TSTP Solution File: GRP613-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP613-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 11:48:17 EDT 2022

% Result   : Unsatisfiable 0.69s 0.91s
% Output   : Refutation 0.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    3
% Syntax   : Number of clauses     :   53 (  53 unt;   0 nHn;  53 RR)
%            Number of literals    :   53 (   0 equ;   3 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    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(double_divide(inverse(double_divide(inverse(double_divide(u,inverse(v))),w)),double_divide(u,w)),v),
    file('GRP613-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(inverse(double_divide(u,v)),multiply(v,u)),
    file('GRP613-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
    file('GRP613-1.p',unknown),
    [] ).

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

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

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

cnf(9,plain,
    equal(double_divide(multiply(u,multiply(multiply(v,w),x)),double_divide(x,u)),double_divide(w,v)),
    inference(spr,[status(thm),theory(equality)],[2,4]),
    [iquote('0:SpR:2.0,4.0')] ).

cnf(14,plain,
    equal(multiply(u,multiply(double_divide(v,w),multiply(inverse(x),multiply(w,multiply(inverse(u),v))))),inverse(x)),
    inference(spr,[status(thm),theory(equality)],[4,6]),
    [iquote('0:SpR:4.0,6.0')] ).

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

cnf(81,plain,
    equal(double_divide(multiply(double_divide(u,v),multiply(inverse(w),multiply(double_divide(x,y),multiply(inverse(z),multiply(y,multiply(multiply(v,u),x)))))),z),w),
    inference(spr,[status(thm),theory(equality)],[9,7]),
    [iquote('0:SpR:9.0,7.0')] ).

cnf(147,plain,
    equal(double_divide(multiply(double_divide(multiply(u,multiply(inverse(inverse(v)),w)),double_divide(w,u)),inverse(x)),x),v),
    inference(spr,[status(thm),theory(equality)],[14,7]),
    [iquote('0:SpR:14.0,7.0')] ).

cnf(148,plain,
    equal(multiply(u,multiply(double_divide(multiply(v,multiply(inverse(inverse(w)),x)),double_divide(x,v)),inverse(u))),inverse(w)),
    inference(spr,[status(thm),theory(equality)],[14]),
    [iquote('0:SpR:14.0,14.0')] ).

cnf(170,plain,
    equal(double_divide(multiply(inverse(u),inverse(v)),v),u),
    inference(rew,[status(thm),theory(equality)],[4,147]),
    [iquote('0:Rew:4.0,147.0')] ).

cnf(171,plain,
    equal(multiply(u,multiply(inverse(v),inverse(u))),inverse(v)),
    inference(rew,[status(thm),theory(equality)],[4,148]),
    [iquote('0:Rew:4.0,148.0')] ).

cnf(230,plain,
    equal(double_divide(multiply(inverse(u),multiply(v,w)),double_divide(w,v)),u),
    inference(spr,[status(thm),theory(equality)],[2,170]),
    [iquote('0:SpR:2.0,170.0')] ).

cnf(242,plain,
    equal(double_divide(inverse(u),double_divide(inverse(v),v)),u),
    inference(spr,[status(thm),theory(equality)],[171,4]),
    [iquote('0:SpR:171.0,4.0')] ).

cnf(244,plain,
    equal(multiply(double_divide(inverse(u),u),inverse(v)),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[171,6]),
    [iquote('0:SpR:171.0,6.0')] ).

cnf(274,plain,
    equal(double_divide(multiply(u,v),double_divide(inverse(w),w)),double_divide(v,u)),
    inference(spr,[status(thm),theory(equality)],[2,242]),
    [iquote('0:SpR:2.0,242.0')] ).

cnf(427,plain,
    equal(double_divide(inverse(u),double_divide(inverse(inverse(v)),inverse(u))),v),
    inference(spr,[status(thm),theory(equality)],[171,230]),
    [iquote('0:SpR:171.0,230.0')] ).

cnf(464,plain,
    equal(double_divide(inverse(u),double_divide(inverse(multiply(v,w)),inverse(u))),double_divide(w,v)),
    inference(spr,[status(thm),theory(equality)],[2,427]),
    [iquote('0:SpR:2.0,427.0')] ).

cnf(720,plain,
    equal(double_divide(multiply(u,inverse(u)),inverse(v)),v),
    inference(spr,[status(thm),theory(equality)],[274,230]),
    [iquote('0:SpR:274.0,230.0')] ).

cnf(769,plain,
    equal(multiply(inverse(u),multiply(v,inverse(v))),inverse(u)),
    inference(spr,[status(thm),theory(equality)],[720,2]),
    [iquote('0:SpR:720.0,2.0')] ).

cnf(770,plain,
    equal(multiply(u,multiply(inverse(u),multiply(inverse(v),multiply(w,inverse(w))))),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[720,6]),
    [iquote('0:SpR:720.0,6.0')] ).

cnf(776,plain,
    equal(double_divide(multiply(inverse(u),multiply(inverse(v),multiply(w,inverse(w)))),u),v),
    inference(spr,[status(thm),theory(equality)],[720,4]),
    [iquote('0:SpR:720.0,4.0')] ).

cnf(793,plain,
    equal(double_divide(multiply(inverse(u),inverse(v)),u),v),
    inference(rew,[status(thm),theory(equality)],[769,776]),
    [iquote('0:Rew:769.0,776.0')] ).

cnf(797,plain,
    equal(multiply(u,multiply(inverse(u),inverse(v))),inverse(v)),
    inference(rew,[status(thm),theory(equality)],[769,770]),
    [iquote('0:Rew:769.0,770.0')] ).

cnf(825,plain,
    equal(double_divide(multiply(inverse(u),multiply(double_divide(v,w),multiply(inverse(double_divide(inverse(x),x)),multiply(w,multiply(inverse(y),v))))),y),u),
    inference(spr,[status(thm),theory(equality)],[80,274]),
    [iquote('0:SpR:80.0,274.0')] ).

cnf(857,plain,
    equal(double_divide(multiply(inverse(u),multiply(double_divide(v,w),multiply(multiply(x,inverse(x)),multiply(w,multiply(inverse(y),v))))),y),u),
    inference(rew,[status(thm),theory(equality)],[2,825]),
    [iquote('0:Rew:2.0,825.0')] ).

cnf(891,plain,
    equal(inverse(inverse(u)),u),
    inference(spr,[status(thm),theory(equality)],[793,720]),
    [iquote('0:SpR:793.0,720.0')] ).

cnf(897,plain,
    equal(double_divide(inverse(u),double_divide(v,inverse(u))),v),
    inference(rew,[status(thm),theory(equality)],[891,427]),
    [iquote('0:Rew:891.0,427.0')] ).

cnf(961,plain,
    equal(inverse(multiply(u,v)),double_divide(v,u)),
    inference(rew,[status(thm),theory(equality)],[897,464]),
    [iquote('0:Rew:897.0,464.0')] ).

cnf(1016,plain,
    equal(double_divide(multiply(u,multiply(v,w)),double_divide(w,u)),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[891,4]),
    [iquote('0:SpR:891.0,4.0')] ).

cnf(1019,plain,
    equal(multiply(u,multiply(v,inverse(u))),v),
    inference(spr,[status(thm),theory(equality)],[891,171]),
    [iquote('0:SpR:891.0,171.0')] ).

cnf(1021,plain,
    equal(multiply(double_divide(inverse(u),u),v),v),
    inference(spr,[status(thm),theory(equality)],[891,244]),
    [iquote('0:SpR:891.0,244.0')] ).

cnf(1082,plain,
    equal(multiply(inverse(u),multiply(v,u)),v),
    inference(spr,[status(thm),theory(equality)],[891,1019]),
    [iquote('0:SpR:891.0,1019.0')] ).

cnf(1111,plain,
    equal(multiply(double_divide(u,inverse(u)),v),v),
    inference(spr,[status(thm),theory(equality)],[891,1021]),
    [iquote('0:SpR:891.0,1021.0')] ).

cnf(1131,plain,
    equal(multiply(inverse(multiply(u,v)),u),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[1082]),
    [iquote('0:SpR:1082.0,1082.0')] ).

cnf(1139,plain,
    equal(multiply(double_divide(u,v),v),inverse(u)),
    inference(rew,[status(thm),theory(equality)],[961,1131]),
    [iquote('0:Rew:961.0,1131.0')] ).

cnf(1145,plain,
    equal(multiply(u,inverse(u)),double_divide(v,inverse(v))),
    inference(spr,[status(thm),theory(equality)],[1111,1019]),
    [iquote('0:SpR:1111.0,1019.0')] ).

cnf(1195,plain,
    equal(multiply(inverse(u),multiply(v,multiply(multiply(w,x),y))),double_divide(multiply(double_divide(x,w),double_divide(y,v)),u)),
    inference(spr,[status(thm),theory(equality)],[1082,81]),
    [iquote('0:SpR:1082.0,81.0')] ).

cnf(1202,plain,
    equal(double_divide(double_divide(multiply(double_divide(inverse(u),u),double_divide(multiply(v,multiply(inverse(w),x)),double_divide(x,v))),y),w),y),
    inference(rew,[status(thm),theory(equality)],[1195,857]),
    [iquote('0:Rew:1195.0,857.0')] ).

cnf(1244,plain,
    equal(double_divide(double_divide(double_divide(multiply(u,multiply(inverse(v),w)),double_divide(w,u)),x),v),x),
    inference(rew,[status(thm),theory(equality)],[1021,1202]),
    [iquote('0:Rew:1021.0,1202.0')] ).

cnf(1245,plain,
    equal(double_divide(double_divide(inverse(inverse(u)),v),u),v),
    inference(rew,[status(thm),theory(equality)],[1016,1244]),
    [iquote('0:Rew:1016.0,1244.0')] ).

cnf(1246,plain,
    equal(double_divide(double_divide(u,v),u),v),
    inference(rew,[status(thm),theory(equality)],[891,1245]),
    [iquote('0:Rew:891.0,1245.0')] ).

cnf(1347,plain,
    equal(multiply(inverse(u),inverse(v)),double_divide(v,u)),
    inference(spr,[status(thm),theory(equality)],[1139,1082]),
    [iquote('0:SpR:1139.0,1082.0')] ).

cnf(1348,plain,
    equal(multiply(u,inverse(v)),double_divide(v,inverse(u))),
    inference(spr,[status(thm),theory(equality)],[1139,1019]),
    [iquote('0:SpR:1139.0,1019.0')] ).

cnf(1375,plain,
    equal(multiply(u,double_divide(v,u)),inverse(v)),
    inference(rew,[status(thm),theory(equality)],[1347,797]),
    [iquote('0:Rew:1347.0,797.0')] ).

cnf(1411,plain,
    equal(double_divide(u,inverse(u)),double_divide(v,inverse(v))),
    inference(rew,[status(thm),theory(equality)],[1348,1145]),
    [iquote('0:Rew:1348.0,1145.0')] ).

cnf(1674,plain,
    equal(inverse(double_divide(u,v)),multiply(u,v)),
    inference(spr,[status(thm),theory(equality)],[1246,1375]),
    [iquote('0:SpR:1246.0,1375.0')] ).

cnf(1675,plain,
    equal(multiply(u,v),multiply(v,u)),
    inference(rew,[status(thm),theory(equality)],[2,1674]),
    [iquote('0:Rew:2.0,1674.0')] ).

cnf(1678,plain,
    ~ equal(multiply(inverse(a1),a1),multiply(b1,inverse(b1))),
    inference(rew,[status(thm),theory(equality)],[1675,3]),
    [iquote('0:Rew:1675.0,3.0')] ).

cnf(1713,plain,
    ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1))),
    inference(rew,[status(thm),theory(equality)],[1348,1678,1675]),
    [iquote('0:Rew:1348.0,1678.0,1675.0,1678.0,1348.0,1678.0')] ).

cnf(1714,plain,
    $false,
    inference(unc,[status(thm)],[1713,1411]),
    [iquote('0:UnC:1713.0,1411.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP613-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n026.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 09:13:05 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.69/0.91  
% 0.69/0.91  SPASS V 3.9 
% 0.69/0.91  SPASS beiseite: Proof found.
% 0.69/0.91  % SZS status Theorem
% 0.69/0.91  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.69/0.91  SPASS derived 1236 clauses, backtracked 0 clauses, performed 0 splits and kept 599 clauses.
% 0.69/0.91  SPASS allocated 67090 KBytes.
% 0.69/0.91  SPASS spent	0:00:00.54 on the problem.
% 0.69/0.91  		0:00:00.03 for the input.
% 0.69/0.91  		0:00:00.00 for the FLOTTER CNF translation.
% 0.69/0.91  		0:00:00.01 for inferences.
% 0.69/0.91  		0:00:00.00 for the backtracking.
% 0.69/0.91  		0:00:00.47 for the reduction.
% 0.69/0.91  
% 0.69/0.91  
% 0.69/0.91  Here is a proof with depth 12, length 53 :
% 0.69/0.91  % SZS output start Refutation
% See solution above
% 0.69/0.91  Formulae used in the proof : single_axiom multiply prove_these_axioms_1
% 0.69/0.91  
%------------------------------------------------------------------------------