TSTP Solution File: GRP590-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP590-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n023.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 11:48:10 EDT 2022

% Result   : Unsatisfiable 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    3
% Syntax   : Number of clauses     :   23 (  23 unt;   0 nHn;  23 RR)
%            Number of literals    :   23 (   0 equ;   3 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(double_divide(inverse(double_divide(double_divide(u,v),inverse(double_divide(u,inverse(w))))),v),w),
    file('GRP590-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(inverse(double_divide(u,v)),multiply(v,u)),
    file('GRP590-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
    file('GRP590-1.p',unknown),
    [] ).

cnf(4,plain,
    equal(double_divide(multiply(multiply(inverse(u),v),double_divide(v,w)),w),u),
    inference(rew,[status(thm),theory(equality)],[2,1]),
    [iquote('0:Rew:2.0,1.0,2.0,1.0')] ).

cnf(6,plain,
    equal(multiply(u,multiply(multiply(inverse(v),w),double_divide(w,u))),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[4,2]),
    [iquote('0:SpR:4.0,2.0')] ).

cnf(7,plain,
    equal(double_divide(multiply(multiply(inverse(u),multiply(multiply(inverse(v),w),double_divide(w,x))),v),x),u),
    inference(spr,[status(thm),theory(equality)],[4]),
    [iquote('0:SpR:4.0,4.0')] ).

cnf(50,plain,
    equal(double_divide(multiply(inverse(u),u),inverse(v)),v),
    inference(spr,[status(thm),theory(equality)],[6,7]),
    [iquote('0:SpR:6.0,7.0')] ).

cnf(51,plain,
    equal(multiply(inverse(u),multiply(inverse(v),v)),inverse(u)),
    inference(spr,[status(thm),theory(equality)],[50,2]),
    [iquote('0:SpR:50.0,2.0')] ).

cnf(52,plain,
    equal(double_divide(multiply(multiply(inverse(u),multiply(inverse(v),v)),w),inverse(w)),u),
    inference(spr,[status(thm),theory(equality)],[50,4]),
    [iquote('0:SpR:50.0,4.0')] ).

cnf(60,plain,
    equal(double_divide(multiply(inverse(u),v),inverse(v)),u),
    inference(rew,[status(thm),theory(equality)],[51,52]),
    [iquote('0:Rew:51.0,52.0')] ).

cnf(98,plain,
    equal(double_divide(inverse(u),inverse(multiply(inverse(v),v))),u),
    inference(spr,[status(thm),theory(equality)],[51,60]),
    [iquote('0:SpR:51.0,60.0')] ).

cnf(101,plain,
    equal(double_divide(inverse(multiply(inverse(u),u)),inverse(v)),v),
    inference(spr,[status(thm),theory(equality)],[51,50]),
    [iquote('0:SpR:51.0,50.0')] ).

cnf(128,plain,
    equal(double_divide(multiply(multiply(inverse(u),inverse(v)),v),inverse(multiply(inverse(w),w))),u),
    inference(spr,[status(thm),theory(equality)],[98,4]),
    [iquote('0:SpR:98.0,4.0')] ).

cnf(137,plain,
    equal(double_divide(multiply(u,v),inverse(multiply(inverse(w),w))),double_divide(v,u)),
    inference(spr,[status(thm),theory(equality)],[2,98]),
    [iquote('0:SpR:2.0,98.0')] ).

cnf(138,plain,
    equal(double_divide(u,multiply(inverse(v),inverse(u))),v),
    inference(rew,[status(thm),theory(equality)],[137,128]),
    [iquote('0:Rew:137.0,128.0')] ).

cnf(192,plain,
    equal(multiply(inverse(u),u),multiply(inverse(v),v)),
    inference(spr,[status(thm),theory(equality)],[101,98]),
    [iquote('0:SpR:101.0,98.0')] ).

cnf(219,plain,
    equal(double_divide(u,multiply(inverse(v),v)),inverse(u)),
    inference(spr,[status(thm),theory(equality)],[192,138]),
    [iquote('0:SpR:192.0,138.0')] ).

cnf(244,plain,
    ~ equal(multiply(multiply(inverse(u),u),a2),a2),
    inference(spl,[status(thm),theory(equality)],[192,3]),
    [iquote('0:SpL:192.0,3.0')] ).

cnf(252,plain,
    equal(multiply(multiply(inverse(u),u),v),inverse(inverse(v))),
    inference(spr,[status(thm),theory(equality)],[219,2]),
    [iquote('0:SpR:219.0,2.0')] ).

cnf(267,plain,
    equal(double_divide(u,inverse(multiply(inverse(v),v))),inverse(u)),
    inference(spr,[status(thm),theory(equality)],[51,219]),
    [iquote('0:SpR:51.0,219.0')] ).

cnf(270,plain,
    ~ equal(inverse(inverse(a2)),a2),
    inference(rew,[status(thm),theory(equality)],[252,244]),
    [iquote('0:Rew:252.0,244.0')] ).

cnf(279,plain,
    equal(inverse(inverse(u)),u),
    inference(rew,[status(thm),theory(equality)],[267,98]),
    [iquote('0:Rew:267.0,98.0')] ).

cnf(281,plain,
    $false,
    inference(unc,[status(thm)],[279,270]),
    [iquote('0:UnC:279.0,270.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP590-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n023.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon Jun 13 17:36:51 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.20/0.50  
% 0.20/0.50  SPASS V 3.9 
% 0.20/0.50  SPASS beiseite: Proof found.
% 0.20/0.50  % SZS status Theorem
% 0.20/0.50  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.50  SPASS derived 305 clauses, backtracked 0 clauses, performed 0 splits and kept 200 clauses.
% 0.20/0.50  SPASS allocated 63931 KBytes.
% 0.20/0.50  SPASS spent	0:00:00.14 on the problem.
% 0.20/0.50  		0:00:00.03 for the input.
% 0.20/0.50  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.50  		0:00:00.00 for inferences.
% 0.20/0.50  		0:00:00.00 for the backtracking.
% 0.20/0.50  		0:00:00.08 for the reduction.
% 0.20/0.50  
% 0.20/0.50  
% 0.20/0.50  Here is a proof with depth 7, length 23 :
% 0.20/0.50  % SZS output start Refutation
% See solution above
% 0.20/0.50  Formulae used in the proof : single_axiom multiply prove_these_axioms_2
% 0.20/0.50  
%------------------------------------------------------------------------------