TSTP Solution File: BOO074-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO074-1 : 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 : Thu Jul 14 23:49:33 EDT 2022
% Result : Unsatisfiable 2.15s 2.34s
% Output : Refutation 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of clauses : 51 ( 51 unt; 0 nHn; 51 RR)
% Number of literals : 51 ( 0 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 15 ( 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(add(inverse(add(inverse(add(u,v)),w)),inverse(add(u,inverse(add(inverse(w),inverse(add(w,x)))))))),w),
file('BOO074-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(add(inverse(add(inverse(a),b)),inverse(add(inverse(a),inverse(b)))),a),
file('BOO074-1.p',unknown),
[] ).
cnf(3,plain,
equal(inverse(add(u,inverse(add(inverse(add(v,w)),inverse(add(inverse(inverse(add(v,inverse(add(inverse(u),inverse(add(u,x))))))),inverse(add(inverse(add(v,inverse(add(inverse(u),inverse(add(u,x)))))),y)))))))),inverse(add(v,inverse(add(inverse(u),inverse(add(u,x))))))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(6,plain,
equal(inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(u)),v)),u)),w)),inverse(u))),u)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(7,plain,
equal(inverse(add(inverse(add(u,v)),inverse(add(inverse(add(inverse(add(w,x)),u)),inverse(add(inverse(v),inverse(add(v,y)))))))),v),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(18,plain,
equal(inverse(add(inverse(add(u,inverse(u))),u)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[1,6]),
[iquote('0:SpR:1.0,6.0')] ).
cnf(19,plain,
equal(inverse(add(inverse(u),inverse(add(u,inverse(add(inverse(u),inverse(add(u,v)))))))),u),
inference(spr,[status(thm),theory(equality)],[18,1]),
[iquote('0:SpR:18.0,1.0')] ).
cnf(52,plain,
equal(inverse(add(inverse(add(inverse(add(u,inverse(add(inverse(v),inverse(add(v,w)))))),x)),inverse(add(v,inverse(add(inverse(x),inverse(add(x,y)))))))),x),
inference(spr,[status(thm),theory(equality)],[1,7]),
[iquote('0:SpR:1.0,7.0')] ).
cnf(56,plain,
equal(inverse(add(inverse(add(inverse(inverse(add(inverse(u),inverse(add(u,v))))),u)),inverse(inverse(add(inverse(u),inverse(add(u,v))))))),u),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(60,plain,
equal(inverse(add(inverse(add(inverse(add(u,v)),w)),inverse(add(u,w)))),w),
inference(spr,[status(thm),theory(equality)],[19,1]),
[iquote('0:SpR:19.0,1.0')] ).
cnf(61,plain,
equal(inverse(add(inverse(u),inverse(add(u,u)))),u),
inference(spr,[status(thm),theory(equality)],[19]),
[iquote('0:SpR:19.0,19.0')] ).
cnf(120,plain,
equal(inverse(add(inverse(add(u,v)),inverse(add(inverse(u),v)))),v),
inference(spr,[status(thm),theory(equality)],[19,60]),
[iquote('0:SpR:19.0,60.0')] ).
cnf(131,plain,
equal(inverse(add(u,inverse(add(v,inverse(add(inverse(v),u)))))),inverse(add(inverse(v),u))),
inference(spr,[status(thm),theory(equality)],[120,60]),
[iquote('0:SpR:120.0,60.0')] ).
cnf(156,plain,
equal(inverse(add(inverse(add(add(u,inverse(u)),u)),inverse(u))),u),
inference(spr,[status(thm),theory(equality)],[18,120]),
[iquote('0:SpR:18.0,120.0')] ).
cnf(255,plain,
equal(inverse(add(u,inverse(add(add(u,inverse(u)),inverse(u))))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[156,60]),
[iquote('0:SpR:156.0,60.0')] ).
cnf(303,plain,
equal(inverse(add(inverse(u),inverse(add(u,inverse(add(inverse(u),inverse(u))))))),u),
inference(spr,[status(thm),theory(equality)],[255,19]),
[iquote('0:SpR:255.0,19.0')] ).
cnf(307,plain,
equal(inverse(add(u,inverse(add(inverse(v),inverse(add(inverse(inverse(add(v,inverse(add(inverse(u),inverse(add(u,w))))))),inverse(add(inverse(add(v,inverse(add(inverse(u),inverse(add(u,w)))))),x)))))))),inverse(add(v,inverse(add(inverse(u),inverse(add(u,w))))))),
inference(spr,[status(thm),theory(equality)],[255,3]),
[iquote('0:SpR:255.0,3.0')] ).
cnf(335,plain,
equal(inverse(add(inverse(u),inverse(u))),u),
inference(rew,[status(thm),theory(equality)],[131,303]),
[iquote('0:Rew:131.0,303.0')] ).
cnf(353,plain,
equal(inverse(add(inverse(add(inverse(add(inverse(u),v)),inverse(u))),u)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[335,60]),
[iquote('0:SpR:335.0,60.0')] ).
cnf(366,plain,
equal(add(inverse(u),inverse(u)),inverse(add(u,u))),
inference(spr,[status(thm),theory(equality)],[335]),
[iquote('0:SpR:335.0,335.0')] ).
cnf(367,plain,
equal(add(inverse(u),inverse(add(u,inverse(add(inverse(u),inverse(add(u,v))))))),inverse(add(u,u))),
inference(spr,[status(thm),theory(equality)],[19,335]),
[iquote('0:SpR:19.0,335.0')] ).
cnf(368,plain,
equal(add(inverse(u),inverse(add(u,u))),inverse(add(u,u))),
inference(spr,[status(thm),theory(equality)],[61,335]),
[iquote('0:SpR:61.0,335.0')] ).
cnf(369,plain,
equal(add(inverse(add(u,v)),inverse(add(inverse(u),v))),inverse(add(v,v))),
inference(spr,[status(thm),theory(equality)],[120,335]),
[iquote('0:SpR:120.0,335.0')] ).
cnf(391,plain,
equal(inverse(inverse(add(u,u))),u),
inference(rew,[status(thm),theory(equality)],[366,335]),
[iquote('0:Rew:366.0,335.0')] ).
cnf(765,plain,
equal(inverse(add(inverse(add(inverse(inverse(inverse(add(u,u)))),u)),inverse(inverse(inverse(add(u,u)))))),u),
inference(spr,[status(thm),theory(equality)],[368,56]),
[iquote('0:SpR:368.0,56.0')] ).
cnf(778,plain,
equal(inverse(add(inverse(add(inverse(u),u)),inverse(u))),u),
inference(rew,[status(thm),theory(equality)],[391,765]),
[iquote('0:Rew:391.0,765.0')] ).
cnf(1727,plain,
equal(inverse(add(u,inverse(add(inverse(u),inverse(add(u,v)))))),inverse(inverse(add(inverse(u),inverse(add(u,v)))))),
inference(spr,[status(thm),theory(equality)],[56,353]),
[iquote('0:SpR:56.0,353.0')] ).
cnf(1728,plain,
equal(inverse(add(u,u)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[778,353]),
[iquote('0:SpR:778.0,353.0')] ).
cnf(1729,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[1728,391]),
[iquote('0:Rew:1728.0,391.0')] ).
cnf(1754,plain,
equal(add(inverse(u),inverse(add(u,inverse(add(inverse(u),inverse(add(u,v))))))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[1728,367]),
[iquote('0:Rew:1728.0,367.0')] ).
cnf(1775,plain,
equal(add(inverse(add(u,v)),inverse(add(inverse(u),v))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[1728,369]),
[iquote('0:Rew:1728.0,369.0')] ).
cnf(2094,plain,
equal(inverse(add(u,inverse(add(inverse(v),inverse(add(add(v,inverse(add(inverse(u),inverse(add(u,w))))),inverse(add(inverse(add(v,inverse(add(inverse(u),inverse(add(u,w)))))),x)))))))),inverse(add(v,inverse(add(inverse(u),inverse(add(u,w))))))),
inference(rew,[status(thm),theory(equality)],[1729,307]),
[iquote('0:Rew:1729.0,307.0')] ).
cnf(2191,plain,
equal(inverse(add(u,inverse(add(inverse(u),inverse(add(u,v)))))),add(inverse(u),inverse(add(u,v)))),
inference(rew,[status(thm),theory(equality)],[1729,1727]),
[iquote('0:Rew:1729.0,1727.0')] ).
cnf(2196,plain,
equal(add(inverse(u),add(inverse(u),inverse(add(u,v)))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[2191,1754]),
[iquote('0:Rew:2191.0,1754.0')] ).
cnf(2487,plain,
equal(add(inverse(add(inverse(add(inverse(u),v)),inverse(u))),u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[353,1729]),
[iquote('0:SpR:353.0,1729.0')] ).
cnf(2671,plain,
equal(add(inverse(add(inverse(add(inverse(u),v)),inverse(u))),u),u),
inference(rew,[status(thm),theory(equality)],[1729,2487]),
[iquote('0:Rew:1729.0,2487.0')] ).
cnf(3130,plain,
equal(add(u,add(u,inverse(add(inverse(u),v)))),u),
inference(spr,[status(thm),theory(equality)],[1729,2196]),
[iquote('0:SpR:1729.0,2196.0')] ).
cnf(3393,plain,
equal(add(u,add(u,inverse(add(inverse(u),inverse(add(u,v)))))),add(u,inverse(add(inverse(u),inverse(add(u,v)))))),
inference(spr,[status(thm),theory(equality)],[52,2671]),
[iquote('0:SpR:52.0,2671.0')] ).
cnf(3483,plain,
equal(add(u,inverse(add(inverse(u),inverse(add(u,v))))),u),
inference(rew,[status(thm),theory(equality)],[3130,3393]),
[iquote('0:Rew:3130.0,3393.0')] ).
cnf(3485,plain,
equal(add(inverse(u),inverse(add(u,v))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[3483,2191]),
[iquote('0:Rew:3483.0,2191.0')] ).
cnf(3503,plain,
equal(inverse(add(u,inverse(add(inverse(v),inverse(add(add(v,inverse(inverse(u))),inverse(add(inverse(add(v,inverse(inverse(u)))),w)))))))),inverse(add(v,inverse(inverse(u))))),
inference(rew,[status(thm),theory(equality)],[3485,2094]),
[iquote('0:Rew:3485.0,2094.0')] ).
cnf(3795,plain,
equal(inverse(add(u,inverse(add(inverse(v),inverse(add(add(v,u),inverse(add(inverse(add(v,u)),w)))))))),inverse(add(v,u))),
inference(rew,[status(thm),theory(equality)],[1729,3503]),
[iquote('0:Rew:1729.0,3503.0')] ).
cnf(4088,plain,
equal(add(u,inverse(add(inverse(u),v))),u),
inference(spr,[status(thm),theory(equality)],[1729,3485]),
[iquote('0:SpR:1729.0,3485.0')] ).
cnf(4107,plain,
equal(inverse(add(u,inverse(add(inverse(v),inverse(add(v,u)))))),inverse(add(v,u))),
inference(rew,[status(thm),theory(equality)],[4088,3795]),
[iquote('0:Rew:4088.0,3795.0')] ).
cnf(4146,plain,
equal(inverse(add(u,inverse(v))),inverse(add(inverse(v),u))),
inference(rew,[status(thm),theory(equality)],[4088,131]),
[iquote('0:Rew:4088.0,131.0')] ).
cnf(4153,plain,
~ equal(add(inverse(add(b,inverse(a))),inverse(add(inverse(a),inverse(b)))),a),
inference(rew,[status(thm),theory(equality)],[4146,2]),
[iquote('0:Rew:4146.0,2.0')] ).
cnf(4249,plain,
equal(inverse(add(u,v)),inverse(add(v,u))),
inference(rew,[status(thm),theory(equality)],[1729,4107,3485]),
[iquote('0:Rew:1729.0,4107.0,3485.0,4107.0')] ).
cnf(4396,plain,
equal(add(inverse(add(u,v)),inverse(add(v,inverse(u)))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[4249,1775]),
[iquote('0:SpR:4249.0,1775.0')] ).
cnf(4473,plain,
~ equal(inverse(inverse(a)),a),
inference(rew,[status(thm),theory(equality)],[4396,4153]),
[iquote('0:Rew:4396.0,4153.0')] ).
cnf(4474,plain,
~ equal(a,a),
inference(rew,[status(thm),theory(equality)],[1729,4473]),
[iquote('0:Rew:1729.0,4473.0')] ).
cnf(4475,plain,
$false,
inference(obv,[status(thm),theory(equality)],[4474]),
[iquote('0:Obv:4474.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : BOO074-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 : Wed Jun 1 22:31:42 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.15/2.34
% 2.15/2.34 SPASS V 3.9
% 2.15/2.34 SPASS beiseite: Proof found.
% 2.15/2.34 % SZS status Theorem
% 2.15/2.34 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.15/2.34 SPASS derived 3025 clauses, backtracked 0 clauses, performed 0 splits and kept 1184 clauses.
% 2.15/2.34 SPASS allocated 75880 KBytes.
% 2.15/2.34 SPASS spent 0:00:01.94 on the problem.
% 2.15/2.34 0:00:00.03 for the input.
% 2.15/2.34 0:00:00.00 for the FLOTTER CNF translation.
% 2.15/2.34 0:00:00.03 for inferences.
% 2.15/2.34 0:00:00.00 for the backtracking.
% 2.15/2.34 0:00:01.85 for the reduction.
% 2.15/2.34
% 2.15/2.34
% 2.15/2.34 Here is a proof with depth 11, length 51 :
% 2.15/2.34 % SZS output start Refutation
% See solution above
% 2.15/2.34 Formulae used in the proof : dn1 huntinton_3
% 2.15/2.34
%------------------------------------------------------------------------------