TSTP Solution File: GRP435-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP435-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 11:47:28 EDT 2022
% Result : Unsatisfiable 3.47s 3.65s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 2
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 60 RR)
% Number of literals : 60 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(u,v),w)),u),v),multiply(x,inverse(x)))),w),
file('GRP435-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP435-1.p',unknown),
[] ).
cnf(4,plain,
equal(inverse(multiply(multiply(multiply(u,multiply(inverse(multiply(multiply(v,w),u)),v)),w),multiply(x,inverse(x)))),multiply(y,inverse(y))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(10,plain,
equal(multiply(u,inverse(u)),multiply(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(35,plain,
equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(u,inverse(u)),v)),w),inverse(w)),multiply(x,inverse(x)))),v),
inference(spr,[status(thm),theory(equality)],[10,1]),
[iquote('0:SpR:10.0,1.0')] ).
cnf(37,plain,
equal(inverse(multiply(multiply(multiply(inverse(multiply(u,inverse(u))),v),w),multiply(x,inverse(x)))),inverse(multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[10,1]),
[iquote('0:SpR:10.0,1.0')] ).
cnf(105,plain,
equal(inverse(multiply(multiply(multiply(u,inverse(u)),v),multiply(w,inverse(w)))),inverse(multiply(inverse(inverse(multiply(x,inverse(x)))),v))),
inference(spr,[status(thm),theory(equality)],[10,37]),
[iquote('0:SpR:10.0,37.0')] ).
cnf(117,plain,
equal(inverse(multiply(u,inverse(u))),inverse(multiply(v,inverse(v)))),
inference(spr,[status(thm),theory(equality)],[35,37]),
[iquote('0:SpR:35.0,37.0')] ).
cnf(168,plain,
equal(multiply(u,inverse(u)),multiply(multiply(v,inverse(v)),inverse(multiply(w,inverse(w))))),
inference(spr,[status(thm),theory(equality)],[117,10]),
[iquote('0:SpR:117.0,10.0')] ).
cnf(196,plain,
equal(inverse(multiply(multiply(multiply(inverse(multiply(multiply(u,inverse(u)),v)),multiply(w,inverse(w))),inverse(multiply(x,inverse(x)))),multiply(y,inverse(y)))),v),
inference(spr,[status(thm),theory(equality)],[117,35]),
[iquote('0:SpR:117.0,35.0')] ).
cnf(239,plain,
equal(inverse(multiply(multiply(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(v)))),inverse(inverse(inverse(multiply(multiply(w,inverse(w)),x))))),multiply(y,inverse(y)))),x),
inference(spr,[status(thm),theory(equality)],[168,35]),
[iquote('0:SpR:168.0,35.0')] ).
cnf(240,plain,
equal(inverse(multiply(multiply(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(v)))),w),multiply(x,inverse(x)))),inverse(multiply(inverse(inverse(multiply(y,inverse(y)))),w))),
inference(spr,[status(thm),theory(equality)],[168,37]),
[iquote('0:SpR:168.0,37.0')] ).
cnf(263,plain,
equal(inverse(multiply(multiply(multiply(inverse(multiply(u,inverse(u))),multiply(inverse(multiply(v,inverse(v))),w)),inverse(w)),multiply(x,inverse(x)))),multiply(y,inverse(y))),
inference(spr,[status(thm),theory(equality)],[168,4]),
[iquote('0:SpR:168.0,4.0')] ).
cnf(300,plain,
equal(inverse(multiply(multiply(inverse(multiply(u,inverse(u))),v),inverse(v))),multiply(w,inverse(w))),
inference(rew,[status(thm),theory(equality)],[37,263]),
[iquote('0:Rew:37.0,263.0')] ).
cnf(414,plain,
equal(inverse(multiply(multiply(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(v)))),w),multiply(x,inverse(x)))),inverse(w)),
inference(spr,[status(thm),theory(equality)],[300,1]),
[iquote('0:SpR:300.0,1.0')] ).
cnf(512,plain,
equal(inverse(inverse(inverse(inverse(multiply(multiply(u,inverse(u)),v))))),v),
inference(rew,[status(thm),theory(equality)],[414,239]),
[iquote('0:Rew:414.0,239.0')] ).
cnf(513,plain,
equal(inverse(multiply(inverse(inverse(multiply(u,inverse(u)))),v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[414,240]),
[iquote('0:Rew:414.0,240.0')] ).
cnf(517,plain,
equal(inverse(multiply(multiply(multiply(u,inverse(u)),v),multiply(w,inverse(w)))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[513,105]),
[iquote('0:Rew:513.0,105.0')] ).
cnf(560,plain,
equal(inverse(inverse(inverse(inverse(multiply(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(v)))),w))))),w),
inference(spr,[status(thm),theory(equality)],[117,512]),
[iquote('0:SpR:117.0,512.0')] ).
cnf(565,plain,
equal(inverse(inverse(inverse(inverse(multiply(inverse(multiply(multiply(inverse(multiply(u,inverse(u))),v),inverse(v))),w))))),w),
inference(spr,[status(thm),theory(equality)],[300,512]),
[iquote('0:SpR:300.0,512.0')] ).
cnf(589,plain,
equal(inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(u,inverse(u))))))),v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[513]),
[iquote('0:SpR:513.0,513.0')] ).
cnf(1098,plain,
equal(inverse(inverse(inverse(inverse(inverse(multiply(u,inverse(u))))))),multiply(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[517,512]),
[iquote('0:SpR:517.0,512.0')] ).
cnf(1151,plain,
equal(inverse(multiply(multiply(multiply(u,inverse(u)),v),multiply(multiply(w,inverse(w)),inverse(multiply(x,inverse(x)))))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[168,517]),
[iquote('0:SpR:168.0,517.0')] ).
cnf(1617,plain,
equal(inverse(multiply(multiply(u,inverse(u)),v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[1098,589]),
[iquote('0:SpR:1098.0,589.0')] ).
cnf(1744,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),v),inverse(v)),multiply(w,inverse(w)))),u),
inference(rew,[status(thm),theory(equality)],[1617,35]),
[iquote('0:Rew:1617.0,35.0')] ).
cnf(1745,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[1617,512]),
[iquote('0:Rew:1617.0,512.0')] ).
cnf(1868,plain,
equal(inverse(multiply(multiply(multiply(inverse(u),multiply(v,inverse(v))),inverse(multiply(w,inverse(w)))),multiply(x,inverse(x)))),u),
inference(rew,[status(thm),theory(equality)],[1617,196]),
[iquote('0:Rew:1617.0,196.0')] ).
cnf(1990,plain,
equal(multiply(inverse(multiply(multiply(inverse(multiply(u,inverse(u))),v),inverse(v))),w),w),
inference(rew,[status(thm),theory(equality)],[1745,565]),
[iquote('0:Rew:1745.0,565.0')] ).
cnf(1994,plain,
equal(multiply(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(v)))),w),w),
inference(rew,[status(thm),theory(equality)],[1745,560]),
[iquote('0:Rew:1745.0,560.0')] ).
cnf(2093,plain,
equal(inverse(multiply(u,multiply(v,inverse(v)))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[1994,414]),
[iquote('0:Rew:1994.0,414.0')] ).
cnf(2101,plain,
equal(inverse(multiply(multiply(u,multiply(inverse(multiply(multiply(v,w),u)),v)),w)),multiply(x,inverse(x))),
inference(rew,[status(thm),theory(equality)],[2093,4]),
[iquote('0:Rew:2093.0,4.0')] ).
cnf(2103,plain,
equal(inverse(multiply(multiply(inverse(multiply(multiply(u,v),w)),u),v)),w),
inference(rew,[status(thm),theory(equality)],[2093,1]),
[iquote('0:Rew:2093.0,1.0')] ).
cnf(2432,plain,
equal(inverse(multiply(multiply(inverse(u),v),inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[2093,1744]),
[iquote('0:Rew:2093.0,1744.0')] ).
cnf(2481,plain,
equal(multiply(multiply(u,inverse(u)),v),v),
inference(rew,[status(thm),theory(equality)],[2432,1990]),
[iquote('0:Rew:2432.0,1990.0')] ).
cnf(2500,plain,
equal(inverse(multiply(multiply(multiply(u,inverse(u)),v),inverse(multiply(w,inverse(w))))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[2481,1151]),
[iquote('0:Rew:2481.0,1151.0')] ).
cnf(2660,plain,
equal(inverse(multiply(u,inverse(multiply(v,inverse(v))))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[2481,2500]),
[iquote('0:Rew:2481.0,2500.0')] ).
cnf(2813,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[2093,1868,2660]),
[iquote('0:Rew:2093.0,1868.0,2660.0,1868.0,2093.0,1868.0')] ).
cnf(3645,plain,
equal(inverse(multiply(multiply(u,inverse(multiply(multiply(v,w),u))),v)),w),
inference(spr,[status(thm),theory(equality)],[2103]),
[iquote('0:SpR:2103.0,2103.0')] ).
cnf(3861,plain,
equal(multiply(multiply(u,inverse(multiply(multiply(v,w),u))),v),inverse(w)),
inference(spr,[status(thm),theory(equality)],[3645,2813]),
[iquote('0:SpR:3645.0,2813.0')] ).
cnf(3868,plain,
equal(inverse(multiply(multiply(u,inverse(multiply(v,u))),multiply(w,inverse(w)))),v),
inference(spr,[status(thm),theory(equality)],[2481,3645]),
[iquote('0:SpR:2481.0,3645.0')] ).
cnf(3889,plain,
equal(inverse(multiply(u,inverse(multiply(v,u)))),v),
inference(rew,[status(thm),theory(equality)],[2093,3868]),
[iquote('0:Rew:2093.0,3868.0')] ).
cnf(3924,plain,
equal(multiply(u,inverse(multiply(v,u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[3889,2813]),
[iquote('0:SpR:3889.0,2813.0')] ).
cnf(3945,plain,
equal(multiply(inverse(multiply(u,v)),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[3924,3861]),
[iquote('0:Rew:3924.0,3861.0')] ).
cnf(4177,plain,
equal(inverse(multiply(multiply(u,multiply(multiply(v,inverse(v)),w)),multiply(inverse(multiply(multiply(x,u),w)),x))),multiply(y,inverse(y))),
inference(spr,[status(thm),theory(equality)],[2101]),
[iquote('0:SpR:2101.0,2101.0')] ).
cnf(4328,plain,
equal(inverse(multiply(multiply(u,v),multiply(inverse(multiply(multiply(w,u),v)),w))),multiply(x,inverse(x))),
inference(rew,[status(thm),theory(equality)],[2481,4177]),
[iquote('0:Rew:2481.0,4177.0')] ).
cnf(4647,plain,
equal(inverse(multiply(multiply(u,v),multiply(inverse(multiply(inverse(w),v)),inverse(multiply(u,w))))),multiply(x,inverse(x))),
inference(spr,[status(thm),theory(equality)],[3945,4328]),
[iquote('0:SpR:3945.0,4328.0')] ).
cnf(4855,plain,
equal(inverse(multiply(inverse(u),v)),multiply(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[2432,3924]),
[iquote('0:SpR:2432.0,3924.0')] ).
cnf(4856,plain,
equal(multiply(u,multiply(inverse(u),v)),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[2432,3945]),
[iquote('0:SpR:2432.0,3945.0')] ).
cnf(4908,plain,
equal(inverse(multiply(multiply(u,v),multiply(multiply(inverse(v),w),inverse(multiply(u,w))))),multiply(x,inverse(x))),
inference(rew,[status(thm),theory(equality)],[4855,4647]),
[iquote('0:Rew:4855.0,4647.0')] ).
cnf(4921,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[2813,4856]),
[iquote('0:Rew:2813.0,4856.0')] ).
cnf(5004,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(spr,[status(thm),theory(equality)],[2813,4921]),
[iquote('0:SpR:2813.0,4921.0')] ).
cnf(5009,plain,
equal(inverse(multiply(u,inverse(v))),multiply(v,inverse(u))),
inference(spr,[status(thm),theory(equality)],[3924,4921]),
[iquote('0:SpR:3924.0,4921.0')] ).
cnf(5014,plain,
equal(multiply(multiply(u,v),inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[3945,4921]),
[iquote('0:SpR:3945.0,4921.0')] ).
cnf(5043,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[5004,3945]),
[iquote('0:SpR:5004.0,3945.0')] ).
cnf(5080,plain,
equal(multiply(multiply(u,inverse(v)),v),u),
inference(spr,[status(thm),theory(equality)],[2813,5014]),
[iquote('0:SpR:2813.0,5014.0')] ).
cnf(5165,plain,
equal(inverse(multiply(multiply(u,multiply(v,w)),multiply(inverse(w),inverse(multiply(u,v))))),multiply(x,inverse(x))),
inference(spr,[status(thm),theory(equality)],[3945,4908]),
[iquote('0:SpR:3945.0,4908.0')] ).
cnf(5224,plain,
equal(multiply(multiply(multiply(u,v),w),inverse(multiply(u,multiply(v,w)))),multiply(x,inverse(x))),
inference(rew,[status(thm),theory(equality)],[5009,5165,5043]),
[iquote('0:Rew:5009.0,5165.0,5043.0,5165.0')] ).
cnf(5534,plain,
equal(multiply(multiply(u,inverse(u)),multiply(v,multiply(w,x))),multiply(multiply(v,w),x)),
inference(spr,[status(thm),theory(equality)],[5224,5080]),
[iquote('0:SpR:5224.0,5080.0')] ).
cnf(5632,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[2481,5534]),
[iquote('0:Rew:2481.0,5534.0')] ).
cnf(5633,plain,
$false,
inference(unc,[status(thm)],[5632,2]),
[iquote('0:UnC:5632.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP435-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n018.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
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 21:54:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.47/3.65
% 3.47/3.65 SPASS V 3.9
% 3.47/3.65 SPASS beiseite: Proof found.
% 3.47/3.65 % SZS status Theorem
% 3.47/3.65 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.47/3.65 SPASS derived 3820 clauses, backtracked 0 clauses, performed 0 splits and kept 1235 clauses.
% 3.47/3.65 SPASS allocated 73061 KBytes.
% 3.47/3.65 SPASS spent 0:00:03.31 on the problem.
% 3.47/3.65 0:00:00.03 for the input.
% 3.47/3.65 0:00:00.00 for the FLOTTER CNF translation.
% 3.47/3.65 0:00:00.03 for inferences.
% 3.47/3.65 0:00:00.00 for the backtracking.
% 3.47/3.65 0:00:03.22 for the reduction.
% 3.47/3.65
% 3.47/3.65
% 3.47/3.65 Here is a proof with depth 10, length 60 :
% 3.47/3.65 % SZS output start Refutation
% See solution above
% 3.47/3.65 Formulae used in the proof : single_axiom prove_these_axioms_3
% 3.47/3.69
%------------------------------------------------------------------------------