TSTP Solution File: GRP452-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP452-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n009.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 11:47:32 EDT 2022

% Result   : Unsatisfiable 0.19s 0.50s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   34 (  34 unt;   0 nHn;  34 RR)
%            Number of literals    :   34 (   0 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    8 (   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(divide(divide(divide(u,u),divide(u,divide(v,divide(divide(divide(u,u),u),w)))),w),v),
    file('GRP452-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
    file('GRP452-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(divide(divide(u,u),v),inverse(v)),
    file('GRP452-1.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
    file('GRP452-1.p',unknown),
    [] ).

cnf(5,plain,
    equal(divide(u,inverse(v)),multiply(u,v)),
    inference(rew,[status(thm),theory(equality)],[3,2]),
    [iquote('0:Rew:3.0,2.0')] ).

cnf(6,plain,
    equal(divide(inverse(divide(u,divide(v,divide(inverse(u),w)))),w),v),
    inference(rew,[status(thm),theory(equality)],[3,1]),
    [iquote('0:Rew:3.0,1.0,3.0,1.0')] ).

cnf(7,plain,
    equal(divide(inverse(divide(u,u)),v),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[3]),
    [iquote('0:SpR:3.0,3.0')] ).

cnf(9,plain,
    equal(divide(multiply(inverse(u),u),v),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[5,3]),
    [iquote('0:SpR:5.0,3.0')] ).

cnf(11,plain,
    equal(multiply(divide(u,u),v),inverse(inverse(v))),
    inference(spr,[status(thm),theory(equality)],[5,3]),
    [iquote('0:SpR:5.0,3.0')] ).

cnf(12,plain,
    equal(divide(inverse(inverse(divide(u,u))),v),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[7,3]),
    [iquote('0:SpR:7.0,3.0')] ).

cnf(18,plain,
    equal(multiply(inverse(divide(u,divide(v,divide(inverse(u),inverse(w))))),w),v),
    inference(spr,[status(thm),theory(equality)],[6,5]),
    [iquote('0:SpR:6.0,5.0')] ).

cnf(19,plain,
    equal(divide(inverse(divide(divide(u,divide(v,divide(inverse(u),w))),divide(x,v))),w),x),
    inference(spr,[status(thm),theory(equality)],[6]),
    [iquote('0:SpR:6.0,6.0')] ).

cnf(23,plain,
    equal(divide(inverse(divide(divide(u,u),divide(v,inverse(w)))),w),v),
    inference(spr,[status(thm),theory(equality)],[7,6]),
    [iquote('0:SpR:7.0,6.0')] ).

cnf(24,plain,
    equal(divide(inverse(divide(u,inverse(divide(inverse(u),v)))),v),divide(w,w)),
    inference(spr,[status(thm),theory(equality)],[3,6]),
    [iquote('0:SpR:3.0,6.0')] ).

cnf(28,plain,
    equal(divide(inverse(inverse(multiply(u,v))),v),u),
    inference(rew,[status(thm),theory(equality)],[3,23,5]),
    [iquote('0:Rew:3.0,23.0,5.0,23.0')] ).

cnf(29,plain,
    equal(multiply(inverse(divide(u,divide(v,multiply(inverse(u),w)))),w),v),
    inference(rew,[status(thm),theory(equality)],[5,18]),
    [iquote('0:Rew:5.0,18.0')] ).

cnf(31,plain,
    equal(divide(inverse(multiply(u,divide(inverse(u),v))),v),divide(w,w)),
    inference(rew,[status(thm),theory(equality)],[5,24]),
    [iquote('0:Rew:5.0,24.0')] ).

cnf(38,plain,
    equal(multiply(multiply(inverse(u),u),v),inverse(inverse(v))),
    inference(spr,[status(thm),theory(equality)],[9,5]),
    [iquote('0:SpR:9.0,5.0')] ).

cnf(42,plain,
    ~ equal(inverse(inverse(a2)),a2),
    inference(rew,[status(thm),theory(equality)],[38,4]),
    [iquote('0:Rew:38.0,4.0')] ).

cnf(55,plain,
    equal(divide(inverse(inverse(inverse(inverse(u)))),u),divide(v,v)),
    inference(spr,[status(thm),theory(equality)],[11,28]),
    [iquote('0:SpR:11.0,28.0')] ).

cnf(56,plain,
    equal(inverse(divide(u,divide(v,multiply(inverse(u),w)))),divide(inverse(inverse(v)),w)),
    inference(spr,[status(thm),theory(equality)],[29,28]),
    [iquote('0:SpR:29.0,28.0')] ).

cnf(70,plain,
    equal(multiply(divide(inverse(inverse(u)),v),v),u),
    inference(rew,[status(thm),theory(equality)],[56,29]),
    [iquote('0:Rew:56.0,29.0')] ).

cnf(78,plain,
    equal(inverse(inverse(inverse(inverse(u)))),u),
    inference(spr,[status(thm),theory(equality)],[70,11]),
    [iquote('0:SpR:70.0,11.0')] ).

cnf(82,plain,
    equal(divide(u,u),divide(v,v)),
    inference(rew,[status(thm),theory(equality)],[78,55]),
    [iquote('0:Rew:78.0,55.0')] ).

cnf(345,plain,
    equal(divide(inverse(divide(divide(u,divide(v,divide(inverse(u),w))),x)),w),inverse(inverse(multiply(x,v)))),
    inference(spr,[status(thm),theory(equality)],[28,19]),
    [iquote('0:SpR:28.0,19.0')] ).

cnf(346,plain,
    equal(divide(inverse(divide(divide(u,divide(v,divide(inverse(u),w))),divide(x,x))),w),inverse(multiply(y,divide(inverse(y),v)))),
    inference(spr,[status(thm),theory(equality)],[31,19]),
    [iquote('0:SpR:31.0,19.0')] ).

cnf(432,plain,
    equal(inverse(inverse(multiply(divide(u,u),v))),inverse(multiply(w,divide(inverse(w),v)))),
    inference(rew,[status(thm),theory(equality)],[345,346]),
    [iquote('0:Rew:345.0,346.0')] ).

cnf(433,plain,
    equal(inverse(multiply(u,divide(inverse(u),v))),v),
    inference(rew,[status(thm),theory(equality)],[78,432,11]),
    [iquote('0:Rew:78.0,432.0,11.0,432.0')] ).

cnf(599,plain,
    equal(divide(inverse(u),divide(inverse(v),u)),v),
    inference(spr,[status(thm),theory(equality)],[433,28]),
    [iquote('0:SpR:433.0,28.0')] ).

cnf(612,plain,
    equal(inverse(multiply(u,divide(v,v))),inverse(u)),
    inference(spr,[status(thm),theory(equality)],[82,433]),
    [iquote('0:SpR:82.0,433.0')] ).

cnf(700,plain,
    equal(inverse(divide(inverse(u),inverse(divide(v,v)))),u),
    inference(spr,[status(thm),theory(equality)],[599,12]),
    [iquote('0:SpR:599.0,12.0')] ).

cnf(775,plain,
    equal(inverse(multiply(inverse(u),divide(v,v))),u),
    inference(rew,[status(thm),theory(equality)],[5,700]),
    [iquote('0:Rew:5.0,700.0')] ).

cnf(776,plain,
    equal(inverse(inverse(u)),u),
    inference(rew,[status(thm),theory(equality)],[612,775]),
    [iquote('0:Rew:612.0,775.0')] ).

cnf(777,plain,
    $false,
    inference(unc,[status(thm)],[776,42]),
    [iquote('0:UnC:776.0,42.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP452-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 13 19:35:08 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.50  
% 0.19/0.50  SPASS V 3.9 
% 0.19/0.50  SPASS beiseite: Proof found.
% 0.19/0.50  % SZS status Theorem
% 0.19/0.50  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.50  SPASS derived 582 clauses, backtracked 0 clauses, performed 0 splits and kept 194 clauses.
% 0.19/0.50  SPASS allocated 64146 KBytes.
% 0.19/0.50  SPASS spent	0:00:00.15 on the problem.
% 0.19/0.50  		0:00:00.04 for the input.
% 0.19/0.50  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.50  		0:00:00.01 for inferences.
% 0.19/0.50  		0:00:00.00 for the backtracking.
% 0.19/0.50  		0:00:00.08 for the reduction.
% 0.19/0.50  
% 0.19/0.50  
% 0.19/0.50  Here is a proof with depth 4, length 34 :
% 0.19/0.50  % SZS output start Refutation
% See solution above
% 0.19/0.50  Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_2
% 0.19/0.50  
%------------------------------------------------------------------------------