TSTP Solution File: GRP682-11 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP682-11 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n016.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 11:48:56 EDT 2022

% Result   : Unsatisfiable 0.55s 0.72s
% Output   : Refutation 0.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   47 (  47 unt;   0 nHn;  47 RR)
%            Number of literals    :   47 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   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(ld(u,mult(u,u)),u),
    file('GRP682-11.p',unknown),
    [] ).

cnf(2,axiom,
    equal(rd(mult(u,u),u),u),
    file('GRP682-11.p',unknown),
    [] ).

cnf(3,axiom,
    equal(mult(u,ld(u,v)),ld(u,mult(u,v))),
    file('GRP682-11.p',unknown),
    [] ).

cnf(4,axiom,
    equal(mult(rd(u,v),v),rd(mult(u,v),v)),
    file('GRP682-11.p',unknown),
    [] ).

cnf(5,axiom,
    equal(ld(ld(u,v),mult(ld(u,v),mult(w,x))),mult(ld(u,mult(u,w)),x)),
    file('GRP682-11.p',unknown),
    [] ).

cnf(6,axiom,
    equal(rd(mult(mult(u,v),rd(w,x)),rd(w,x)),mult(u,rd(mult(v,x),x))),
    file('GRP682-11.p',unknown),
    [] ).

cnf(7,axiom,
    equal(rd(mult(rd(u,u),v),v),ld(u,mult(u,ld(v,v)))),
    file('GRP682-11.p',unknown),
    [] ).

cnf(8,axiom,
    ~ equal(ld(rd(x0__dfg,x1__dfg),mult(rd(x0__dfg,x1__dfg),x2__dfg)),ld(x0__dfg,mult(x0__dfg,x2__dfg))),
    file('GRP682-11.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)],[7,4]),
    [iquote('0:SpR:7.0,4.0')] ).

cnf(19,plain,
    equal(rd(rd(mult(u,u),u),u),ld(u,mult(u,ld(u,u)))),
    inference(spr,[status(thm),theory(equality)],[4,7]),
    [iquote('0:SpR:4.0,7.0')] ).

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(21,plain,
    equal(rd(mult(ld(u,u),v),v),ld(u,mult(u,ld(v,v)))),
    inference(rew,[status(thm),theory(equality)],[20,7]),
    [iquote('0:Rew:20.0,7.0')] ).

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)],[2,6]),
    [iquote('0:SpR:2.0,6.0')] ).

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)],[27,6]),
    [iquote('0:SpR:27.0,6.0')] ).

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(105,plain,
    equal(mult(u,ld(v,mult(v,ld(w,w)))),rd(mult(mult(u,ld(v,v)),w),w)),
    inference(spr,[status(thm),theory(equality)],[21,53]),
    [iquote('0:SpR:21.0,53.0')] ).

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(139,plain,
    equal(rd(mult(u,mult(v,w)),mult(v,w)),rd(mult(u,w),w)),
    inference(spr,[status(thm),theory(equality)],[102,73]),
    [iquote('0:SpR:102.0,73.0')] ).

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(177,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)],[27,5]),
    [iquote('0:SpR:27.0,5.0')] ).

cnf(178,plain,
    equal(mult(ld(u,mult(u,v)),w),ld(u,mult(u,mult(v,w)))),
    inference(spr,[status(thm),theory(equality)],[1,5]),
    [iquote('0:SpR:1.0,5.0')] ).

cnf(191,plain,
    equal(ld(u,mult(u,mult(ld(v,v),v))),mult(ld(u,u),v)),
    inference(rew,[status(thm),theory(equality)],[178,106]),
    [iquote('0:Rew:178.0,106.0')] ).

cnf(192,plain,
    equal(mult(ld(u,u),v),ld(u,mult(u,v))),
    inference(rew,[status(thm),theory(equality)],[27,191]),
    [iquote('0:Rew:27.0,191.0')] ).

cnf(198,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)],[192,177,178]),
    [iquote('0:Rew:192.0,177.0,178.0,177.0')] ).

cnf(199,plain,
    equal(ld(ld(u,v),mult(ld(u,v),w)),ld(u,mult(u,w))),
    inference(rew,[status(thm),theory(equality)],[1,198]),
    [iquote('0:Rew:1.0,198.0')] ).

cnf(398,plain,
    equal(rd(mult(u,ld(v,mult(v,w))),ld(v,mult(v,w))),rd(mult(u,w),w)),
    inference(spr,[status(thm),theory(equality)],[192,139]),
    [iquote('0:SpR:192.0,139.0')] ).

cnf(399,plain,
    equal(rd(mult(u,ld(v,mult(v,w))),ld(v,mult(v,w))),rd(mult(u,ld(v,w)),ld(v,w))),
    inference(spr,[status(thm),theory(equality)],[3,139]),
    [iquote('0:SpR:3.0,139.0')] ).

cnf(412,plain,
    equal(rd(mult(u,ld(v,w)),ld(v,w)),rd(mult(u,w),w)),
    inference(rew,[status(thm),theory(equality)],[398,399]),
    [iquote('0:Rew:398.0,399.0')] ).

cnf(470,plain,
    equal(ld(u,mult(u,mult(u,v))),mult(u,v)),
    inference(spr,[status(thm),theory(equality)],[1,178]),
    [iquote('0:SpR:1.0,178.0')] ).

cnf(796,plain,
    equal(ld(mult(u,v),mult(mult(u,v),w)),ld(u,mult(u,w))),
    inference(spr,[status(thm),theory(equality)],[470,199]),
    [iquote('0:SpR:470.0,199.0')] ).

cnf(1243,plain,
    equal(rd(rd(mult(u,v),v),ld(w,v)),rd(u,ld(w,v))),
    inference(spr,[status(thm),theory(equality)],[412,148]),
    [iquote('0:SpR:412.0,148.0')] ).

cnf(1454,plain,
    equal(rd(mult(mult(u,ld(u,u)),v),v),ld(u,mult(u,mult(u,ld(v,v))))),
    inference(spr,[status(thm),theory(equality)],[105,3]),
    [iquote('0:SpR:105.0,3.0')] ).

cnf(1486,plain,
    equal(mult(u,ld(v,v)),rd(mult(u,v),v)),
    inference(rew,[status(thm),theory(equality)],[1,1454,3,470]),
    [iquote('0:Rew:1.0,1454.0,3.0,1454.0,470.0,1454.0')] ).

cnf(1616,plain,
    equal(rd(rd(mult(u,v),v),ld(v,v)),rd(mult(u,v),v)),
    inference(spr,[status(thm),theory(equality)],[1486,412]),
    [iquote('0:SpR:1486.0,412.0')] ).

cnf(1644,plain,
    equal(rd(mult(u,v),v),rd(u,ld(v,v))),
    inference(rew,[status(thm),theory(equality)],[1243,1616]),
    [iquote('0:Rew:1243.0,1616.0')] ).

cnf(1657,plain,
    equal(mult(rd(u,v),v),rd(u,ld(v,v))),
    inference(rew,[status(thm),theory(equality)],[1644,4]),
    [iquote('0:Rew:1644.0,4.0')] ).

cnf(1664,plain,
    equal(mult(u,ld(v,v)),rd(u,ld(v,v))),
    inference(rew,[status(thm),theory(equality)],[1644,1486]),
    [iquote('0:Rew:1644.0,1486.0')] ).

cnf(2116,plain,
    equal(ld(rd(u,ld(v,v)),mult(rd(u,ld(v,v)),w)),ld(u,mult(u,w))),
    inference(spr,[status(thm),theory(equality)],[1664,796]),
    [iquote('0:SpR:1664.0,796.0')] ).

cnf(2129,plain,
    equal(ld(rd(u,ld(v,v)),mult(rd(u,ld(v,v)),w)),ld(rd(u,v),mult(rd(u,v),w))),
    inference(spr,[status(thm),theory(equality)],[1657,796]),
    [iquote('0:SpR:1657.0,796.0')] ).

cnf(2138,plain,
    equal(ld(rd(u,v),mult(rd(u,v),w)),ld(u,mult(u,w))),
    inference(rew,[status(thm),theory(equality)],[2116,2129]),
    [iquote('0:Rew:2116.0,2129.0')] ).

cnf(2139,plain,
    $false,
    inference(unc,[status(thm)],[2138,8]),
    [iquote('0:UnC:2138.0,8.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP682-11 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n016.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue Jun 14 07:41:45 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.55/0.72  
% 0.55/0.72  SPASS V 3.9 
% 0.55/0.72  SPASS beiseite: Proof found.
% 0.55/0.72  % SZS status Theorem
% 0.55/0.72  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.55/0.72  SPASS derived 1299 clauses, backtracked 0 clauses, performed 0 splits and kept 506 clauses.
% 0.55/0.72  SPASS allocated 66544 KBytes.
% 0.55/0.72  SPASS spent	0:00:00.35 on the problem.
% 0.55/0.72  		0:00:00.04 for the input.
% 0.55/0.72  		0:00:00.00 for the FLOTTER CNF translation.
% 0.55/0.72  		0:00:00.01 for inferences.
% 0.55/0.72  		0:00:00.00 for the backtracking.
% 0.55/0.72  		0:00:00.28 for the reduction.
% 0.55/0.72  
% 0.55/0.72  
% 0.55/0.72  Here is a proof with depth 6, length 47 :
% 0.55/0.72  % SZS output start Refutation
% See solution above
% 0.55/0.72  Formulae used in the proof : f01 f02 f03 f04 f05 f06 f07 goal
% 0.55/0.72  
%------------------------------------------------------------------------------