TSTP Solution File: GRP486-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP486-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 11:47:42 EDT 2022
% Result : Unsatisfiable 0.41s 0.58s
% Output : Refutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 5
% Syntax : Number of clauses : 85 ( 85 unt; 0 nHn; 85 RR)
% Number of literals : 85 ( 0 equ; 1 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 : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(double_divide(u,double_divide(double_divide(double_divide(u,v),w),double_divide(v,identity))),double_divide(identity,identity)),w),
file('GRP486-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP486-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP486-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP486-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP486-1.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(double_divide(u,v),w),inverse(v))),inverse(identity)),w),
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(51,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(double_divide(u,double_divide(v,w)),x),multiply(w,v))),inverse(identity)),x),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(52,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(identity,v),inverse(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(u,double_divide(double_divide(inverse(u),v),inverse(identity))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(56,plain,
equal(double_divide(double_divide(u,double_divide(inverse(double_divide(u,v)),inverse(v))),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(59,plain,
equal(double_divide(double_divide(u,double_divide(multiply(v,u),inverse(v))),inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[6,56]),
[iquote('0:Rew:6.0,56.0')] ).
cnf(72,plain,
equal(double_divide(double_divide(u,double_divide(inverse(identity),inverse(inverse(u)))),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[12,59]),
[iquote('0:SpR:12.0,59.0')] ).
cnf(73,plain,
equal(double_divide(double_divide(u,double_divide(inverse(inverse(u)),inverse(identity))),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[13,59]),
[iquote('0:SpR:13.0,59.0')] ).
cnf(83,plain,
equal(double_divide(inverse(identity),inverse(inverse(double_divide(u,identity)))),double_divide(double_divide(u,identity),inverse(identity))),
inference(spr,[status(thm),theory(equality)],[72,7]),
[iquote('0:SpR:72.0,7.0')] ).
cnf(87,plain,
equal(double_divide(double_divide(identity,identity),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[4,72]),
[iquote('0:SpR:4.0,72.0')] ).
cnf(88,plain,
equal(double_divide(inverse(identity),inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[3,87]),
[iquote('0:Rew:3.0,87.0')] ).
cnf(90,plain,
equal(double_divide(inverse(identity),inverse(inverse(inverse(u)))),double_divide(inverse(u),inverse(identity))),
inference(rew,[status(thm),theory(equality)],[3,83]),
[iquote('0:Rew:3.0,83.0')] ).
cnf(95,plain,
equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,u),inverse(inverse(identity)))),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[88,7]),
[iquote('0:SpR:88.0,7.0')] ).
cnf(118,plain,
equal(double_divide(double_divide(identity,u),inverse(inverse(double_divide(v,identity)))),double_divide(double_divide(v,u),inverse(identity))),
inference(spr,[status(thm),theory(equality)],[52,7]),
[iquote('0:SpR:52.0,7.0')] ).
cnf(126,plain,
equal(double_divide(double_divide(identity,u),inverse(inverse(inverse(v)))),double_divide(double_divide(v,u),inverse(identity))),
inference(rew,[status(thm),theory(equality)],[3,118]),
[iquote('0:Rew:3.0,118.0')] ).
cnf(164,plain,
equal(double_divide(double_divide(inverse(inverse(u)),v),inverse(identity)),double_divide(double_divide(u,v),inverse(identity))),
inference(spr,[status(thm),theory(equality)],[53]),
[iquote('0:SpR:53.0,53.0')] ).
cnf(168,plain,
equal(double_divide(double_divide(identity,double_divide(identity,inverse(identity))),inverse(identity)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[88,53]),
[iquote('0:SpR:88.0,53.0')] ).
cnf(176,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[88,168,3,4]),
[iquote('0:Rew:88.0,168.0,3.0,168.0,4.0,168.0')] ).
cnf(177,plain,
equal(multiply(inverse(u),u),identity),
inference(rew,[status(thm),theory(equality)],[176,12]),
[iquote('0:Rew:176.0,12.0')] ).
cnf(180,plain,
equal(double_divide(double_divide(u,double_divide(multiply(v,u),inverse(v))),identity),identity),
inference(rew,[status(thm),theory(equality)],[176,59]),
[iquote('0:Rew:176.0,59.0')] ).
cnf(190,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(inverse(u),v),identity)),identity),v),
inference(rew,[status(thm),theory(equality)],[176,53]),
[iquote('0:Rew:176.0,53.0')] ).
cnf(195,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(double_divide(u,double_divide(v,w)),x),multiply(w,v))),identity),x),
inference(rew,[status(thm),theory(equality)],[176,51]),
[iquote('0:Rew:176.0,51.0')] ).
cnf(198,plain,
equal(double_divide(double_divide(u,double_divide(inverse(inverse(u)),identity)),identity),identity),
inference(rew,[status(thm),theory(equality)],[176,73]),
[iquote('0:Rew:176.0,73.0')] ).
cnf(206,plain,
equal(double_divide(identity,inverse(inverse(inverse(u)))),double_divide(inverse(u),identity)),
inference(rew,[status(thm),theory(equality)],[176,90]),
[iquote('0:Rew:176.0,90.0')] ).
cnf(209,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(identity,u),inverse(identity))),identity),u),
inference(rew,[status(thm),theory(equality)],[176,95]),
[iquote('0:Rew:176.0,95.0')] ).
cnf(212,plain,
equal(double_divide(double_divide(identity,u),inverse(inverse(inverse(v)))),double_divide(double_divide(v,u),identity)),
inference(rew,[status(thm),theory(equality)],[176,126]),
[iquote('0:Rew:176.0,126.0')] ).
cnf(234,plain,
equal(multiply(inverse(inverse(inverse(u))),u),identity),
inference(rew,[status(thm),theory(equality)],[6,198,3]),
[iquote('0:Rew:6.0,198.0,3.0,198.0,3.0,198.0')] ).
cnf(237,plain,
equal(double_divide(identity,inverse(inverse(inverse(u)))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[3,206]),
[iquote('0:Rew:3.0,206.0')] ).
cnf(238,plain,
equal(multiply(double_divide(multiply(u,v),inverse(u)),v),identity),
inference(rew,[status(thm),theory(equality)],[6,180,3]),
[iquote('0:Rew:6.0,180.0,3.0,180.0')] ).
cnf(239,plain,
equal(multiply(multiply(u,inverse(v)),v),u),
inference(rew,[status(thm),theory(equality)],[6,190,3]),
[iquote('0:Rew:6.0,190.0,3.0,190.0,6.0,190.0,3.0,190.0')] ).
cnf(245,plain,
equal(multiply(double_divide(double_divide(identity,u),inverse(identity)),identity),u),
inference(rew,[status(thm),theory(equality)],[6,209,3]),
[iquote('0:Rew:6.0,209.0,3.0,209.0')] ).
cnf(246,plain,
equal(multiply(double_divide(double_divide(identity,u),identity),identity),u),
inference(rew,[status(thm),theory(equality)],[176,245]),
[iquote('0:Rew:176.0,245.0')] ).
cnf(247,plain,
equal(multiply(multiply(u,identity),identity),u),
inference(rew,[status(thm),theory(equality)],[6,246,3]),
[iquote('0:Rew:6.0,246.0,3.0,246.0')] ).
cnf(273,plain,
equal(double_divide(double_divide(identity,u),inverse(inverse(inverse(v)))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[6,212,3]),
[iquote('0:Rew:6.0,212.0,3.0,212.0')] ).
cnf(280,plain,
equal(double_divide(double_divide(inverse(inverse(u)),v),identity),double_divide(double_divide(u,v),identity)),
inference(rew,[status(thm),theory(equality)],[176,164]),
[iquote('0:Rew:176.0,164.0')] ).
cnf(281,plain,
equal(multiply(u,inverse(inverse(v))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[6,280,3]),
[iquote('0:Rew:6.0,280.0,3.0,280.0,6.0,280.0,3.0,280.0')] ).
cnf(310,plain,
equal(multiply(double_divide(double_divide(double_divide(u,double_divide(v,w)),x),multiply(w,v)),u),x),
inference(rew,[status(thm),theory(equality)],[6,195,3]),
[iquote('0:Rew:6.0,195.0,3.0,195.0')] ).
cnf(337,plain,
equal(double_divide(double_divide(identity,multiply(u,identity)),u),identity),
inference(spr,[status(thm),theory(equality)],[247,10]),
[iquote('0:SpR:247.0,10.0')] ).
cnf(375,plain,
equal(inverse(inverse(inverse(inverse(u)))),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[234,239]),
[iquote('0:SpR:234.0,239.0')] ).
cnf(378,plain,
equal(inverse(inverse(inverse(inverse(u)))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[13,375]),
[iquote('0:Rew:13.0,375.0')] ).
cnf(380,plain,
equal(multiply(u,double_divide(identity,multiply(u,identity))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[337,6]),
[iquote('0:SpR:337.0,6.0')] ).
cnf(394,plain,
equal(multiply(u,double_divide(identity,multiply(u,identity))),identity),
inference(rew,[status(thm),theory(equality)],[176,380]),
[iquote('0:Rew:176.0,380.0')] ).
cnf(411,plain,
equal(multiply(multiply(u,inverse(inverse(v))),inverse(inverse(inverse(v)))),u),
inference(spr,[status(thm),theory(equality)],[378,239]),
[iquote('0:SpR:378.0,239.0')] ).
cnf(416,plain,
equal(multiply(multiply(u,v),inverse(v)),u),
inference(rew,[status(thm),theory(equality)],[281,411]),
[iquote('0:Rew:281.0,411.0,281.0,411.0')] ).
cnf(425,plain,
equal(multiply(identity,inverse(u)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[177,416]),
[iquote('0:SpR:177.0,416.0')] ).
cnf(430,plain,
equal(inverse(inverse(inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[13,425]),
[iquote('0:Rew:13.0,425.0')] ).
cnf(432,plain,
equal(double_divide(double_divide(identity,u),inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[430,273]),
[iquote('0:Rew:430.0,273.0')] ).
cnf(434,plain,
equal(double_divide(identity,inverse(u)),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[430,237]),
[iquote('0:Rew:430.0,237.0')] ).
cnf(459,plain,
equal(double_divide(multiply(u,v),inverse(u)),multiply(identity,inverse(v))),
inference(spr,[status(thm),theory(equality)],[238,416]),
[iquote('0:SpR:238.0,416.0')] ).
cnf(476,plain,
equal(double_divide(multiply(u,v),inverse(u)),inverse(inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[13,459]),
[iquote('0:Rew:13.0,459.0')] ).
cnf(477,plain,
equal(double_divide(multiply(u,v),inverse(u)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[430,476]),
[iquote('0:Rew:430.0,476.0')] ).
cnf(500,plain,
equal(multiply(inverse(u),identity),inverse(inverse(inverse(u)))),
inference(spr,[status(thm),theory(equality)],[434,6]),
[iquote('0:SpR:434.0,6.0')] ).
cnf(503,plain,
equal(double_divide(identity,multiply(u,v)),inverse(multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[6,434]),
[iquote('0:SpR:6.0,434.0')] ).
cnf(507,plain,
equal(multiply(inverse(u),identity),inverse(u)),
inference(rew,[status(thm),theory(equality)],[430,500]),
[iquote('0:Rew:430.0,500.0')] ).
cnf(510,plain,
equal(multiply(u,inverse(multiply(u,identity))),identity),
inference(rew,[status(thm),theory(equality)],[503,394]),
[iquote('0:Rew:503.0,394.0')] ).
cnf(519,plain,
equal(multiply(multiply(u,v),identity),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[6,507]),
[iquote('0:SpR:6.0,507.0')] ).
cnf(525,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[519,247]),
[iquote('0:Rew:519.0,247.0')] ).
cnf(529,plain,
equal(multiply(u,inverse(u)),identity),
inference(rew,[status(thm),theory(equality)],[525,510]),
[iquote('0:Rew:525.0,510.0')] ).
cnf(587,plain,
equal(multiply(identity,u),u),
inference(spr,[status(thm),theory(equality)],[529,239]),
[iquote('0:SpR:529.0,239.0')] ).
cnf(593,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[13,587]),
[iquote('0:Rew:13.0,587.0')] ).
cnf(594,plain,
equal(multiply(identity,u),u),
inference(rew,[status(thm),theory(equality)],[593,13]),
[iquote('0:Rew:593.0,13.0')] ).
cnf(595,plain,
equal(double_divide(identity,inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[593,434]),
[iquote('0:Rew:593.0,434.0')] ).
cnf(612,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[6,593]),
[iquote('0:SpR:6.0,593.0')] ).
cnf(634,plain,
equal(multiply(double_divide(double_divide(double_divide(u,double_divide(v,identity)),w),v),u),w),
inference(spr,[status(thm),theory(equality)],[594,310]),
[iquote('0:SpR:594.0,310.0')] ).
cnf(647,plain,
equal(multiply(double_divide(double_divide(double_divide(u,inverse(v)),w),v),u),w),
inference(rew,[status(thm),theory(equality)],[3,634]),
[iquote('0:Rew:3.0,634.0')] ).
cnf(674,plain,
equal(double_divide(identity,u),inverse(u)),
inference(spr,[status(thm),theory(equality)],[593,595]),
[iquote('0:SpR:593.0,595.0')] ).
cnf(679,plain,
equal(double_divide(inverse(u),inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[674,432]),
[iquote('0:Rew:674.0,432.0')] ).
cnf(756,plain,
equal(double_divide(u,inverse(v)),multiply(inverse(u),v)),
inference(spr,[status(thm),theory(equality)],[593,679]),
[iquote('0:SpR:593.0,679.0')] ).
cnf(766,plain,
equal(multiply(double_divide(double_divide(multiply(inverse(u),v),w),v),u),w),
inference(rew,[status(thm),theory(equality)],[756,647]),
[iquote('0:Rew:756.0,647.0')] ).
cnf(768,plain,
equal(multiply(inverse(multiply(u,v)),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[756,477]),
[iquote('0:Rew:756.0,477.0')] ).
cnf(773,plain,
equal(multiply(double_divide(u,v),v),inverse(u)),
inference(rew,[status(thm),theory(equality)],[612,768]),
[iquote('0:Rew:612.0,768.0')] ).
cnf(1099,plain,
equal(double_divide(double_divide(multiply(inverse(inverse(u)),v),w),v),multiply(w,u)),
inference(spr,[status(thm),theory(equality)],[766,239]),
[iquote('0:SpR:766.0,239.0')] ).
cnf(1132,plain,
equal(double_divide(double_divide(multiply(u,v),w),v),multiply(w,u)),
inference(rew,[status(thm),theory(equality)],[593,1099]),
[iquote('0:Rew:593.0,1099.0')] ).
cnf(2137,plain,
equal(inverse(double_divide(multiply(u,v),w)),multiply(multiply(w,u),v)),
inference(spr,[status(thm),theory(equality)],[1132,773]),
[iquote('0:SpR:1132.0,773.0')] ).
cnf(2212,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[6,2137]),
[iquote('0:Rew:6.0,2137.0')] ).
cnf(2213,plain,
$false,
inference(unc,[status(thm)],[2212,5]),
[iquote('0:UnC:2212.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP486-1 : TPTP v8.1.0. Released v2.6.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n005.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 13 10:30:24 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.41/0.58
% 0.41/0.58 SPASS V 3.9
% 0.41/0.58 SPASS beiseite: Proof found.
% 0.41/0.58 % SZS status Theorem
% 0.41/0.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.41/0.58 SPASS derived 1231 clauses, backtracked 0 clauses, performed 0 splits and kept 226 clauses.
% 0.41/0.58 SPASS allocated 65329 KBytes.
% 0.41/0.58 SPASS spent 0:00:00.21 on the problem.
% 0.41/0.58 0:00:00.03 for the input.
% 0.41/0.58 0:00:00.00 for the FLOTTER CNF translation.
% 0.41/0.58 0:00:00.01 for inferences.
% 0.41/0.58 0:00:00.00 for the backtracking.
% 0.41/0.58 0:00:00.14 for the reduction.
% 0.41/0.58
% 0.41/0.58
% 0.41/0.58 Here is a proof with depth 8, length 85 :
% 0.41/0.58 % SZS output start Refutation
% See solution above
% 0.41/0.61 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_3
% 0.41/0.61
%------------------------------------------------------------------------------