%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP551-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 11:48:00 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of clauses : 45 ( 45 unt; 0 nHn; 45 RR)
% Number of literals : 45 ( 0 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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(divide(identity,u),divide(divide(divide(v,u),w),v)),w),
file('GRP551-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(identity,v)),multiply(u,v)),
file('GRP551-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(identity,u),inverse(u)),
file('GRP551-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP551-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP551-1.p',unknown),
[] ).
cnf(6,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(7,plain,
equal(divide(inverse(u),divide(divide(divide(v,u),w),v)),w),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0')] ).
cnf(9,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[6,3]),
[iquote('0:SpR:6.0,3.0')] ).
cnf(15,plain,
equal(divide(u,identity),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[9,6]),
[iquote('0:SpR:9.0,6.0')] ).
cnf(28,plain,
equal(divide(inverse(u),divide(divide(identity,v),u)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(30,plain,
equal(divide(inverse(inverse(u)),divide(divide(multiply(v,u),w),v)),w),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(32,plain,
equal(divide(inverse(u),divide(identity,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(37,plain,
equal(divide(identity,divide(divide(divide(u,identity),v),u)),v),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(38,plain,
equal(divide(inverse(u),divide(inverse(v),u)),v),
inference(rew,[status(thm),theory(equality)],[3,28]),
[iquote('0:Rew:3.0,28.0')] ).
cnf(39,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(rew,[status(thm),theory(equality)],[6,32,3]),
[iquote('0:Rew:6.0,32.0,3.0,32.0')] ).
cnf(42,plain,
equal(inverse(divide(divide(multiply(u,identity),v),u)),v),
inference(rew,[status(thm),theory(equality)],[3,37,15]),
[iquote('0:Rew:3.0,37.0,15.0,37.0')] ).
cnf(48,plain,
equal(divide(u,identity),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[9,39]),
[iquote('0:SpR:9.0,39.0')] ).
cnf(49,plain,
equal(multiply(u,identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[15,48,13]),
[iquote('0:Rew:15.0,48.0,13.0,48.0')] ).
cnf(50,plain,
equal(divide(u,identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[49,15]),
[iquote('0:Rew:49.0,15.0')] ).
cnf(51,plain,
equal(inverse(divide(divide(inverse(inverse(u)),v),u)),v),
inference(rew,[status(thm),theory(equality)],[49,42]),
[iquote('0:Rew:49.0,42.0')] ).
cnf(56,plain,
equal(inverse(inverse(inverse(u))),divide(identity,u)),
inference(spr,[status(thm),theory(equality)],[49,39]),
[iquote('0:SpR:49.0,39.0')] ).
cnf(57,plain,
equal(inverse(inverse(inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[3,56]),
[iquote('0:Rew:3.0,56.0')] ).
cnf(94,plain,
equal(divide(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[4,38]),
[iquote('0:SpR:4.0,38.0')] ).
cnf(95,plain,
equal(divide(inverse(inverse(u)),multiply(inverse(v),u)),v),
inference(spr,[status(thm),theory(equality)],[6,38]),
[iquote('0:SpR:6.0,38.0')] ).
cnf(100,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[57,94,50]),
[iquote('0:Rew:57.0,94.0,50.0,94.0')] ).
cnf(104,plain,
equal(divide(u,divide(divide(multiply(v,u),w),v)),w),
inference(rew,[status(thm),theory(equality)],[100,30]),
[iquote('0:Rew:100.0,30.0')] ).
cnf(105,plain,
equal(inverse(divide(divide(u,v),u)),v),
inference(rew,[status(thm),theory(equality)],[100,51]),
[iquote('0:Rew:100.0,51.0')] ).
cnf(111,plain,
equal(divide(inverse(inverse(u)),divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[39,95]),
[iquote('0:Rew:39.0,95.0')] ).
cnf(112,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[100,111]),
[iquote('0:Rew:100.0,111.0')] ).
cnf(118,plain,
equal(divide(u,inverse(v)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[100,39]),
[iquote('0:SpR:100.0,39.0')] ).
cnf(126,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[6,118]),
[iquote('0:Rew:6.0,118.0')] ).
cnf(127,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[126,5]),
[iquote('0:Rew:126.0,5.0')] ).
cnf(152,plain,
equal(divide(u,multiply(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[6,112]),
[iquote('0:SpR:6.0,112.0')] ).
cnf(179,plain,
equal(divide(divide(u,v),u),inverse(v)),
inference(spr,[status(thm),theory(equality)],[105,100]),
[iquote('0:SpR:105.0,100.0')] ).
cnf(233,plain,
equal(divide(u,divide(inverse(v),w)),multiply(multiply(w,u),v)),
inference(spr,[status(thm),theory(equality)],[152,104]),
[iquote('0:SpR:152.0,104.0')] ).
cnf(291,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[152,179]),
[iquote('0:SpR:152.0,179.0')] ).
cnf(302,plain,
equal(divide(u,inverse(multiply(v,w))),multiply(multiply(v,u),w)),
inference(rew,[status(thm),theory(equality)],[291,233]),
[iquote('0:Rew:291.0,233.0')] ).
cnf(309,plain,
equal(multiply(multiply(u,v),w),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[6,302]),
[iquote('0:Rew:6.0,302.0')] ).
cnf(586,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[309,126]),
[iquote('0:SpR:309.0,126.0')] ).
cnf(598,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[126,309]),
[iquote('0:SpR:126.0,309.0')] ).
cnf(607,plain,
~ equal(multiply(b3,multiply(a3,c3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[586,127]),
[iquote('0:Rew:586.0,127.0')] ).
cnf(608,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[309,598]),
[iquote('0:Rew:309.0,598.0')] ).
cnf(622,plain,
~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[608,607]),
[iquote('0:Rew:608.0,607.0')] ).
cnf(623,plain,
$false,
inference(obv,[status(thm),theory(equality)],[622]),
[iquote('0:Obv:622.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP551-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 19:19:05 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.20/0.45
% 0.20/0.45 SPASS V 3.9
% 0.20/0.45 SPASS beiseite: Proof found.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 SPASS derived 350 clauses, backtracked 0 clauses, performed 0 splits and kept 102 clauses.
% 0.20/0.45 SPASS allocated 63642 KBytes.
% 0.20/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.20/0.45 0:00:00.04 for the input.
% 0.20/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.45 0:00:00.00 for inferences.
% 0.20/0.45 0:00:00.00 for the backtracking.
% 0.20/0.45 0:00:00.03 for the reduction.
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 Here is a proof with depth 5, length 45 :
% 0.20/0.45 % SZS output start Refutation
% See solution above
% 0.20/0.45 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_3
% 0.20/0.45
%------------------------------------------------------------------------------