,v),v),w),mult(u,w)),
    inference(rew,[status(thm),theory(equality)],[102,1677,4]),
    [iquote('0:Rew:102.0,1677.0,102.0,1677.0,4.0,1677.0')] ).

cnf(2078,plain,
    equal(ld(rd(mult(u,v),v),mult(rd(mult(u,v),v),w)),ld(rd(u,v),mult(rd(u,v),w))),
    inference(spr,[status(thm),theory(equality)],[4,1011]),
    [iquote('0:SpR:4.0,1011.0')] ).

cnf(2081,plain,
    equal(ld(mult(u,v),mult(mult(u,v),w)),ld(rd(mult(u,x),x),mult(rd(mult(u,x),x),w))),
    inference(spr,[status(thm),theory(equality)],[1749,1011]),
    [iquote('0:SpR:1749.0,1011.0')] ).

cnf(2085,plain,
    equal(ld(rd(mult(u,v),v),mult(u,w)),ld(u,mult(u,w))),
    inference(rew,[status(thm),theory(equality)],[1011,2081,1749]),
    [iquote('0:Rew:1011.0,2081.0,1749.0,2081.0')] ).

cnf(2097,plain,
    equal(ld(rd(mult(u,v),v),mult(u,w)),ld(rd(u,v),mult(rd(u,v),w))),
    inference(rew,[status(thm),theory(equality)],[1749,2078]),
    [iquote('0:Rew:1749.0,2078.0')] ).

cnf(2098,plain,
    equal(ld(rd(u,v),mult(rd(u,v),w)),ld(u,mult(u,w))),
    inference(rew,[status(thm),theory(equality)],[2085,2097]),
    [iquote('0:Rew:2085.0,2097.0')] ).

cnf(2099,plain,
    $false,
    inference(unc,[status(thm)],[2098,237]),
    [iquote('0:UnC:2098.0,237.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : GRP682+1 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.11  % Command  : run_spass %d %s
% 0.12/0.32  % Computer : n021.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 600
% 0.12/0.32  % DateTime : Tue Jun 14 04:20:42 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.52/0.73  
% 0.52/0.73  SPASS V 3.9 
% 0.52/0.73  SPASS beiseite: Proof found.
% 0.52/0.73  % SZS status Theorem
% 0.52/0.73  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.52/0.73  SPASS derived 1242 clauses, backtracked 0 clauses, performed 0 splits and kept 412 clauses.
% 0.52/0.73  SPASS allocated 88311 KBytes.
% 0.52/0.73  SPASS spent	0:00:00.38 on the problem.
% 0.52/0.73  		0:00:00.04 for the input.
% 0.52/0.73  		0:00:00.03 for the FLOTTER CNF translation.
% 0.52/0.73  		0:00:00.01 for inferences.
% 0.52/0.73  		0:00:00.00 for the backtracking.
% 0.52/0.73  		0:00:00.27 for the reduction.
% 0.52/0.73  
% 0.52/0.73  
% 0.52/0.73  Here is a proof with depth 7, length 47 :
% 0.52/0.73  % SZS output start Refutation
% See solution above
% 0.52/0.73  Formulae used in the proof : f01 f02 f03 f04 f07 f05 f06 goals
% 0.52/0.73  
%------------------------------------------------------------------------------