TSTP Solution File: GRP748-3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP748-3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n014.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   : Unsatisfiable 0.21s 0.51s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   31 (  23 unt;   8 nHn;  31 RR)
%            Number of literals    :   39 (   0 equ;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(mult(u,ld(u,v)),v),
    file('GRP748-3.p',unknown),
    [] ).

cnf(2,axiom,
    equal(ld(u,mult(u,v)),v),
    file('GRP748-3.p',unknown),
    [] ).

cnf(3,axiom,
    equal(mult(rd(u,v),v),u),
    file('GRP748-3.p',unknown),
    [] ).

cnf(4,axiom,
    equal(rd(mult(u,v),v),u),
    file('GRP748-3.p',unknown),
    [] ).

cnf(6,axiom,
    equal(mult(unit,u),u),
    file('GRP748-3.p',unknown),
    [] ).

cnf(7,axiom,
    equal(mult(mult(mult(u,v),w),v),mult(u,mult(mult(v,w),v))),
    file('GRP748-3.p',unknown),
    [] ).

cnf(8,axiom,
    equal(mult(mult(u,v),i(v)),u),
    file('GRP748-3.p',unknown),
    [] ).

cnf(9,axiom,
    equal(mult(u,i(u)),unit),
    file('GRP748-3.p',unknown),
    [] ).

cnf(10,axiom,
    equal(mult(i(u),u),unit),
    file('GRP748-3.p',unknown),
    [] ).

cnf(11,axiom,
    ( equal(mult(u,v),mult(v,u))
    | equal(mult(i(u),mult(u,v)),v) ),
    file('GRP748-3.p',unknown),
    [] ).

cnf(12,axiom,
    ~ equal(mult(mult(mult(a,b),c),b),mult(a,mult(b,mult(c,b)))),
    file('GRP748-3.p',unknown),
    [] ).

cnf(13,plain,
    ~ equal(mult(a,mult(mult(b,c),b)),mult(a,mult(b,mult(c,b)))),
    inference(rew,[status(thm),theory(equality)],[7,12]),
    [iquote('0:Rew:7.0,12.0')] ).

cnf(26,plain,
    equal(rd(unit,u),i(u)),
    inference(spr,[status(thm),theory(equality)],[10,4]),
    [iquote('0:SpR:10.0,4.0')] ).

cnf(28,plain,
    equal(rd(unit,i(u)),u),
    inference(spr,[status(thm),theory(equality)],[9,4]),
    [iquote('0:SpR:9.0,4.0')] ).

cnf(29,plain,
    equal(i(i(u)),u),
    inference(rew,[status(thm),theory(equality)],[26,28]),
    [iquote('0:Rew:26.0,28.0')] ).

cnf(102,plain,
    equal(mult(u,i(v)),rd(u,v)),
    inference(spr,[status(thm),theory(equality)],[3,8]),
    [iquote('0:SpR:3.0,8.0')] ).

cnf(112,plain,
    ( equal(mult(u,v),mult(v,u))
    | equal(ld(i(u),v),mult(u,v)) ),
    inference(spr,[status(thm),theory(equality)],[11,2]),
    [iquote('0:SpR:11.1,2.0')] ).

cnf(118,plain,
    ( equal(mult(ld(u,v),u),mult(u,ld(u,v)))
    | equal(mult(i(u),v),ld(u,v)) ),
    inference(spr,[status(thm),theory(equality)],[1,11]),
    [iquote('0:SpR:1.0,11.1')] ).

cnf(126,plain,
    ( equal(mult(ld(u,v),u),v)
    | equal(mult(i(u),v),ld(u,v)) ),
    inference(rew,[status(thm),theory(equality)],[1,118]),
    [iquote('0:Rew:1.0,118.0')] ).

cnf(196,plain,
    equal(mult(i(u),mult(mult(u,v),u)),mult(mult(unit,v),u)),
    inference(spr,[status(thm),theory(equality)],[10,7]),
    [iquote('0:SpR:10.0,7.0')] ).

cnf(208,plain,
    equal(mult(i(u),mult(mult(u,v),u)),mult(v,u)),
    inference(rew,[status(thm),theory(equality)],[6,196]),
    [iquote('0:Rew:6.0,196.0')] ).

cnf(399,plain,
    equal(ld(i(u),mult(v,u)),mult(mult(u,v),u)),
    inference(spr,[status(thm),theory(equality)],[208,2]),
    [iquote('0:SpR:208.0,2.0')] ).

cnf(793,plain,
    ( equal(mult(i(u),v),mult(v,i(u)))
    | equal(mult(i(u),v),ld(u,v)) ),
    inference(spr,[status(thm),theory(equality)],[29,112]),
    [iquote('0:SpR:29.0,112.1')] ).

cnf(801,plain,
    ( equal(mult(i(u),v),rd(v,u))
    | equal(mult(i(u),v),ld(u,v)) ),
    inference(rew,[status(thm),theory(equality)],[102,793]),
    [iquote('0:Rew:102.0,793.0')] ).

cnf(1005,plain,
    ( equal(mult(i(u),v),ld(u,v))
    | equal(rd(v,u),ld(u,v)) ),
    inference(spr,[status(thm),theory(equality)],[126,4]),
    [iquote('0:SpR:126.0,4.0')] ).

cnf(1033,plain,
    ( equal(mult(i(u),v),ld(u,v))
    | equal(mult(i(u),v),ld(u,v)) ),
    inference(rew,[status(thm),theory(equality)],[1005,801]),
    [iquote('0:Rew:1005.1,801.0')] ).

cnf(1034,plain,
    equal(mult(i(u),v),ld(u,v)),
    inference(obv,[status(thm),theory(equality)],[1033]),
    [iquote('0:Obv:1033.0')] ).

cnf(1087,plain,
    equal(ld(i(u),v),mult(u,v)),
    inference(spr,[status(thm),theory(equality)],[29,1034]),
    [iquote('0:SpR:29.0,1034.0')] ).

cnf(1094,plain,
    equal(mult(mult(u,v),u),mult(u,mult(v,u))),
    inference(rew,[status(thm),theory(equality)],[1087,399]),
    [iquote('0:Rew:1087.0,399.0')] ).

cnf(1113,plain,
    ~ equal(mult(a,mult(b,mult(c,b))),mult(a,mult(b,mult(c,b)))),
    inference(rew,[status(thm),theory(equality)],[1094,13]),
    [iquote('0:Rew:1094.0,13.0')] ).

cnf(1160,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[1113]),
    [iquote('0:Obv:1113.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRP748-3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n014.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Tue Jun 14 06:04:06 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.21/0.51  
% 0.21/0.51  SPASS V 3.9 
% 0.21/0.51  SPASS beiseite: Proof found.
% 0.21/0.51  % SZS status Theorem
% 0.21/0.51  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.51  SPASS derived 737 clauses, backtracked 0 clauses, performed 0 splits and kept 217 clauses.
% 0.21/0.51  SPASS allocated 64306 KBytes.
% 0.21/0.51  SPASS spent	0:00:00.14 on the problem.
% 0.21/0.51  		0:00:00.03 for the input.
% 0.21/0.51  		0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.51  		0:00:00.01 for inferences.
% 0.21/0.51  		0:00:00.00 for the backtracking.
% 0.21/0.51  		0:00:00.08 for the reduction.
% 0.21/0.51  
% 0.21/0.51  
% 0.21/0.51  Here is a proof with depth 3, length 31 :
% 0.21/0.51  % SZS output start Refutation
% See solution above
% 0.21/0.51  Formulae used in the proof : f01 f02 f03 f04 f06 f07 f08 f09 f10 f11 goals
% 0.21/0.51  
%------------------------------------------------------------------------------