TSTP Solution File: GRP700-10 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP700-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n015.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 11:49:02 EDT 2022

% Result   : Unsatisfiable 0.40s 0.57s
% Output   : Refutation 0.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   18 (  18 unt;   0 nHn;  18 RR)
%            Number of literals    :   18 (   0 equ;   3 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    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    equal(mult(rd(u,v),v),u),
    file('GRP700-10.p',unknown),
    [] ).

cnf(4,axiom,
    equal(rd(mult(u,v),v),u),
    file('GRP700-10.p',unknown),
    [] ).

cnf(5,axiom,
    equal(mult(u,unit),u),
    file('GRP700-10.p',unknown),
    [] ).

cnf(6,axiom,
    equal(mult(unit,u),u),
    file('GRP700-10.p',unknown),
    [] ).

cnf(7,axiom,
    equal(mult(mult(mult(u,v),u),mult(u,w)),mult(u,mult(mult(mult(v,u),u),w))),
    file('GRP700-10.p',unknown),
    [] ).

cnf(9,axiom,
    ~ equal(tuple(mult(u,x0__dfg),mult(x0__dfg,u)),tuple(unit,unit)),
    file('GRP700-10.p',unknown),
    [] ).

cnf(14,plain,
    equal(rd(u,u),unit),
    inference(spr,[status(thm),theory(equality)],[6,4]),
    [iquote('0:SpR:6.0,4.0')] ).

cnf(56,plain,
    ~ equal(tuple(u,mult(x0__dfg,rd(u,x0__dfg))),tuple(unit,unit)),
    inference(spl,[status(thm),theory(equality)],[3,9]),
    [iquote('0:SpL:3.0,9.0')] ).

cnf(66,plain,
    equal(mult(u,mult(mult(mult(v,u),u),unit)),mult(mult(mult(u,v),u),u)),
    inference(spr,[status(thm),theory(equality)],[5,7]),
    [iquote('0:SpR:5.0,7.0')] ).

cnf(75,plain,
    equal(mult(mult(mult(u,v),u),u),mult(u,mult(mult(v,u),u))),
    inference(rew,[status(thm),theory(equality)],[5,66]),
    [iquote('0:Rew:5.0,66.0')] ).

cnf(86,plain,
    equal(rd(mult(u,mult(mult(v,u),u)),u),mult(mult(u,v),u)),
    inference(spr,[status(thm),theory(equality)],[75,4]),
    [iquote('0:SpR:75.0,4.0')] ).

cnf(223,plain,
    equal(rd(mult(u,mult(v,u)),u),mult(mult(u,rd(v,u)),u)),
    inference(spr,[status(thm),theory(equality)],[3,86]),
    [iquote('0:SpR:3.0,86.0')] ).

cnf(656,plain,
    equal(mult(mult(u,rd(unit,u)),u),rd(mult(u,u),u)),
    inference(spr,[status(thm),theory(equality)],[6,223]),
    [iquote('0:SpR:6.0,223.0')] ).

cnf(672,plain,
    equal(mult(mult(u,rd(unit,u)),u),u),
    inference(rew,[status(thm),theory(equality)],[4,656]),
    [iquote('0:Rew:4.0,656.0')] ).

cnf(689,plain,
    equal(mult(u,rd(unit,u)),rd(u,u)),
    inference(spr,[status(thm),theory(equality)],[672,4]),
    [iquote('0:SpR:672.0,4.0')] ).

cnf(708,plain,
    equal(mult(u,rd(unit,u)),unit),
    inference(rew,[status(thm),theory(equality)],[14,689]),
    [iquote('0:Rew:14.0,689.0')] ).

cnf(831,plain,
    ~ equal(tuple(unit,unit),tuple(unit,unit)),
    inference(spl,[status(thm),theory(equality)],[708,56]),
    [iquote('0:SpL:708.0,56.0')] ).

cnf(835,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[831]),
    [iquote('0:Obv:831.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP700-10 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n015.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 02:28:23 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.40/0.57  
% 0.40/0.57  SPASS V 3.9 
% 0.40/0.57  SPASS beiseite: Proof found.
% 0.40/0.57  % SZS status Theorem
% 0.40/0.57  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.40/0.57  SPASS derived 514 clauses, backtracked 0 clauses, performed 0 splits and kept 230 clauses.
% 0.40/0.57  SPASS allocated 64762 KBytes.
% 0.40/0.57  SPASS spent	0:00:00.22 on the problem.
% 0.40/0.57  		0:00:00.03 for the input.
% 0.40/0.57  		0:00:00.00 for the FLOTTER CNF translation.
% 0.40/0.57  		0:00:00.01 for inferences.
% 0.40/0.57  		0:00:00.00 for the backtracking.
% 0.40/0.57  		0:00:00.16 for the reduction.
% 0.40/0.57  
% 0.40/0.57  
% 0.40/0.57  Here is a proof with depth 6, length 18 :
% 0.40/0.57  % SZS output start Refutation
% See solution above
% 0.40/0.57  Formulae used in the proof : f03 f04 f05 f06 f07 goal
% 0.40/0.57  
%------------------------------------------------------------------------------