TSTP Solution File: BOO072-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO072-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 7.12s 7.30s
% Output : Refutation 7.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 2
% Syntax : Number of clauses : 53 ( 53 unt; 0 nHn; 53 RR)
% Number of literals : 53 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 21 ( 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(add(inverse(add(inverse(add(u,v)),w)),inverse(add(u,inverse(add(inverse(w),inverse(add(w,x)))))))),w),
file('BOO072-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(add(a,b),add(b,a)),
file('BOO072-1.p',unknown),
[] ).
cnf(4,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(6,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(7,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(18,plain,
equal(inverse(add(inverse(add(u,inverse(u))),u)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(22,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(48,plain,
equal(inverse(add(inverse(add(u,v)),inverse(add(inverse(add(w,u)),inverse(add(inverse(v),inverse(add(v,x)))))))),v),
inference(spr,[status(thm),theory(equality)],[1,6]),
[iquote('0:SpR:1.0,6.0')] ).
cnf(61,plain,
equal(inverse(add(inverse(add(inverse(add(u,v)),w)),inverse(add(u,w)))),w),
inference(spr,[status(thm),theory(equality)],[22,1]),
[iquote('0:SpR:22.0,1.0')] ).
cnf(67,plain,
equal(inverse(add(inverse(u),inverse(add(u,u)))),u),
inference(spr,[status(thm),theory(equality)],[22]),
[iquote('0:SpR:22.0,22.0')] ).
cnf(86,plain,
equal(inverse(add(add(u,v),inverse(add(u,inverse(add(inverse(inverse(add(add(u,v),add(u,v)))),inverse(add(inverse(add(add(u,v),add(u,v))),w)))))))),inverse(add(add(u,v),add(u,v)))),
inference(spr,[status(thm),theory(equality)],[67,1]),
[iquote('0:SpR:67.0,1.0')] ).
cnf(123,plain,
equal(inverse(add(inverse(add(u,v)),inverse(add(inverse(u),v)))),v),
inference(spr,[status(thm),theory(equality)],[22,61]),
[iquote('0:SpR:22.0,61.0')] ).
cnf(128,plain,
equal(inverse(add(add(u,v),inverse(add(u,inverse(add(add(u,v),inverse(add(inverse(add(u,v)),inverse(add(add(u,v),w)))))))))),inverse(add(add(u,v),inverse(add(inverse(add(u,v)),inverse(add(add(u,v),w))))))),
inference(spr,[status(thm),theory(equality)],[22,61]),
[iquote('0:SpR:22.0,61.0')] ).
cnf(133,plain,
equal(inverse(add(inverse(add(u,v)),inverse(add(inverse(add(w,u)),v)))),v),
inference(spr,[status(thm),theory(equality)],[123,61]),
[iquote('0:SpR:123.0,61.0')] ).
cnf(138,plain,
equal(inverse(add(u,inverse(add(v,inverse(add(inverse(v),u)))))),inverse(add(inverse(v),u))),
inference(spr,[status(thm),theory(equality)],[123,61]),
[iquote('0:SpR:123.0,61.0')] ).
cnf(157,plain,
equal(inverse(add(inverse(add(add(u,inverse(u)),u)),inverse(u))),u),
inference(spr,[status(thm),theory(equality)],[18,123]),
[iquote('0:SpR:18.0,123.0')] ).
cnf(238,plain,
equal(inverse(add(u,inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(inverse(add(inverse(u),inverse(add(u,v)))))),w)),inverse(add(inverse(u),inverse(add(u,v)))))),x)),inverse(inverse(add(inverse(u),inverse(add(u,v))))))),y)),inverse(add(inverse(inverse(inverse(add(inverse(u),inverse(add(u,v)))))),inverse(add(inverse(inverse(add(inverse(u),inverse(add(u,v))))),z)))))))),inverse(inverse(add(inverse(u),inverse(add(u,v)))))),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(264,plain,
equal(inverse(add(u,inverse(add(add(u,inverse(u)),inverse(u))))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[157,61]),
[iquote('0:SpR:157.0,61.0')] ).
cnf(295,plain,
equal(inverse(add(inverse(add(inverse(u),v)),inverse(add(u,v)))),v),
inference(spr,[status(thm),theory(equality)],[264,61]),
[iquote('0:SpR:264.0,61.0')] ).
cnf(296,plain,
equal(inverse(add(inverse(u),inverse(add(u,inverse(add(inverse(u),inverse(u))))))),u),
inference(spr,[status(thm),theory(equality)],[264,22]),
[iquote('0:SpR:264.0,22.0')] ).
cnf(335,plain,
equal(inverse(add(inverse(u),inverse(u))),u),
inference(rew,[status(thm),theory(equality)],[138,296]),
[iquote('0:Rew:138.0,296.0')] ).
cnf(347,plain,
equal(inverse(add(inverse(add(inverse(add(inverse(u),v)),inverse(u))),u)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[335,61]),
[iquote('0:SpR:335.0,61.0')] ).
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(372,plain,
equal(add(inverse(add(inverse(add(u,v)),w)),inverse(add(u,w))),inverse(add(w,w))),
inference(spr,[status(thm),theory(equality)],[61,335]),
[iquote('0:SpR:61.0,335.0')] ).
cnf(373,plain,
equal(add(inverse(add(u,inverse(u))),u),inverse(add(inverse(u),inverse(u)))),
inference(spr,[status(thm),theory(equality)],[18,335]),
[iquote('0:SpR:18.0,335.0')] ).
cnf(375,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)],[22,335]),
[iquote('0:SpR:22.0,335.0')] ).
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(392,plain,
equal(inverse(add(add(u,v),inverse(add(u,inverse(add(add(u,v),inverse(add(inverse(add(add(u,v),add(u,v))),w)))))))),inverse(add(add(u,v),add(u,v)))),
inference(rew,[status(thm),theory(equality)],[391,86]),
[iquote('0:Rew:391.0,86.0')] ).
cnf(403,plain,
equal(add(inverse(add(u,inverse(u))),u),u),
inference(rew,[status(thm),theory(equality)],[391,373,366]),
[iquote('0:Rew:391.0,373.0,366.0,373.0')] ).
cnf(857,plain,
equal(inverse(add(inverse(add(inverse(add(u,v)),u)),inverse(add(u,v)))),u),
inference(spr,[status(thm),theory(equality)],[295,48]),
[iquote('0:SpR:295.0,48.0')] ).
cnf(1853,plain,
equal(inverse(add(inverse(add(inverse(u),u)),inverse(u))),u),
inference(spr,[status(thm),theory(equality)],[403,133]),
[iquote('0:SpR:403.0,133.0')] ).
cnf(2109,plain,
equal(inverse(add(u,u)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[1853,347]),
[iquote('0:SpR:1853.0,347.0')] ).
cnf(2180,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[2109,391]),
[iquote('0:Rew:2109.0,391.0')] ).
cnf(2202,plain,
equal(inverse(add(add(u,v),inverse(add(u,inverse(add(add(u,v),inverse(add(inverse(add(u,v)),w)))))))),inverse(add(u,v))),
inference(rew,[status(thm),theory(equality)],[2109,392]),
[iquote('0:Rew:2109.0,392.0')] ).
cnf(2210,plain,
equal(add(inverse(u),inverse(add(u,inverse(add(inverse(u),inverse(add(u,v))))))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[2109,375]),
[iquote('0:Rew:2109.0,375.0')] ).
cnf(2226,plain,
equal(add(inverse(add(inverse(add(u,v)),w)),inverse(add(u,w))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[2109,372]),
[iquote('0:Rew:2109.0,372.0')] ).
cnf(2369,plain,
equal(inverse(add(u,inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(u),inverse(add(u,v)))),w)),inverse(add(inverse(u),inverse(add(u,v)))))),x)),inverse(inverse(add(inverse(u),inverse(add(u,v))))))),y)),inverse(add(inverse(add(inverse(u),inverse(add(u,v)))),inverse(add(inverse(inverse(add(inverse(u),inverse(add(u,v))))),z)))))))),inverse(inverse(add(inverse(u),inverse(add(u,v)))))),
inference(rew,[status(thm),theory(equality)],[2180,238]),
[iquote('0:Rew:2180.0,238.0')] ).
cnf(2770,plain,
equal(inverse(add(add(u,v),inverse(add(inverse(add(u,v)),inverse(add(add(u,v),w)))))),inverse(add(u,v))),
inference(rew,[status(thm),theory(equality)],[2202,128]),
[iquote('0:Rew:2202.0,128.0')] ).
cnf(2976,plain,
equal(inverse(add(u,inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(u),inverse(add(u,v)))),w)),inverse(add(inverse(u),inverse(add(u,v)))))),x)),add(inverse(u),inverse(add(u,v))))),y)),inverse(add(inverse(add(inverse(u),inverse(add(u,v)))),inverse(add(add(inverse(u),inverse(add(u,v))),z)))))))),add(inverse(u),inverse(add(u,v)))),
inference(rew,[status(thm),theory(equality)],[2180,2369]),
[iquote('0:Rew:2180.0,2369.0')] ).
cnf(3018,plain,
equal(add(inverse(add(inverse(u),v)),inverse(add(u,v))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[295,2180]),
[iquote('0:SpR:295.0,2180.0')] ).
cnf(3019,plain,
equal(add(inverse(add(inverse(add(inverse(u),v)),inverse(u))),u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[347,2180]),
[iquote('0:SpR:347.0,2180.0')] ).
cnf(3105,plain,
equal(add(inverse(add(inverse(add(inverse(u),v)),inverse(u))),u),u),
inference(rew,[status(thm),theory(equality)],[2180,3019]),
[iquote('0:Rew:2180.0,3019.0')] ).
cnf(4607,plain,
equal(add(u,add(u,v)),add(u,v)),
inference(spr,[status(thm),theory(equality)],[857,3105]),
[iquote('0:SpR:857.0,3105.0')] ).
cnf(6468,plain,
equal(add(inverse(inverse(u)),inverse(add(inverse(v),inverse(add(v,u))))),inverse(inverse(add(v,u)))),
inference(spr,[status(thm),theory(equality)],[3018,2226]),
[iquote('0:SpR:3018.0,2226.0')] ).
cnf(6501,plain,
equal(add(u,inverse(add(inverse(v),inverse(add(v,u))))),add(v,u)),
inference(rew,[status(thm),theory(equality)],[2180,6468]),
[iquote('0:Rew:2180.0,6468.0,2180.0,6468.0')] ).
cnf(7576,plain,
equal(inverse(add(u,inverse(add(inverse(inverse(add(inverse(u),inverse(add(u,v))))),inverse(add(inverse(add(inverse(u),inverse(add(u,v)))),inverse(add(add(inverse(u),inverse(add(u,v))),w)))))))),add(inverse(u),inverse(add(u,v)))),
inference(spr,[status(thm),theory(equality)],[2226,2976]),
[iquote('0:SpR:2226.0,2976.0')] ).
cnf(7607,plain,
equal(inverse(add(u,inverse(add(add(inverse(u),inverse(add(u,v))),inverse(add(inverse(add(inverse(u),inverse(add(u,v)))),inverse(add(add(inverse(u),inverse(add(u,v))),w)))))))),add(inverse(u),inverse(add(u,v)))),
inference(rew,[status(thm),theory(equality)],[2180,7576]),
[iquote('0:Rew:2180.0,7576.0')] ).
cnf(7608,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)],[2770,7607]),
[iquote('0:Rew:2770.0,7607.0')] ).
cnf(7613,plain,
equal(add(inverse(u),add(inverse(u),inverse(add(u,v)))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[7608,2210]),
[iquote('0:Rew:7608.0,2210.0')] ).
cnf(7616,plain,
equal(add(inverse(u),inverse(add(u,v))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[4607,7613]),
[iquote('0:Rew:4607.0,7613.0')] ).
cnf(7619,plain,
equal(add(u,inverse(inverse(v))),add(v,u)),
inference(rew,[status(thm),theory(equality)],[7616,6501]),
[iquote('0:Rew:7616.0,6501.0')] ).
cnf(7827,plain,
equal(add(u,v),add(v,u)),
inference(rew,[status(thm),theory(equality)],[2180,7619]),
[iquote('0:Rew:2180.0,7619.0')] ).
cnf(7828,plain,
$false,
inference(unc,[status(thm)],[7827,2]),
[iquote('0:UnC:7827.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : BOO072-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jun 1 20:23:40 EDT 2022
% 0.14/0.35 % CPUTime :
% 7.12/7.30
% 7.12/7.30 SPASS V 3.9
% 7.12/7.30 SPASS beiseite: Proof found.
% 7.12/7.30 % SZS status Theorem
% 7.12/7.30 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.12/7.30 SPASS derived 5520 clauses, backtracked 0 clauses, performed 0 splits and kept 1642 clauses.
% 7.12/7.30 SPASS allocated 95379 KBytes.
% 7.12/7.30 SPASS spent 0:00:06.76 on the problem.
% 7.12/7.30 0:00:00.03 for the input.
% 7.12/7.30 0:00:00.00 for the FLOTTER CNF translation.
% 7.12/7.30 0:00:00.07 for inferences.
% 7.12/7.30 0:00:00.00 for the backtracking.
% 7.12/7.30 0:00:06.63 for the reduction.
% 7.12/7.30
% 7.12/7.30
% 7.12/7.30 Here is a proof with depth 11, length 53 :
% 7.12/7.30 % SZS output start Refutation
% See solution above
% 7.12/7.30 Formulae used in the proof : dn1 huntinton_1
% 7.12/7.30
%------------------------------------------------------------------------------