TSTP Solution File: GRP450-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP450-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 11:47:32 EDT 2022
% Result : Unsatisfiable 0.39s 0.59s
% Output : Refutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of clauses : 56 ( 56 unt; 0 nHn; 56 RR)
% Number of literals : 56 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(u,divide(divide(divide(divide(v,v),v),w),divide(divide(divide(v,v),u),w))),v),
file('GRP450-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP450-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP450-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP450-1.p',unknown),
[] ).
cnf(5,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(6,plain,
equal(divide(u,divide(divide(inverse(v),w),divide(inverse(u),w))),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0,3.0,1.0')] ).
cnf(7,plain,
equal(divide(inverse(divide(u,u)),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(11,plain,
equal(multiply(divide(u,u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(14,plain,
equal(multiply(inverse(divide(u,u)),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(58,plain,
equal(divide(u,divide(divide(inverse(v),divide(divide(inverse(w),x),divide(inverse(inverse(u)),x))),w)),v),
inference(spr,[status(thm),theory(equality)],[6]),
[iquote('0:SpR:6.0,6.0')] ).
cnf(61,plain,
equal(divide(divide(u,u),divide(divide(inverse(v),w),inverse(w))),v),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(68,plain,
equal(divide(u,inverse(divide(inverse(u),inverse(v)))),v),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(69,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[5,68]),
[iquote('0:Rew:5.0,68.0,5.0,68.0')] ).
cnf(70,plain,
equal(inverse(multiply(divide(inverse(u),v),v)),u),
inference(rew,[status(thm),theory(equality)],[3,61,5]),
[iquote('0:Rew:3.0,61.0,5.0,61.0')] ).
cnf(84,plain,
equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[69]),
[iquote('0:SpR:69.0,69.0')] ).
cnf(86,plain,
equal(multiply(divide(u,u),inverse(inverse(v))),v),
inference(spr,[status(thm),theory(equality)],[14,69]),
[iquote('0:SpR:14.0,69.0')] ).
cnf(92,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[11,86]),
[iquote('0:Rew:11.0,86.0')] ).
cnf(100,plain,
equal(multiply(u,inverse(inverse(inverse(v)))),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[92,5]),
[iquote('0:SpR:92.0,5.0')] ).
cnf(105,plain,
equal(multiply(inverse(inverse(inverse(u))),multiply(u,v)),v),
inference(spr,[status(thm),theory(equality)],[92,69]),
[iquote('0:SpR:92.0,69.0')] ).
cnf(110,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[84,105]),
[iquote('0:Rew:84.0,105.0')] ).
cnf(137,plain,
equal(inverse(multiply(inverse(u),u)),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[7,70]),
[iquote('0:SpR:7.0,70.0')] ).
cnf(188,plain,
equal(divide(u,divide(v,v)),multiply(u,multiply(inverse(w),w))),
inference(spr,[status(thm),theory(equality)],[137,5]),
[iquote('0:SpR:137.0,5.0')] ).
cnf(197,plain,
equal(divide(u,u),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[137]),
[iquote('0:SpR:137.0,137.0')] ).
cnf(210,plain,
equal(inverse(multiply(u,inverse(inverse(inverse(u))))),divide(v,v)),
inference(spr,[status(thm),theory(equality)],[92,137]),
[iquote('0:SpR:92.0,137.0')] ).
cnf(213,plain,
equal(inverse(divide(u,u)),divide(v,v)),
inference(rew,[status(thm),theory(equality)],[100,210]),
[iquote('0:Rew:100.0,210.0')] ).
cnf(229,plain,
equal(divide(u,u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[197,5]),
[iquote('0:SpR:197.0,5.0')] ).
cnf(251,plain,
equal(divide(u,divide(v,v)),multiply(u,divide(w,w))),
inference(spr,[status(thm),theory(equality)],[213,5]),
[iquote('0:SpR:213.0,5.0')] ).
cnf(318,plain,
equal(divide(u,divide(divide(inverse(v),divide(multiply(inverse(w),x),divide(inverse(inverse(u)),inverse(x)))),w)),v),
inference(spr,[status(thm),theory(equality)],[5,58]),
[iquote('0:SpR:5.0,58.0')] ).
cnf(327,plain,
equal(divide(u,divide(divide(inverse(v),inverse(divide(w,w))),inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[213,58]),
[iquote('0:SpR:213.0,58.0')] ).
cnf(339,plain,
equal(divide(u,multiply(multiply(inverse(v),divide(w,w)),u)),v),
inference(rew,[status(thm),theory(equality)],[5,327]),
[iquote('0:Rew:5.0,327.0,5.0,327.0')] ).
cnf(351,plain,
equal(divide(u,divide(divide(inverse(v),divide(multiply(inverse(w),x),multiply(u,x))),w)),v),
inference(rew,[status(thm),theory(equality)],[84,318,5]),
[iquote('0:Rew:84.0,318.0,5.0,318.0')] ).
cnf(406,plain,
equal(multiply(u,divide(v,v)),u),
inference(spr,[status(thm),theory(equality)],[229,69]),
[iquote('0:SpR:229.0,69.0')] ).
cnf(417,plain,
equal(divide(u,divide(v,v)),u),
inference(rew,[status(thm),theory(equality)],[406,251]),
[iquote('0:Rew:406.0,251.0')] ).
cnf(418,plain,
equal(divide(u,multiply(inverse(v),u)),v),
inference(rew,[status(thm),theory(equality)],[406,339]),
[iquote('0:Rew:406.0,339.0')] ).
cnf(422,plain,
equal(multiply(u,multiply(inverse(v),v)),u),
inference(rew,[status(thm),theory(equality)],[417,188]),
[iquote('0:Rew:417.0,188.0')] ).
cnf(433,plain,
equal(multiply(u,divide(v,v)),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[406,84]),
[iquote('0:SpR:406.0,84.0')] ).
cnf(450,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[406,433]),
[iquote('0:Rew:406.0,433.0')] ).
cnf(478,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(rew,[status(thm),theory(equality)],[450,100]),
[iquote('0:Rew:450.0,100.0')] ).
cnf(586,plain,
equal(divide(u,multiply(v,u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[450,418]),
[iquote('0:SpR:450.0,418.0')] ).
cnf(589,plain,
equal(divide(multiply(u,v),v),u),
inference(spr,[status(thm),theory(equality)],[110,418]),
[iquote('0:SpR:110.0,418.0')] ).
cnf(602,plain,
equal(multiply(multiply(u,inverse(v)),v),u),
inference(spr,[status(thm),theory(equality)],[589,5]),
[iquote('0:SpR:589.0,5.0')] ).
cnf(611,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[478,602]),
[iquote('0:Rew:478.0,602.0')] ).
cnf(915,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[611,586]),
[iquote('0:SpR:611.0,586.0')] ).
cnf(955,plain,
equal(multiply(u,multiply(divide(v,w),divide(w,v))),u),
inference(spr,[status(thm),theory(equality)],[915,422]),
[iquote('0:SpR:915.0,422.0')] ).
cnf(963,plain,
equal(multiply(divide(u,v),multiply(divide(v,u),w)),w),
inference(spr,[status(thm),theory(equality)],[915,69]),
[iquote('0:SpR:915.0,69.0')] ).
cnf(969,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[5,915]),
[iquote('0:SpR:5.0,915.0')] ).
cnf(1000,plain,
equal(divide(u,divide(inverse(multiply(divide(multiply(inverse(v),w),multiply(u,w)),x)),v)),x),
inference(rew,[status(thm),theory(equality)],[969,351]),
[iquote('0:Rew:969.0,351.0')] ).
cnf(1040,plain,
equal(divide(u,inverse(multiply(v,multiply(divide(multiply(inverse(v),w),multiply(u,w)),x)))),x),
inference(rew,[status(thm),theory(equality)],[969,1000]),
[iquote('0:Rew:969.0,1000.0')] ).
cnf(1041,plain,
equal(multiply(u,multiply(v,multiply(divide(multiply(inverse(v),w),multiply(u,w)),x))),x),
inference(rew,[status(thm),theory(equality)],[5,1040]),
[iquote('0:Rew:5.0,1040.0')] ).
cnf(1210,plain,
equal(inverse(multiply(inverse(u),v)),multiply(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[969,5]),
[iquote('0:SpR:969.0,5.0')] ).
cnf(1276,plain,
equal(divide(u,multiply(inverse(v),w)),multiply(u,multiply(inverse(w),v))),
inference(spr,[status(thm),theory(equality)],[1210,5]),
[iquote('0:SpR:1210.0,5.0')] ).
cnf(1796,plain,
equal(multiply(divide(multiply(u,v),multiply(inverse(w),v)),x),multiply(u,multiply(w,x))),
inference(spr,[status(thm),theory(equality)],[963,1041]),
[iquote('0:SpR:963.0,1041.0')] ).
cnf(1799,plain,
equal(divide(multiply(u,v),multiply(inverse(w),v)),multiply(u,w)),
inference(spr,[status(thm),theory(equality)],[955,1041]),
[iquote('0:SpR:955.0,1041.0')] ).
cnf(1804,plain,
equal(multiply(multiply(u,v),multiply(inverse(v),w)),multiply(u,w)),
inference(rew,[status(thm),theory(equality)],[1276,1799]),
[iquote('0:Rew:1276.0,1799.0')] ).
cnf(1831,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[1804,1796,1276]),
[iquote('0:Rew:1804.0,1796.0,1276.0,1796.0')] ).
cnf(1832,plain,
$false,
inference(unc,[status(thm)],[1831,4]),
[iquote('0:UnC:1831.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : GRP450-1 : TPTP v8.1.0. Released v2.6.0.
% 0.05/0.15 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n023.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Tue Jun 14 02:51:36 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.39/0.59
% 0.39/0.59 SPASS V 3.9
% 0.39/0.59 SPASS beiseite: Proof found.
% 0.39/0.59 % SZS status Theorem
% 0.39/0.59 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.59 SPASS derived 1215 clauses, backtracked 0 clauses, performed 0 splits and kept 240 clauses.
% 0.39/0.59 SPASS allocated 64989 KBytes.
% 0.39/0.59 SPASS spent 0:00:00.20 on the problem.
% 0.39/0.59 0:00:00.03 for the input.
% 0.39/0.59 0:00:00.00 for the FLOTTER CNF translation.
% 0.39/0.59 0:00:00.01 for inferences.
% 0.39/0.59 0:00:00.00 for the backtracking.
% 0.39/0.59 0:00:00.13 for the reduction.
% 0.39/0.59
% 0.39/0.59
% 0.39/0.59 Here is a proof with depth 12, length 56 :
% 0.39/0.59 % SZS output start Refutation
% See solution above
% 0.39/0.59 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_3
% 0.39/0.59
%------------------------------------------------------------------------------