TSTP Solution File: GRP575-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP575-1 : 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 11:48:06 EDT 2022

% Result   : Unsatisfiable 0.19s 0.47s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   75 (  75 unt;   0 nHn;  75 RR)
%            Number of literals    :   75 (   0 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    9 (   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(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(w,u)),double_divide(w,identity))),double_divide(identity,identity)),v),
    file('GRP575-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
    file('GRP575-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(double_divide(u,identity),inverse(u)),
    file('GRP575-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(double_divide(u,inverse(u)),identity),
    file('GRP575-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
    file('GRP575-1.p',unknown),
    [] ).

cnf(6,plain,
    equal(inverse(double_divide(u,v)),multiply(v,u)),
    inference(rew,[status(thm),theory(equality)],[3,2]),
    [iquote('0:Rew:3.0,2.0')] ).

cnf(7,plain,
    equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(w,u)),inverse(w))),inverse(identity)),v),
    inference(rew,[status(thm),theory(equality)],[3,1]),
    [iquote('0:Rew:3.0,1.0,3.0,1.0')] ).

cnf(10,plain,
    equal(double_divide(double_divide(u,v),multiply(v,u)),identity),
    inference(spr,[status(thm),theory(equality)],[6,4]),
    [iquote('0:SpR:6.0,4.0')] ).

cnf(12,plain,
    equal(multiply(inverse(u),u),inverse(identity)),
    inference(spr,[status(thm),theory(equality)],[4,6]),
    [iquote('0:SpR:4.0,6.0')] ).

cnf(13,plain,
    equal(multiply(identity,u),inverse(inverse(u))),
    inference(spr,[status(thm),theory(equality)],[3,6]),
    [iquote('0:SpR:3.0,6.0')] ).

cnf(50,plain,
    equal(double_divide(double_divide(inverse(u),double_divide(double_divide(v,identity),inverse(u))),inverse(identity)),v),
    inference(spr,[status(thm),theory(equality)],[4,7]),
    [iquote('0:SpR:4.0,7.0')] ).

cnf(53,plain,
    equal(double_divide(double_divide(inverse(u),double_divide(inverse(v),inverse(u))),inverse(identity)),v),
    inference(rew,[status(thm),theory(equality)],[3,50]),
    [iquote('0:Rew:3.0,50.0')] ).

cnf(65,plain,
    equal(double_divide(double_divide(inverse(inverse(u)),identity),inverse(identity)),u),
    inference(spr,[status(thm),theory(equality)],[4,53]),
    [iquote('0:SpR:4.0,53.0')] ).

cnf(67,plain,
    equal(double_divide(inverse(inverse(inverse(u))),inverse(identity)),u),
    inference(rew,[status(thm),theory(equality)],[3,65]),
    [iquote('0:Rew:3.0,65.0')] ).

cnf(74,plain,
    equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(u,v),inverse(inverse(inverse(inverse(v)))))),inverse(identity)),u),
    inference(spr,[status(thm),theory(equality)],[67,7]),
    [iquote('0:SpR:67.0,7.0')] ).

cnf(75,plain,
    equal(double_divide(double_divide(inverse(identity),u),inverse(identity)),inverse(inverse(u))),
    inference(spr,[status(thm),theory(equality)],[67,53]),
    [iquote('0:SpR:67.0,53.0')] ).

cnf(77,plain,
    equal(double_divide(inverse(inverse(multiply(u,v))),inverse(identity)),double_divide(v,u)),
    inference(spr,[status(thm),theory(equality)],[6,67]),
    [iquote('0:SpR:6.0,67.0')] ).

cnf(83,plain,
    equal(inverse(inverse(double_divide(double_divide(u,v),inverse(inverse(inverse(inverse(v))))))),u),
    inference(rew,[status(thm),theory(equality)],[75,74]),
    [iquote('0:Rew:75.0,74.0')] ).

cnf(84,plain,
    equal(inverse(multiply(inverse(inverse(inverse(inverse(u)))),double_divide(v,u))),v),
    inference(rew,[status(thm),theory(equality)],[6,83]),
    [iquote('0:Rew:6.0,83.0')] ).

cnf(96,plain,
    equal(inverse(inverse(double_divide(inverse(u),inverse(identity)))),u),
    inference(spr,[status(thm),theory(equality)],[75,53]),
    [iquote('0:SpR:75.0,53.0')] ).

cnf(100,plain,
    equal(inverse(inverse(inverse(inverse(identity)))),double_divide(identity,inverse(identity))),
    inference(spr,[status(thm),theory(equality)],[4,75]),
    [iquote('0:SpR:4.0,75.0')] ).

cnf(102,plain,
    equal(inverse(multiply(inverse(identity),inverse(u))),u),
    inference(rew,[status(thm),theory(equality)],[6,96]),
    [iquote('0:Rew:6.0,96.0')] ).

cnf(103,plain,
    equal(inverse(inverse(inverse(inverse(identity)))),identity),
    inference(rew,[status(thm),theory(equality)],[4,100]),
    [iquote('0:Rew:4.0,100.0')] ).

cnf(116,plain,
    equal(double_divide(identity,inverse(identity)),inverse(identity)),
    inference(spr,[status(thm),theory(equality)],[103,67]),
    [iquote('0:SpR:103.0,67.0')] ).

cnf(119,plain,
    equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(inverse(inverse(inverse(identity))),u)),identity)),inverse(identity)),v),
    inference(spr,[status(thm),theory(equality)],[103,7]),
    [iquote('0:SpR:103.0,7.0')] ).

cnf(121,plain,
    equal(inverse(identity),identity),
    inference(rew,[status(thm),theory(equality)],[4,116]),
    [iquote('0:Rew:4.0,116.0')] ).

cnf(122,plain,
    equal(multiply(inverse(u),u),identity),
    inference(rew,[status(thm),theory(equality)],[121,12]),
    [iquote('0:Rew:121.0,12.0')] ).

cnf(124,plain,
    equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(w,u)),inverse(w))),identity),v),
    inference(rew,[status(thm),theory(equality)],[121,7]),
    [iquote('0:Rew:121.0,7.0')] ).

cnf(128,plain,
    equal(double_divide(double_divide(identity,u),identity),inverse(inverse(u))),
    inference(rew,[status(thm),theory(equality)],[121,75]),
    [iquote('0:Rew:121.0,75.0')] ).

cnf(136,plain,
    equal(double_divide(inverse(inverse(multiply(u,v))),identity),double_divide(v,u)),
    inference(rew,[status(thm),theory(equality)],[121,77]),
    [iquote('0:Rew:121.0,77.0')] ).

cnf(138,plain,
    equal(inverse(multiply(identity,inverse(u))),u),
    inference(rew,[status(thm),theory(equality)],[121,102]),
    [iquote('0:Rew:121.0,102.0')] ).

cnf(145,plain,
    equal(inverse(inverse(inverse(inverse(u)))),u),
    inference(rew,[status(thm),theory(equality)],[13,138]),
    [iquote('0:Rew:13.0,138.0')] ).

cnf(146,plain,
    equal(inverse(multiply(u,double_divide(v,u))),v),
    inference(rew,[status(thm),theory(equality)],[145,84]),
    [iquote('0:Rew:145.0,84.0')] ).

cnf(161,plain,
    equal(multiply(u,identity),inverse(inverse(u))),
    inference(rew,[status(thm),theory(equality)],[6,128,3]),
    [iquote('0:Rew:6.0,128.0,3.0,128.0')] ).

cnf(173,plain,
    equal(inverse(inverse(inverse(multiply(u,v)))),double_divide(v,u)),
    inference(rew,[status(thm),theory(equality)],[3,136]),
    [iquote('0:Rew:3.0,136.0')] ).

cnf(184,plain,
    equal(multiply(double_divide(double_divide(u,double_divide(v,w)),inverse(v)),w),u),
    inference(rew,[status(thm),theory(equality)],[6,124,3]),
    [iquote('0:Rew:6.0,124.0,3.0,124.0')] ).

cnf(192,plain,
    equal(double_divide(double_divide(u,multiply(double_divide(inverse(inverse(inverse(identity))),u),v)),inverse(identity)),v),
    inference(rew,[status(thm),theory(equality)],[6,119,3]),
    [iquote('0:Rew:6.0,119.0,3.0,119.0')] ).

cnf(193,plain,
    equal(double_divide(double_divide(u,multiply(double_divide(identity,u),v)),identity),v),
    inference(rew,[status(thm),theory(equality)],[121,192]),
    [iquote('0:Rew:121.0,192.0,121.0,192.0,121.0,192.0')] ).

cnf(194,plain,
    equal(multiply(multiply(double_divide(identity,u),v),u),v),
    inference(rew,[status(thm),theory(equality)],[6,193,3]),
    [iquote('0:Rew:6.0,193.0,3.0,193.0')] ).

cnf(217,plain,
    equal(double_divide(inverse(inverse(inverse(u))),u),identity),
    inference(spr,[status(thm),theory(equality)],[145,4]),
    [iquote('0:SpR:145.0,4.0')] ).

cnf(219,plain,
    equal(multiply(u,inverse(inverse(inverse(u)))),identity),
    inference(spr,[status(thm),theory(equality)],[145,122]),
    [iquote('0:SpR:145.0,122.0')] ).

cnf(227,plain,
    equal(double_divide(double_divide(identity,u),inverse(inverse(u))),identity),
    inference(spr,[status(thm),theory(equality)],[161,10]),
    [iquote('0:SpR:161.0,10.0')] ).

cnf(274,plain,
    equal(multiply(double_divide(identity,inverse(u)),v),inverse(inverse(inverse(double_divide(u,v))))),
    inference(spr,[status(thm),theory(equality)],[217,184]),
    [iquote('0:SpR:217.0,184.0')] ).

cnf(286,plain,
    equal(multiply(double_divide(identity,inverse(u)),v),inverse(inverse(multiply(v,u)))),
    inference(rew,[status(thm),theory(equality)],[6,274]),
    [iquote('0:Rew:6.0,274.0')] ).

cnf(334,plain,
    equal(multiply(u,double_divide(v,u)),inverse(inverse(inverse(v)))),
    inference(spr,[status(thm),theory(equality)],[146,145]),
    [iquote('0:SpR:146.0,145.0')] ).

cnf(386,plain,
    equal(double_divide(double_divide(identity,inverse(inverse(u))),u),identity),
    inference(spr,[status(thm),theory(equality)],[145,227]),
    [iquote('0:SpR:145.0,227.0')] ).

cnf(401,plain,
    equal(multiply(u,double_divide(identity,inverse(inverse(u)))),inverse(identity)),
    inference(spr,[status(thm),theory(equality)],[386,6]),
    [iquote('0:SpR:386.0,6.0')] ).

cnf(415,plain,
    equal(multiply(u,double_divide(identity,inverse(inverse(u)))),identity),
    inference(rew,[status(thm),theory(equality)],[121,401]),
    [iquote('0:Rew:121.0,401.0')] ).

cnf(503,plain,
    equal(inverse(inverse(inverse(double_divide(identity,u)))),multiply(identity,u)),
    inference(spr,[status(thm),theory(equality)],[219,194]),
    [iquote('0:SpR:219.0,194.0')] ).

cnf(504,plain,
    equal(double_divide(identity,inverse(inverse(double_divide(identity,u)))),multiply(identity,u)),
    inference(spr,[status(thm),theory(equality)],[415,194]),
    [iquote('0:SpR:415.0,194.0')] ).

cnf(510,plain,
    equal(inverse(inverse(u)),u),
    inference(rew,[status(thm),theory(equality)],[145,503,161,6,13]),
    [iquote('0:Rew:145.0,503.0,161.0,503.0,6.0,503.0,13.0,503.0')] ).

cnf(515,plain,
    equal(multiply(identity,u),u),
    inference(rew,[status(thm),theory(equality)],[510,13]),
    [iquote('0:Rew:510.0,13.0')] ).

cnf(516,plain,
    equal(multiply(u,identity),u),
    inference(rew,[status(thm),theory(equality)],[510,161]),
    [iquote('0:Rew:510.0,161.0')] ).

cnf(522,plain,
    equal(multiply(u,double_divide(v,u)),inverse(v)),
    inference(rew,[status(thm),theory(equality)],[510,334]),
    [iquote('0:Rew:510.0,334.0')] ).

cnf(525,plain,
    equal(multiply(double_divide(identity,inverse(u)),v),multiply(v,u)),
    inference(rew,[status(thm),theory(equality)],[510,286]),
    [iquote('0:Rew:510.0,286.0')] ).

cnf(527,plain,
    equal(inverse(multiply(u,v)),double_divide(v,u)),
    inference(rew,[status(thm),theory(equality)],[510,173]),
    [iquote('0:Rew:510.0,173.0')] ).

cnf(538,plain,
    equal(double_divide(identity,inverse(multiply(u,identity))),multiply(identity,u)),
    inference(rew,[status(thm),theory(equality)],[6,504]),
    [iquote('0:Rew:6.0,504.0')] ).

cnf(539,plain,
    equal(double_divide(identity,inverse(u)),u),
    inference(rew,[status(thm),theory(equality)],[516,538,515]),
    [iquote('0:Rew:516.0,538.0,515.0,538.0')] ).

cnf(540,plain,
    equal(multiply(u,v),multiply(v,u)),
    inference(rew,[status(thm),theory(equality)],[539,525]),
    [iquote('0:Rew:539.0,525.0')] ).

cnf(542,plain,
    equal(multiply(u,double_divide(double_divide(v,double_divide(w,u)),inverse(w))),v),
    inference(rew,[status(thm),theory(equality)],[540,184]),
    [iquote('0:Rew:540.0,184.0')] ).

cnf(543,plain,
    ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
    inference(rew,[status(thm),theory(equality)],[540,5]),
    [iquote('0:Rew:540.0,5.0')] ).

cnf(544,plain,
    equal(multiply(u,multiply(double_divide(identity,u),v)),v),
    inference(rew,[status(thm),theory(equality)],[540,194]),
    [iquote('0:Rew:540.0,194.0')] ).

cnf(594,plain,
    equal(double_divide(identity,u),inverse(u)),
    inference(spr,[status(thm),theory(equality)],[510,539]),
    [iquote('0:SpR:510.0,539.0')] ).

cnf(604,plain,
    equal(multiply(u,multiply(inverse(u),v)),v),
    inference(rew,[status(thm),theory(equality)],[594,544]),
    [iquote('0:Rew:594.0,544.0')] ).

cnf(680,plain,
    equal(inverse(multiply(u,v)),double_divide(u,v)),
    inference(spr,[status(thm),theory(equality)],[540,527]),
    [iquote('0:SpR:540.0,527.0')] ).

cnf(689,plain,
    equal(double_divide(u,v),double_divide(v,u)),
    inference(rew,[status(thm),theory(equality)],[527,680]),
    [iquote('0:Rew:527.0,680.0')] ).

cnf(691,plain,
    equal(multiply(u,double_divide(inverse(v),double_divide(w,double_divide(v,u)))),w),
    inference(rew,[status(thm),theory(equality)],[689,542]),
    [iquote('0:Rew:689.0,542.0')] ).

cnf(756,plain,
    equal(multiply(u,double_divide(u,v)),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[689,522]),
    [iquote('0:SpR:689.0,522.0')] ).

cnf(828,plain,
    equal(multiply(u,multiply(v,inverse(u))),v),
    inference(spr,[status(thm),theory(equality)],[540,604]),
    [iquote('0:SpR:540.0,604.0')] ).

cnf(920,plain,
    equal(double_divide(inverse(u),v),multiply(u,inverse(v))),
    inference(spr,[status(thm),theory(equality)],[756,604]),
    [iquote('0:SpR:756.0,604.0')] ).

cnf(934,plain,
    equal(multiply(u,multiply(v,inverse(double_divide(w,double_divide(v,u))))),w),
    inference(rew,[status(thm),theory(equality)],[920,691]),
    [iquote('0:Rew:920.0,691.0')] ).

cnf(947,plain,
    equal(multiply(u,multiply(v,multiply(double_divide(v,u),w))),w),
    inference(rew,[status(thm),theory(equality)],[6,934]),
    [iquote('0:Rew:6.0,934.0')] ).

cnf(1082,plain,
    equal(multiply(u,inverse(double_divide(v,w))),multiply(w,multiply(v,u))),
    inference(spr,[status(thm),theory(equality)],[828,947]),
    [iquote('0:SpR:828.0,947.0')] ).

cnf(1116,plain,
    equal(multiply(u,multiply(v,w)),multiply(v,multiply(w,u))),
    inference(rew,[status(thm),theory(equality)],[6,1082]),
    [iquote('0:Rew:6.0,1082.0')] ).

cnf(1117,plain,
    $false,
    inference(unc,[status(thm)],[1116,543]),
    [iquote('0:UnC:1116.0,543.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP575-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n023.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
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue Jun 14 05:32:21 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.47  
% 0.19/0.47  SPASS V 3.9 
% 0.19/0.47  SPASS beiseite: Proof found.
% 0.19/0.47  % SZS status Theorem
% 0.19/0.47  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.47  SPASS derived 690 clauses, backtracked 0 clauses, performed 0 splits and kept 183 clauses.
% 0.19/0.47  SPASS allocated 64220 KBytes.
% 0.19/0.47  SPASS spent	0:00:00.13 on the problem.
% 0.19/0.47  		0:00:00.04 for the input.
% 0.19/0.47  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.47  		0:00:00.01 for inferences.
% 0.19/0.47  		0:00:00.00 for the backtracking.
% 0.19/0.47  		0:00:00.06 for the reduction.
% 0.19/0.47  
% 0.19/0.47  
% 0.19/0.47  Here is a proof with depth 9, length 75 :
% 0.19/0.47  % SZS output start Refutation
% See solution above
% 0.19/0.48  Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_3
% 0.19/0.48  
%------------------------------------------------------------------------------