TSTP Solution File: GRP615-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP615-1 : 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 11:48:18 EDT 2022

% Result   : Unsatisfiable 1.81s 2.04s
% Output   : Refutation 1.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :    3
% Syntax   : Number of clauses     :   82 (  82 unt;   0 nHn;  82 RR)
%            Number of literals    :   82 (   0 equ;   5 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   11 (   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(double_divide(inverse(double_divide(u,inverse(v))),w)),double_divide(u,w)),v),
    file('GRP615-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(inverse(double_divide(u,v)),multiply(v,u)),
    file('GRP615-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
    file('GRP615-1.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(69,plain,
    equal(double_divide(multiply(u,multiply(inverse(v),multiply(w,multiply(inverse(x),multiply(double_divide(y,z),multiply(inverse(u),multiply(z,multiply(inverse(w),y)))))))),x),v),
    inference(spr,[status(thm),theory(equality)],[7]),
    [iquote('0:SpR:7.0,7.0')] ).

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(1024,plain,
    equal(multiply(double_divide(u,v),multiply(v,multiply(w,u))),w),
    inference(spr,[status(thm),theory(equality)],[891,6]),
    [iquote('0:SpR:891.0,6.0')] ).

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(1147,plain,
    equal(multiply(u,inverse(double_divide(v,inverse(v)))),u),
    inference(spr,[status(thm),theory(equality)],[1111,1019]),
    [iquote('0:SpR:1111.0,1019.0')] ).

cnf(1154,plain,
    equal(multiply(u,multiply(inverse(v),v)),u),
    inference(rew,[status(thm),theory(equality)],[2,1147]),
    [iquote('0:Rew:2.0,1147.0')] ).

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(1337,plain,
    equal(multiply(u,double_divide(u,v)),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[1246,2]),
    [iquote('0:SpR:1246.0,2.0')] ).

cnf(1338,plain,
    equal(double_divide(u,double_divide(v,u)),v),
    inference(spr,[status(thm),theory(equality)],[1246]),
    [iquote('0:SpR:1246.0,1246.0')] ).

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(1529,plain,
    equal(inverse(multiply(u,multiply(inverse(v),multiply(w,multiply(inverse(x),multiply(double_divide(y,z),multiply(inverse(u),multiply(z,multiply(inverse(w),y))))))))),multiply(v,x)),
    inference(spr,[status(thm),theory(equality)],[69,1139]),
    [iquote('0:SpR:69.0,1139.0')] ).

cnf(1563,plain,
    equal(multiply(inverse(u),multiply(double_divide(v,w),multiply(inverse(x),multiply(w,multiply(inverse(y),v))))),double_divide(multiply(x,y),u)),
    inference(spr,[status(thm),theory(equality)],[1082,69]),
    [iquote('0:SpR:1082.0,69.0')] ).

cnf(1564,plain,
    equal(multiply(u,multiply(inverse(v),multiply(double_divide(w,x),multiply(inverse(y),multiply(x,multiply(inverse(u),w)))))),double_divide(y,v)),
    inference(spr,[status(thm),theory(equality)],[1154,69]),
    [iquote('0:SpR:1154.0,69.0')] ).

cnf(1575,plain,
    equal(multiply(u,double_divide(multiply(v,u),w)),double_divide(v,w)),
    inference(rew,[status(thm),theory(equality)],[1563,1564]),
    [iquote('0:Rew:1563.0,1564.0')] ).

cnf(1643,plain,
    equal(double_divide(multiply(inverse(u),multiply(v,multiply(inverse(w),multiply(double_divide(x,y),multiply(inverse(z),multiply(y,multiply(inverse(v),x))))))),z),multiply(u,w)),
    inference(rew,[status(thm),theory(equality)],[961,1529]),
    [iquote('0:Rew:961.0,1529.0')] ).

cnf(1644,plain,
    equal(double_divide(multiply(inverse(u),double_divide(v,w)),v),multiply(u,w)),
    inference(rew,[status(thm),theory(equality)],[1575,1643,1563]),
    [iquote('0:Rew:1575.0,1643.0,1563.0,1643.0')] ).

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(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
    inference(rew,[status(thm),theory(equality)],[1675,3]),
    [iquote('0:Rew:1675.0,3.0')] ).

cnf(1713,plain,
    equal(multiply(inverse(u),multiply(u,v)),v),
    inference(spr,[status(thm),theory(equality)],[1675,1082]),
    [iquote('0:SpR:1675.0,1082.0')] ).

cnf(1715,plain,
    equal(inverse(multiply(u,v)),double_divide(u,v)),
    inference(spr,[status(thm),theory(equality)],[1675,961]),
    [iquote('0:SpR:1675.0,961.0')] ).

cnf(1725,plain,
    equal(double_divide(u,v),double_divide(v,u)),
    inference(rew,[status(thm),theory(equality)],[961,1715]),
    [iquote('0:Rew:961.0,1715.0')] ).

cnf(1798,plain,
    equal(double_divide(u,multiply(inverse(v),double_divide(u,w))),multiply(v,w)),
    inference(rew,[status(thm),theory(equality)],[1725,1644]),
    [iquote('0:Rew:1725.0,1644.0')] ).

cnf(1891,plain,
    equal(multiply(multiply(u,v),multiply(double_divide(v,u),w)),w),
    inference(spr,[status(thm),theory(equality)],[2,1713]),
    [iquote('0:SpR:2.0,1713.0')] ).

cnf(2022,plain,
    equal(multiply(inverse(u),v),double_divide(u,inverse(v))),
    inference(spr,[status(thm),theory(equality)],[1348,1675]),
    [iquote('0:SpR:1348.0,1675.0')] ).

cnf(2052,plain,
    equal(double_divide(u,double_divide(v,inverse(double_divide(u,w)))),multiply(v,w)),
    inference(rew,[status(thm),theory(equality)],[2022,1798]),
    [iquote('0:Rew:2022.0,1798.0')] ).

cnf(2187,plain,
    equal(double_divide(u,double_divide(v,multiply(w,u))),multiply(v,w)),
    inference(rew,[status(thm),theory(equality)],[2,2052]),
    [iquote('0:Rew:2.0,2052.0')] ).

cnf(3312,plain,
    equal(double_divide(u,double_divide(v,multiply(u,w))),multiply(w,v)),
    inference(spr,[status(thm),theory(equality)],[1338,1575]),
    [iquote('0:SpR:1338.0,1575.0')] ).

cnf(3402,plain,
    equal(multiply(multiply(u,v),w),multiply(u,multiply(w,v))),
    inference(spr,[status(thm),theory(equality)],[1024,1891]),
    [iquote('0:SpR:1024.0,1891.0')] ).

cnf(4082,plain,
    equal(inverse(double_divide(u,multiply(v,w))),multiply(w,multiply(u,v))),
    inference(spr,[status(thm),theory(equality)],[2187,1337]),
    [iquote('0:SpR:2187.0,1337.0')] ).

cnf(4112,plain,
    equal(multiply(multiply(u,v),w),multiply(v,multiply(w,u))),
    inference(rew,[status(thm),theory(equality)],[2,4082]),
    [iquote('0:Rew:2.0,4082.0')] ).

cnf(4113,plain,
    equal(multiply(u,multiply(v,w)),multiply(w,multiply(v,u))),
    inference(rew,[status(thm),theory(equality)],[3402,4112]),
    [iquote('0:Rew:3402.0,4112.0')] ).

cnf(4114,plain,
    ~ equal(multiply(b3,multiply(a3,c3)),multiply(a3,multiply(b3,c3))),
    inference(rew,[status(thm),theory(equality)],[4113,1678]),
    [iquote('0:Rew:4113.0,1678.0')] ).

cnf(4414,plain,
    equal(double_divide(u,double_divide(v,multiply(multiply(u,w),x))),multiply(w,multiply(x,v))),
    inference(spr,[status(thm),theory(equality)],[3312,1575]),
    [iquote('0:SpR:3312.0,1575.0')] ).

cnf(4486,plain,
    equal(double_divide(u,double_divide(v,multiply(u,multiply(w,x)))),multiply(x,multiply(w,v))),
    inference(rew,[status(thm),theory(equality)],[3402,4414]),
    [iquote('0:Rew:3402.0,4414.0')] ).

cnf(4487,plain,
    equal(multiply(multiply(u,v),w),multiply(v,multiply(u,w))),
    inference(rew,[status(thm),theory(equality)],[3312,4486]),
    [iquote('0:Rew:3312.0,4486.0')] ).

cnf(4488,plain,
    equal(multiply(u,multiply(v,w)),multiply(w,multiply(u,v))),
    inference(rew,[status(thm),theory(equality)],[3402,4487]),
    [iquote('0:Rew:3402.0,4487.0')] ).

cnf(4489,plain,
    ~ equal(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(b3,c3))),
    inference(rew,[status(thm),theory(equality)],[4488,4114]),
    [iquote('0:Rew:4488.0,4114.0')] ).

cnf(4493,plain,
    ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))),
    inference(rew,[status(thm),theory(equality)],[1675,4489]),
    [iquote('0:Rew:1675.0,4489.0')] ).

cnf(4494,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[4493]),
    [iquote('0:Obv:4493.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : GRP615-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n026.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 12:33:21 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 1.81/2.04  
% 1.81/2.04  SPASS V 3.9 
% 1.81/2.04  SPASS beiseite: Proof found.
% 1.81/2.04  % SZS status Theorem
% 1.81/2.04  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.81/2.04  SPASS derived 2728 clauses, backtracked 0 clauses, performed 0 splits and kept 1240 clauses.
% 1.81/2.04  SPASS allocated 72430 KBytes.
% 1.81/2.04  SPASS spent	0:00:01.69 on the problem.
% 1.81/2.04  		0:00:00.04 for the input.
% 1.81/2.04  		0:00:00.00 for the FLOTTER CNF translation.
% 1.81/2.04  		0:00:00.02 for inferences.
% 1.81/2.04  		0:00:00.00 for the backtracking.
% 1.81/2.04  		0:00:01.60 for the reduction.
% 1.81/2.04  
% 1.81/2.04  
% 1.81/2.04  Here is a proof with depth 14, length 82 :
% 1.81/2.04  % SZS output start Refutation
% See solution above
% 1.91/2.08  Formulae used in the proof : single_axiom multiply prove_these_axioms_3
% 1.91/2.08  
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