TSTP Solution File: GRP433-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP433-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 11:47:27 EDT 2022
% Result : Unsatisfiable 3.26s 3.44s
% Output : Refutation 3.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 40 RR)
% Number of literals : 40 ( 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 : 9 ( 9 usr; 7 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('GRP433-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP433-1.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(215,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(216,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)],[414,215]),
[iquote('0:Rew:414.0,215.0')] ).
cnf(513,plain,
equal(inverse(multiply(inverse(inverse(multiply(u,inverse(u)))),v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[414,216]),
[iquote('0:Rew:414.0,216.0')] ).
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(536,plain,
equal(multiply(u,inverse(u)),multiply(inverse(inverse(inverse(multiply(multiply(v,inverse(v)),w)))),w)),
inference(spr,[status(thm),theory(equality)],[512,10]),
[iquote('0:SpR:512.0,10.0')] ).
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(1780,plain,
equal(multiply(u,inverse(u)),multiply(inverse(inverse(inverse(v))),v)),
inference(rew,[status(thm),theory(equality)],[1617,536]),
[iquote('0:Rew:1617.0,536.0')] ).
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(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(2816,plain,
equal(multiply(u,inverse(u)),multiply(inverse(v),v)),
inference(rew,[status(thm),theory(equality)],[2813,1780]),
[iquote('0:Rew:2813.0,1780.0')] ).
cnf(3784,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[2816]),
[iquote('0:SpR:2816.0,2816.0')] ).
cnf(3797,plain,
$false,
inference(unc,[status(thm)],[3784,2]),
[iquote('0:UnC:3784.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP433-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n016.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 15:49:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.26/3.44
% 3.26/3.44 SPASS V 3.9
% 3.26/3.44 SPASS beiseite: Proof found.
% 3.26/3.44 % SZS status Theorem
% 3.26/3.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.26/3.44 SPASS derived 2730 clauses, backtracked 0 clauses, performed 0 splits and kept 1104 clauses.
% 3.26/3.44 SPASS allocated 71526 KBytes.
% 3.26/3.44 SPASS spent 0:00:03.06 on the problem.
% 3.26/3.44 0:00:00.03 for the input.
% 3.26/3.44 0:00:00.00 for the FLOTTER CNF translation.
% 3.26/3.44 0:00:00.03 for inferences.
% 3.26/3.44 0:00:00.00 for the backtracking.
% 3.26/3.44 0:00:02.97 for the reduction.
% 3.26/3.44
% 3.26/3.44
% 3.26/3.44 Here is a proof with depth 8, length 40 :
% 3.26/3.44 % SZS output start Refutation
% See solution above
% 3.26/3.44 Formulae used in the proof : single_axiom prove_these_axioms_1
% 3.26/3.44
%------------------------------------------------------------------------------