TSTP Solution File: GRP747+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP747+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 11:49:15 EDT 2022

% Result   : Theorem 11.79s 12.02s
% Output   : Refutation 11.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   59 (  40 unt;   9 nHn;  59 RR)
%            Number of literals    :   78 (   0 equ;  15 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 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,unit),u),
    file('GRP747+1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(mult(unit,u),u),
    file('GRP747+1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(mult(u,ld(u,v)),v),
    file('GRP747+1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(ld(u,mult(u,v)),v),
    file('GRP747+1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(mult(rd(u,v),v),u),
    file('GRP747+1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(rd(mult(u,v),v),u),
    file('GRP747+1.p',unknown),
    [] ).

cnf(7,axiom,
    ~ equal(mult(mult(a,b),c),mult(a,mult(b,c))),
    file('GRP747+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(mult(mult(mult(u,v),w),v),mult(u,mult(mult(v,w),v))),
    file('GRP747+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( equal(mult(mult(u,v),w),mult(mult(u,w),v))
    | skP0(w,v,u) ),
    file('GRP747+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( equal(mult(u,mult(v,w)),mult(u,mult(w,v)))
    | skP0(w,v,u) ),
    file('GRP747+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ skP0(u,v,w)
    | equal(mult(mult(w,v),u),mult(w,mult(u,v))) ),
    file('GRP747+1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ skP0(u,v,w)
    | equal(mult(mult(w,u),v),mult(w,mult(v,u))) ),
    file('GRP747+1.p',unknown),
    [] ).

cnf(66,plain,
    equal(mult(u,mult(mult(v,unit),v)),mult(mult(u,v),v)),
    inference(spr,[status(thm),theory(equality)],[1,8]),
    [iquote('0:SpR:1.0,8.0')] ).

cnf(67,plain,
    equal(mult(u,mult(mult(v,ld(mult(u,v),w)),v)),mult(w,v)),
    inference(spr,[status(thm),theory(equality)],[3,8]),
    [iquote('0:SpR:3.0,8.0')] ).

cnf(70,plain,
    equal(mult(mult(u,v),v),mult(u,mult(v,v))),
    inference(rew,[status(thm),theory(equality)],[1,66]),
    [iquote('0:Rew:1.0,66.0')] ).

cnf(99,plain,
    ( equal(mult(mult(rd(u,v),w),v),mult(u,w))
    | skP0(v,w,rd(u,v)) ),
    inference(spr,[status(thm),theory(equality)],[5,9]),
    [iquote('0:SpR:5.0,9.0')] ).

cnf(110,plain,
    equal(rd(mult(u,mult(v,v)),v),mult(u,v)),
    inference(spr,[status(thm),theory(equality)],[70,6]),
    [iquote('0:SpR:70.0,6.0')] ).

cnf(144,plain,
    equal(mult(rd(u,mult(v,v)),v),rd(u,v)),
    inference(spr,[status(thm),theory(equality)],[5,110]),
    [iquote('0:SpR:5.0,110.0')] ).

cnf(185,plain,
    ( skP0(u,v,w)
    | equal(ld(w,mult(w,mult(u,v))),mult(v,u)) ),
    inference(spr,[status(thm),theory(equality)],[10,4]),
    [iquote('0:SpR:10.0,4.0')] ).

cnf(247,plain,
    ( skP0(u,v,w)
    | equal(mult(u,v),mult(v,u)) ),
    inference(rew,[status(thm),theory(equality)],[4,185]),
    [iquote('0:Rew:4.0,185.1')] ).

cnf(283,plain,
    equal(rd(rd(u,v),v),rd(u,mult(v,v))),
    inference(spr,[status(thm),theory(equality)],[144,6]),
    [iquote('0:SpR:144.0,6.0')] ).

cnf(382,plain,
    ( ~ skP0(u,v,unit)
    | equal(mult(unit,mult(v,u)),mult(u,v)) ),
    inference(spr,[status(thm),theory(equality)],[2,12]),
    [iquote('0:SpR:2.0,12.1')] ).

cnf(387,plain,
    ( ~ skP0(u,v,rd(w,u))
    | equal(mult(rd(w,u),mult(v,u)),mult(w,v)) ),
    inference(spr,[status(thm),theory(equality)],[5,12]),
    [iquote('0:SpR:5.0,12.1')] ).

cnf(396,plain,
    ( ~ skP0(u,v,unit)
    | equal(mult(v,u),mult(u,v)) ),
    inference(rew,[status(thm),theory(equality)],[2,382]),
    [iquote('0:Rew:2.0,382.1')] ).

cnf(397,plain,
    equal(mult(u,v),mult(v,u)),
    inference(mrr,[status(thm)],[396,247]),
    [iquote('0:MRR:396.0,247.0')] ).

cnf(398,plain,
    ~ equal(mult(c,mult(a,b)),mult(a,mult(b,c))),
    inference(rew,[status(thm),theory(equality)],[397,7]),
    [iquote('0:Rew:397.0,7.0')] ).

cnf(400,plain,
    equal(mult(u,mult(mult(v,u),w)),mult(v,mult(mult(u,w),u))),
    inference(rew,[status(thm),theory(equality)],[397,8]),
    [iquote('0:Rew:397.0,8.0')] ).

cnf(402,plain,
    equal(mult(u,rd(v,u)),v),
    inference(rew,[status(thm),theory(equality)],[397,5]),
    [iquote('0:Rew:397.0,5.0')] ).

cnf(428,plain,
    ( equal(mult(u,mult(rd(v,u),w)),mult(v,w))
    | skP0(u,w,rd(v,u)) ),
    inference(rew,[status(thm),theory(equality)],[397,99]),
    [iquote('0:Rew:397.0,99.0')] ).

cnf(438,plain,
    equal(mult(u,mult(v,mult(v,ld(mult(u,v),w)))),mult(w,v)),
    inference(rew,[status(thm),theory(equality)],[397,67]),
    [iquote('0:Rew:397.0,67.0')] ).

cnf(459,plain,
    equal(mult(u,mult(mult(v,u),w)),mult(v,mult(u,mult(u,w)))),
    inference(rew,[status(thm),theory(equality)],[397,400]),
    [iquote('0:Rew:397.0,400.0')] ).

cnf(599,plain,
    equal(rd(u,v),ld(v,u)),
    inference(spr,[status(thm),theory(equality)],[402,4]),
    [iquote('0:SpR:402.0,4.0')] ).

cnf(655,plain,
    equal(rd(rd(u,v),v),ld(mult(v,v),u)),
    inference(rew,[status(thm),theory(equality)],[599,283]),
    [iquote('0:Rew:599.0,283.0')] ).

cnf(657,plain,
    ( ~ skP0(u,v,ld(u,w))
    | equal(mult(rd(w,u),mult(v,u)),mult(w,v)) ),
    inference(rew,[status(thm),theory(equality)],[599,387]),
    [iquote('0:Rew:599.0,387.0')] ).

cnf(660,plain,
    ( equal(mult(u,mult(ld(u,v),w)),mult(v,w))
    | skP0(u,w,rd(v,u)) ),
    inference(rew,[status(thm),theory(equality)],[599,428]),
    [iquote('0:Rew:599.0,428.0')] ).

cnf(685,plain,
    equal(ld(mult(u,u),v),ld(u,ld(u,v))),
    inference(rew,[status(thm),theory(equality)],[599,655]),
    [iquote('0:Rew:599.0,655.0,599.0,655.0')] ).

cnf(699,plain,
    ( equal(mult(u,mult(ld(u,v),w)),mult(v,w))
    | skP0(u,w,ld(u,v)) ),
    inference(rew,[status(thm),theory(equality)],[599,660]),
    [iquote('0:Rew:599.0,660.1')] ).

cnf(701,plain,
    ( ~ skP0(u,v,ld(u,w))
    | equal(mult(ld(u,w),mult(v,u)),mult(w,v)) ),
    inference(rew,[status(thm),theory(equality)],[599,657]),
    [iquote('0:Rew:599.0,657.1')] ).

cnf(888,plain,
    equal(mult(u,mult(mult(u,v),w)),mult(v,mult(u,mult(u,w)))),
    inference(spr,[status(thm),theory(equality)],[397,459]),
    [iquote('0:SpR:397.0,459.0')] ).

cnf(897,plain,
    equal(mult(u,mult(v,mult(w,u))),mult(w,mult(u,mult(u,v)))),
    inference(spr,[status(thm),theory(equality)],[397,459]),
    [iquote('0:SpR:397.0,459.0')] ).

cnf(910,plain,
    equal(mult(u,mult(mult(v,u),ld(u,w))),mult(v,mult(u,w))),
    inference(spr,[status(thm),theory(equality)],[3,459]),
    [iquote('0:SpR:3.0,459.0')] ).

cnf(1631,plain,
    equal(mult(u,mult(mult(v,u),mult(u,ld(mult(u,u),w)))),mult(v,mult(w,u))),
    inference(spr,[status(thm),theory(equality)],[438,459]),
    [iquote('0:SpR:438.0,459.0')] ).

cnf(1690,plain,
    equal(mult(u,mult(mult(v,u),ld(u,w))),mult(v,mult(w,u))),
    inference(rew,[status(thm),theory(equality)],[3,1631,685]),
    [iquote('0:Rew:3.0,1631.0,685.0,1631.0')] ).

cnf(1691,plain,
    equal(mult(u,mult(v,w)),mult(u,mult(w,v))),
    inference(rew,[status(thm),theory(equality)],[910,1690]),
    [iquote('0:Rew:910.0,1690.0')] ).

cnf(2082,plain,
    equal(mult(mult(u,v),w),mult(w,mult(v,u))),
    inference(spr,[status(thm),theory(equality)],[1691,397]),
    [iquote('0:SpR:1691.0,397.0')] ).

cnf(2239,plain,
    ( ~ skP0(u,v,w)
    | equal(mult(u,mult(v,w)),mult(w,mult(u,v))) ),
    inference(spr,[status(thm),theory(equality)],[2082,11]),
    [iquote('0:SpR:2082.0,11.1')] ).

cnf(7236,plain,
    equal(mult(u,mult(mult(u,v),ld(u,w))),mult(v,mult(u,w))),
    inference(spr,[status(thm),theory(equality)],[3,888]),
    [iquote('0:SpR:3.0,888.0')] ).

cnf(7769,plain,
    equal(mult(u,mult(ld(u,v),mult(w,u))),mult(w,mult(u,v))),
    inference(spr,[status(thm),theory(equality)],[3,897]),
    [iquote('0:SpR:3.0,897.0')] ).

cnf(8123,plain,
    ( skP0(u,v,ld(u,w))
    | equal(mult(u,mult(v,ld(u,w))),mult(w,v)) ),
    inference(spr,[status(thm),theory(equality)],[699,1691]),
    [iquote('0:SpR:699.0,1691.0')] ).

cnf(11825,plain,
    ( ~ skP0(u,v,ld(u,w))
    | equal(mult(ld(u,w),mult(u,v)),mult(w,v)) ),
    inference(spr,[status(thm),theory(equality)],[701,1691]),
    [iquote('0:SpR:701.1,1691.0')] ).

cnf(11923,plain,
    ( ~ skP0(u,v,ld(u,w))
    | equal(mult(u,mult(v,ld(u,w))),mult(w,v)) ),
    inference(rew,[status(thm),theory(equality)],[2239,11825]),
    [iquote('0:Rew:2239.1,11825.1')] ).

cnf(11924,plain,
    equal(mult(u,mult(v,ld(u,w))),mult(w,v)),
    inference(mrr,[status(thm)],[11923,8123]),
    [iquote('0:MRR:11923.0,8123.0')] ).

cnf(11936,plain,
    equal(mult(u,mult(v,w)),mult(w,mult(v,u))),
    inference(rew,[status(thm),theory(equality)],[11924,7236]),
    [iquote('0:Rew:11924.0,7236.0')] ).

cnf(11946,plain,
    ~ equal(mult(b,mult(a,c)),mult(a,mult(b,c))),
    inference(rew,[status(thm),theory(equality)],[11936,398]),
    [iquote('0:Rew:11936.0,398.0')] ).

cnf(11955,plain,
    equal(mult(u,mult(u,mult(v,ld(u,w)))),mult(v,mult(u,w))),
    inference(rew,[status(thm),theory(equality)],[11936,7769]),
    [iquote('0:Rew:11936.0,7769.0')] ).

cnf(11991,plain,
    equal(mult(u,mult(v,w)),mult(w,mult(u,v))),
    inference(rew,[status(thm),theory(equality)],[11924,11955]),
    [iquote('0:Rew:11924.0,11955.0')] ).

cnf(11992,plain,
    ~ equal(mult(a,mult(c,b)),mult(a,mult(b,c))),
    inference(rew,[status(thm),theory(equality)],[11991,11946]),
    [iquote('0:Rew:11991.0,11946.0')] ).

cnf(12151,plain,
    ~ equal(mult(a,mult(b,c)),mult(a,mult(b,c))),
    inference(rew,[status(thm),theory(equality)],[397,11992]),
    [iquote('0:Rew:397.0,11992.0')] ).

cnf(12152,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[12151]),
    [iquote('0:Obv:12151.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GRP747+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n026.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 : Tue Jun 14 07:26:06 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 11.79/12.02  
% 11.79/12.02  SPASS V 3.9 
% 11.79/12.02  SPASS beiseite: Proof found.
% 11.79/12.02  % SZS status Theorem
% 11.79/12.02  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 11.79/12.02  SPASS derived 8022 clauses, backtracked 0 clauses, performed 0 splits and kept 3475 clauses.
% 11.79/12.02  SPASS allocated 103069 KBytes.
% 11.79/12.02  SPASS spent	0:0:11.57 on the problem.
% 11.79/12.02  		0:00:00.03 for the input.
% 11.79/12.02  		0:00:00.02 for the FLOTTER CNF translation.
% 11.79/12.02  		0:00:00.07 for inferences.
% 11.79/12.02  		0:00:00.00 for the backtracking.
% 11.79/12.02  		0:0:11.43 for the reduction.
% 11.79/12.02  
% 11.79/12.02  
% 11.79/12.02  Here is a proof with depth 4, length 59 :
% 11.79/12.02  % SZS output start Refutation
% See solution above
% 11.79/12.02  Formulae used in the proof : f05 f06 f01 f02 f03 f04 goals f07 f08
% 11.79/12.02  
%------------------------------------------------------------------------------