TSTP Solution File: GRP682-10 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP682-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 0.20s 0.45s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   24 (  24 unt;   0 nHn;  24 RR)
%            Number of literals    :   24 (   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('GRP682-10.p',unknown),
    [] ).

cnf(2,axiom,
    equal(rd(mult(u,u),u),u),
    file('GRP682-10.p',unknown),
    [] ).

cnf(3,axiom,
    equal(mult(u,ld(u,v)),ld(u,mult(u,v))),
    file('GRP682-10.p',unknown),
    [] ).

cnf(4,axiom,
    equal(mult(rd(u,v),v),rd(mult(u,v),v)),
    file('GRP682-10.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('GRP682-10.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('GRP682-10.p',unknown),
    [] ).

cnf(7,axiom,
    equal(rd(mult(rd(u,u),v),v),ld(u,mult(u,ld(v,v)))),
    file('GRP682-10.p',unknown),
    [] ).

cnf(8,axiom,
    ~ equal(ld(ld(x0__dfg,x1__dfg),mult(ld(x0__dfg,x1__dfg),x2__dfg)),ld(x0__dfg,mult(x0__dfg,x2__dfg))),
    file('GRP682-10.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(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(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(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(200,plain,
    $false,
    inference(unc,[status(thm)],[199,8]),
    [iquote('0:UnC:199.0,8.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP682-10 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n020.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 : Mon Jun 13 14:32:05 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.45  
% 0.20/0.45  SPASS V 3.9 
% 0.20/0.45  SPASS beiseite: Proof found.
% 0.20/0.45  % SZS status Theorem
% 0.20/0.45  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.45  SPASS derived 138 clauses, backtracked 0 clauses, performed 0 splits and kept 89 clauses.
% 0.20/0.45  SPASS allocated 63591 KBytes.
% 0.20/0.45  SPASS spent	0:00:00.08 on the problem.
% 0.20/0.45  		0:00:00.03 for the input.
% 0.20/0.45  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.45  		0:00:00.00 for inferences.
% 0.20/0.45  		0:00:00.00 for the backtracking.
% 0.20/0.45  		0:00:00.03 for the reduction.
% 0.20/0.45  
% 0.20/0.45  
% 0.20/0.45  Here is a proof with depth 3, length 24 :
% 0.20/0.45  % SZS output start Refutation
% See solution above
% 0.20/0.45  Formulae used in the proof : f01 f02 f03 f04 f05 f06 f07 goal
% 0.20/0.45  
%------------------------------------------------------------------------------