TSTP Solution File: GRP499-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP499-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 11:47:46 EDT 2022

% Result   : Unsatisfiable 4.26s 4.43s
% Output   : Refutation 4.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   41
%            Number of leaves      :    3
% Syntax   : Number of clauses     :   77 (  77 unt;   0 nHn;  77 RR)
%            Number of literals    :   77 (   0 equ;   3 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(double_divide(inverse(u),inverse(double_divide(inverse(double_divide(u,double_divide(v,w))),double_divide(x,double_divide(v,x))))),w),
    file('GRP499-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(inverse(double_divide(u,v)),multiply(v,u)),
    file('GRP499-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
    file('GRP499-1.p',unknown),
    [] ).

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

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

cnf(10,plain,
    equal(double_divide(multiply(u,v),multiply(double_divide(w,double_divide(x,w)),multiply(double_divide(x,y),double_divide(v,u)))),y),
    inference(spr,[status(thm),theory(equality)],[2,4]),
    [iquote('0:SpR:2.0,4.0')] ).

cnf(80,plain,
    equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,double_divide(inverse(w),x)),w)),x),
    inference(spr,[status(thm),theory(equality)],[7,4]),
    [iquote('0:SpR:7.0,4.0')] ).

cnf(85,plain,
    equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,w),x)),multiply(double_divide(y,double_divide(z,y)),multiply(double_divide(z,w),x))),
    inference(spr,[status(thm),theory(equality)],[7]),
    [iquote('0:SpR:7.0,7.0')] ).

cnf(91,plain,
    equal(double_divide(inverse(u),double_divide(inverse(v),multiply(double_divide(w,double_divide(inverse(u),w)),multiply(x,v)))),x),
    inference(spr,[status(thm),theory(equality)],[7,4]),
    [iquote('0:SpR:7.0,4.0')] ).

cnf(95,plain,
    equal(double_divide(multiply(u,v),double_divide(inverse(w),multiply(double_divide(x,double_divide(inverse(double_divide(v,u)),x)),multiply(y,w)))),y),
    inference(spr,[status(thm),theory(equality)],[7,10]),
    [iquote('0:SpR:7.0,10.0')] ).

cnf(116,plain,
    equal(double_divide(multiply(u,v),double_divide(inverse(w),multiply(double_divide(x,double_divide(multiply(u,v),x)),multiply(y,w)))),y),
    inference(rew,[status(thm),theory(equality)],[2,95]),
    [iquote('0:Rew:2.0,95.0')] ).

cnf(121,plain,
    equal(double_divide(inverse(multiply(double_divide(u,double_divide(inverse(v),w)),v)),multiply(double_divide(x,double_divide(y,x)),w)),double_divide(u,y)),
    inference(spr,[status(thm),theory(equality)],[80,4]),
    [iquote('0:SpR:80.0,4.0')] ).

cnf(171,plain,
    equal(double_divide(inverse(u),double_divide(inverse(multiply(double_divide(v,double_divide(inverse(w),x)),w)),multiply(double_divide(y,double_divide(inverse(u),y)),x))),double_divide(z,double_divide(v,z))),
    inference(spr,[status(thm),theory(equality)],[80,91]),
    [iquote('0:SpR:80.0,91.0')] ).

cnf(186,plain,
    equal(double_divide(inverse(u),double_divide(v,inverse(u))),double_divide(w,double_divide(v,w))),
    inference(rew,[status(thm),theory(equality)],[121,171]),
    [iquote('0:Rew:121.0,171.0')] ).

cnf(219,plain,
    equal(double_divide(u,double_divide(v,u)),double_divide(w,double_divide(v,w))),
    inference(spr,[status(thm),theory(equality)],[186]),
    [iquote('0:SpR:186.0,186.0')] ).

cnf(271,plain,
    equal(inverse(double_divide(u,double_divide(v,u))),multiply(double_divide(v,w),w)),
    inference(spr,[status(thm),theory(equality)],[219,2]),
    [iquote('0:SpR:219.0,2.0')] ).

cnf(286,plain,
    equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(w,double_divide(inverse(x),w)),x)),v),
    inference(spr,[status(thm),theory(equality)],[219,80]),
    [iquote('0:SpR:219.0,80.0')] ).

cnf(289,plain,
    equal(double_divide(u,double_divide(v,u)),double_divide(double_divide(w,v),double_divide(x,double_divide(w,x)))),
    inference(spr,[status(thm),theory(equality)],[219]),
    [iquote('0:SpR:219.0,219.0')] ).

cnf(349,plain,
    equal(multiply(double_divide(u,v),v),multiply(double_divide(u,w),w)),
    inference(rew,[status(thm),theory(equality)],[2,271]),
    [iquote('0:Rew:2.0,271.0')] ).

cnf(355,plain,
    equal(double_divide(inverse(u),multiply(double_divide(v,double_divide(w,v)),multiply(double_divide(w,x),x))),u),
    inference(spr,[status(thm),theory(equality)],[349,4]),
    [iquote('0:SpR:349.0,4.0')] ).

cnf(461,plain,
    equal(multiply(double_divide(u,double_divide(double_divide(v,w),u)),multiply(double_divide(x,double_divide(w,x)),y)),double_divide(v,inverse(y))),
    inference(spr,[status(thm),theory(equality)],[289,80]),
    [iquote('0:SpR:289.0,80.0')] ).

cnf(715,plain,
    equal(double_divide(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,w),w)),x),double_divide(y,double_divide(inverse(x),y))),
    inference(spr,[status(thm),theory(equality)],[355,219]),
    [iquote('0:SpR:355.0,219.0')] ).

cnf(744,plain,
    equal(double_divide(inverse(u),multiply(double_divide(v,double_divide(double_divide(w,x),v)),multiply(double_divide(y,double_divide(x,y)),double_divide(z,double_divide(w,z))))),u),
    inference(spr,[status(thm),theory(equality)],[289,355]),
    [iquote('0:SpR:289.0,355.0')] ).

cnf(764,plain,
    equal(double_divide(inverse(u),double_divide(v,inverse(double_divide(w,double_divide(v,w))))),u),
    inference(rew,[status(thm),theory(equality)],[461,744]),
    [iquote('0:Rew:461.0,744.0')] ).

cnf(765,plain,
    equal(double_divide(inverse(u),double_divide(v,multiply(double_divide(v,w),w))),u),
    inference(rew,[status(thm),theory(equality)],[2,764]),
    [iquote('0:Rew:2.0,764.0')] ).

cnf(769,plain,
    equal(multiply(double_divide(u,multiply(double_divide(u,v),v)),inverse(w)),inverse(w)),
    inference(spr,[status(thm),theory(equality)],[765,2]),
    [iquote('0:SpR:765.0,2.0')] ).

cnf(784,plain,
    equal(double_divide(u,double_divide(inverse(v),u)),double_divide(double_divide(w,multiply(double_divide(w,x),x)),v)),
    inference(spr,[status(thm),theory(equality)],[765,219]),
    [iquote('0:SpR:765.0,219.0')] ).

cnf(804,plain,
    equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,w),w)),double_divide(x,multiply(double_divide(x,y),y))),
    inference(spr,[status(thm),theory(equality)],[765,80]),
    [iquote('0:SpR:765.0,80.0')] ).

cnf(870,plain,
    equal(double_divide(u,double_divide(inverse(v),multiply(double_divide(w,double_divide(u,w)),multiply(x,v)))),x),
    inference(spr,[status(thm),theory(equality)],[80,116]),
    [iquote('0:SpR:80.0,116.0')] ).

cnf(924,plain,
    equal(multiply(double_divide(u,multiply(double_divide(u,v),v)),multiply(w,x)),multiply(w,x)),
    inference(spr,[status(thm),theory(equality)],[2,769]),
    [iquote('0:SpR:2.0,769.0')] ).

cnf(1054,plain,
    equal(multiply(double_divide(u,multiply(double_divide(u,v),v)),w),w),
    inference(spr,[status(thm),theory(equality)],[80,924]),
    [iquote('0:SpR:80.0,924.0')] ).

cnf(1086,plain,
    equal(double_divide(inverse(u),multiply(double_divide(v,double_divide(w,v)),u)),multiply(double_divide(w,x),x)),
    inference(spr,[status(thm),theory(equality)],[1054,4]),
    [iquote('0:SpR:1054.0,4.0')] ).

cnf(1107,plain,
    equal(multiply(double_divide(u,multiply(double_divide(v,double_divide(w,v)),double_divide(w,u))),x),x),
    inference(spr,[status(thm),theory(equality)],[219,1054]),
    [iquote('0:SpR:219.0,1054.0')] ).

cnf(2082,plain,
    equal(double_divide(inverse(double_divide(u,v)),multiply(double_divide(v,w),w)),multiply(double_divide(u,x),x)),
    inference(spr,[status(thm),theory(equality)],[349,1086]),
    [iquote('0:SpR:349.0,1086.0')] ).

cnf(2104,plain,
    equal(double_divide(multiply(u,v),multiply(double_divide(u,w),w)),multiply(double_divide(v,x),x)),
    inference(rew,[status(thm),theory(equality)],[2,2082]),
    [iquote('0:Rew:2.0,2082.0')] ).

cnf(2115,plain,
    equal(inverse(multiply(double_divide(u,v),v)),multiply(multiply(double_divide(w,x),x),multiply(w,u))),
    inference(spr,[status(thm),theory(equality)],[2104,2]),
    [iquote('0:SpR:2104.0,2.0')] ).

cnf(2175,plain,
    equal(multiply(double_divide(u,double_divide(multiply(v,u),multiply(double_divide(v,w),w))),x),x),
    inference(spr,[status(thm),theory(equality)],[2104,1107]),
    [iquote('0:SpR:2104.0,1107.0')] ).

cnf(2288,plain,
    equal(multiply(double_divide(u,double_divide(multiply(v,multiply(double_divide(v,w),w)),u)),x),x),
    inference(spr,[status(thm),theory(equality)],[2175,1107]),
    [iquote('0:SpR:2175.0,1107.0')] ).

cnf(2604,plain,
    equal(multiply(double_divide(double_divide(inverse(u),multiply(double_divide(v,double_divide(multiply(w,multiply(double_divide(w,x),x)),v)),multiply(y,u))),y),z),z),
    inference(spr,[status(thm),theory(equality)],[870,2288]),
    [iquote('0:SpR:870.0,2288.0')] ).

cnf(2613,plain,
    equal(multiply(double_divide(double_divide(inverse(u),multiply(v,u)),v),w),w),
    inference(rew,[status(thm),theory(equality)],[2288,2604]),
    [iquote('0:Rew:2288.0,2604.0')] ).

cnf(2681,plain,
    equal(multiply(double_divide(u,double_divide(inverse(double_divide(inverse(v),v)),u)),w),w),
    inference(spr,[status(thm),theory(equality)],[784,2613]),
    [iquote('0:SpR:784.0,2613.0')] ).

cnf(2682,plain,
    equal(multiply(double_divide(u,double_divide(multiply(v,inverse(v)),u)),w),w),
    inference(rew,[status(thm),theory(equality)],[2,2681]),
    [iquote('0:Rew:2.0,2681.0')] ).

cnf(2809,plain,
    equal(multiply(double_divide(u,v),v),double_divide(multiply(w,inverse(w)),u)),
    inference(spr,[status(thm),theory(equality)],[2682,349]),
    [iquote('0:SpR:2682.0,349.0')] ).

cnf(3103,plain,
    equal(inverse(multiply(double_divide(u,v),v)),multiply(u,multiply(w,inverse(w)))),
    inference(spr,[status(thm),theory(equality)],[2809,2]),
    [iquote('0:SpR:2809.0,2.0')] ).

cnf(3149,plain,
    equal(multiply(double_divide(u,double_divide(multiply(v,inverse(v)),u)),multiply(multiply(double_divide(double_divide(inverse(w),x),y),y),w)),x),
    inference(spr,[status(thm),theory(equality)],[2809,80]),
    [iquote('0:SpR:2809.0,80.0')] ).

cnf(3189,plain,
    equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,w),x)),multiply(double_divide(y,double_divide(multiply(z,inverse(z)),y)),multiply(multiply(double_divide(w,x1),x1),x))),
    inference(spr,[status(thm),theory(equality)],[2809,85]),
    [iquote('0:SpR:2809.0,85.0')] ).

cnf(3195,plain,
    equal(multiply(double_divide(u,double_divide(v,u)),multiply(multiply(double_divide(double_divide(inverse(w),multiply(x,inverse(x))),y),y),w)),v),
    inference(spr,[status(thm),theory(equality)],[2809,286]),
    [iquote('0:SpR:2809.0,286.0')] ).

cnf(3225,plain,
    equal(multiply(double_divide(u,v),v),double_divide(inverse(double_divide(w,multiply(double_divide(w,x),x))),u)),
    inference(spr,[status(thm),theory(equality)],[1054,2809]),
    [iquote('0:SpR:1054.0,2809.0')] ).

cnf(3231,plain,
    equal(multiply(double_divide(u,v),v),double_divide(multiply(multiply(double_divide(w,x),x),w),u)),
    inference(rew,[status(thm),theory(equality)],[2,3225]),
    [iquote('0:Rew:2.0,3225.0')] ).

cnf(3249,plain,
    equal(multiply(multiply(double_divide(double_divide(inverse(u),v),w),w),u),v),
    inference(rew,[status(thm),theory(equality)],[2682,3149]),
    [iquote('0:Rew:2682.0,3149.0')] ).

cnf(3250,plain,
    equal(multiply(double_divide(u,double_divide(v,u)),multiply(w,inverse(w))),v),
    inference(rew,[status(thm),theory(equality)],[3249,3195]),
    [iquote('0:Rew:3249.0,3195.0')] ).

cnf(3270,plain,
    equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,w),x)),multiply(multiply(double_divide(w,y),y),x)),
    inference(rew,[status(thm),theory(equality)],[2682,3189]),
    [iquote('0:Rew:2682.0,3189.0')] ).

cnf(3338,plain,
    equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,w),x)),double_divide(inverse(inverse(w)),inverse(x))),
    inference(spr,[status(thm),theory(equality)],[3250,7]),
    [iquote('0:SpR:3250.0,7.0')] ).

cnf(3344,plain,
    equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,w),inverse(double_divide(x,w)))),x),
    inference(spr,[status(thm),theory(equality)],[3250,85]),
    [iquote('0:SpR:3250.0,85.0')] ).

cnf(3351,plain,
    equal(double_divide(u,double_divide(inverse(inverse(v)),u)),v),
    inference(spr,[status(thm),theory(equality)],[3250,870]),
    [iquote('0:SpR:3250.0,870.0')] ).

cnf(3410,plain,
    equal(multiply(double_divide(u,double_divide(v,u)),multiply(double_divide(v,w),multiply(w,x))),x),
    inference(rew,[status(thm),theory(equality)],[2,3344]),
    [iquote('0:Rew:2.0,3344.0')] ).

cnf(3484,plain,
    equal(double_divide(inverse(inverse(u)),inverse(multiply(u,v))),v),
    inference(rew,[status(thm),theory(equality)],[3338,3410]),
    [iquote('0:Rew:3338.0,3410.0')] ).

cnf(3546,plain,
    equal(double_divide(double_divide(inverse(inverse(u)),inverse(u)),v),double_divide(w,double_divide(inverse(v),w))),
    inference(rew,[status(thm),theory(equality)],[3338,715]),
    [iquote('0:Rew:3338.0,715.0')] ).

cnf(3558,plain,
    equal(double_divide(inverse(inverse(u)),inverse(u)),double_divide(v,multiply(double_divide(v,w),w))),
    inference(rew,[status(thm),theory(equality)],[3338,804]),
    [iquote('0:Rew:3338.0,804.0')] ).

cnf(3870,plain,
    equal(multiply(multiply(double_divide(u,v),v),w),double_divide(inverse(inverse(u)),inverse(w))),
    inference(rew,[status(thm),theory(equality)],[3338,3270]),
    [iquote('0:Rew:3338.0,3270.0')] ).

cnf(4027,plain,
    equal(multiply(double_divide(u,v),v),double_divide(double_divide(inverse(inverse(w)),inverse(w)),u)),
    inference(rew,[status(thm),theory(equality)],[3870,3231]),
    [iquote('0:Rew:3870.0,3231.0')] ).

cnf(4061,plain,
    equal(inverse(multiply(double_divide(u,v),v)),double_divide(inverse(inverse(w)),inverse(multiply(w,u)))),
    inference(rew,[status(thm),theory(equality)],[3870,2115]),
    [iquote('0:Rew:3870.0,2115.0')] ).

cnf(4138,plain,
    equal(inverse(multiply(double_divide(u,v),v)),u),
    inference(rew,[status(thm),theory(equality)],[3484,4061]),
    [iquote('0:Rew:3484.0,4061.0')] ).

cnf(4146,plain,
    equal(multiply(u,multiply(v,inverse(v))),u),
    inference(rew,[status(thm),theory(equality)],[4138,3103]),
    [iquote('0:Rew:4138.0,3103.0')] ).

cnf(4148,plain,
    equal(double_divide(u,double_divide(v,u)),v),
    inference(rew,[status(thm),theory(equality)],[4146,3250]),
    [iquote('0:Rew:4146.0,3250.0')] ).

cnf(4166,plain,
    equal(inverse(inverse(u)),u),
    inference(rew,[status(thm),theory(equality)],[4148,3351]),
    [iquote('0:Rew:4148.0,3351.0')] ).

cnf(4426,plain,
    equal(double_divide(double_divide(inverse(inverse(u)),inverse(u)),v),inverse(v)),
    inference(rew,[status(thm),theory(equality)],[4148,3546]),
    [iquote('0:Rew:4148.0,3546.0')] ).

cnf(4830,plain,
    equal(multiply(double_divide(u,v),v),double_divide(double_divide(w,inverse(w)),u)),
    inference(rew,[status(thm),theory(equality)],[4166,4027]),
    [iquote('0:Rew:4166.0,4027.0')] ).

cnf(4840,plain,
    equal(double_divide(u,inverse(u)),double_divide(v,multiply(double_divide(v,w),w))),
    inference(rew,[status(thm),theory(equality)],[4166,3558]),
    [iquote('0:Rew:4166.0,3558.0')] ).

cnf(4841,plain,
    equal(multiply(multiply(double_divide(u,v),v),w),double_divide(u,inverse(w))),
    inference(rew,[status(thm),theory(equality)],[4166,3870]),
    [iquote('0:Rew:4166.0,3870.0')] ).

cnf(4851,plain,
    equal(double_divide(double_divide(u,inverse(u)),v),inverse(v)),
    inference(rew,[status(thm),theory(equality)],[4166,4426]),
    [iquote('0:Rew:4166.0,4426.0')] ).

cnf(4966,plain,
    equal(multiply(double_divide(u,v),v),inverse(u)),
    inference(rew,[status(thm),theory(equality)],[4851,4830]),
    [iquote('0:Rew:4851.0,4830.0')] ).

cnf(5094,plain,
    equal(double_divide(u,inverse(u)),double_divide(v,inverse(v))),
    inference(rew,[status(thm),theory(equality)],[4966,4840]),
    [iquote('0:Rew:4966.0,4840.0')] ).

cnf(5095,plain,
    equal(multiply(inverse(u),v),double_divide(u,inverse(v))),
    inference(rew,[status(thm),theory(equality)],[4966,4841]),
    [iquote('0:Rew:4966.0,4841.0')] ).

cnf(5096,plain,
    ~ equal(multiply(inverse(a1),a1),double_divide(b1,inverse(b1))),
    inference(rew,[status(thm),theory(equality)],[5095,3]),
    [iquote('0:Rew:5095.0,3.0')] ).

cnf(5104,plain,
    ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1))),
    inference(rew,[status(thm),theory(equality)],[5095,5096]),
    [iquote('0:Rew:5095.0,5096.0')] ).

cnf(5105,plain,
    $false,
    inference(unc,[status(thm)],[5104,5094]),
    [iquote('0:UnC:5104.0,5094.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRP499-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.14  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n025.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 05:51:38 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 4.26/4.43  
% 4.26/4.43  SPASS V 3.9 
% 4.26/4.43  SPASS beiseite: Proof found.
% 4.26/4.43  % SZS status Theorem
% 4.26/4.43  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 4.26/4.43  SPASS derived 4704 clauses, backtracked 0 clauses, performed 0 splits and kept 1935 clauses.
% 4.26/4.43  SPASS allocated 76405 KBytes.
% 4.26/4.43  SPASS spent	0:00:04.06 on the problem.
% 4.26/4.43  		0:00:00.03 for the input.
% 4.26/4.43  		0:00:00.00 for the FLOTTER CNF translation.
% 4.26/4.43  		0:00:00.04 for inferences.
% 4.26/4.43  		0:00:00.00 for the backtracking.
% 4.26/4.43  		0:00:03.97 for the reduction.
% 4.26/4.43  
% 4.26/4.43  
% 4.26/4.43  Here is a proof with depth 19, length 77 :
% 4.26/4.43  % SZS output start Refutation
% See solution above
% 4.29/4.50  Formulae used in the proof : single_axiom multiply prove_these_axioms_1
% 4.29/4.50  
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