%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP489-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 11:47:43 EDT 2022
% Result : Unsatisfiable 0.18s 0.50s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 5
% Syntax : Number of clauses : 67 ( 67 unt; 0 nHn; 67 RR)
% Number of literals : 67 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(u,double_divide(double_divide(double_divide(identity,double_divide(double_divide(u,identity),double_divide(v,w))),v),identity)),w),
file('GRP489-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP489-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP489-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP489-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP489-1.p',unknown),
[] ).
cnf(6,plain,
equal(inverse(double_divide(u,v)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(7,plain,
equal(double_divide(u,multiply(v,double_divide(identity,double_divide(inverse(u),double_divide(v,w))))),w),
inference(rew,[status(thm),theory(equality)],[6,1,3]),
[iquote('0:Rew:6.0,1.0,3.0,1.0,3.0,1.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,6]),
[iquote('0:SpR:4.0,6.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(15,plain,
equal(multiply(multiply(u,v),double_divide(v,u)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[6,12]),
[iquote('0:SpR:6.0,12.0')] ).
cnf(48,plain,
equal(double_divide(u,multiply(v,double_divide(identity,double_divide(inverse(u),w)))),multiply(x,double_divide(identity,double_divide(inverse(v),double_divide(x,w))))),
inference(spr,[status(thm),theory(equality)],[7]),
[iquote('0:SpR:7.0,7.0')] ).
cnf(49,plain,
equal(double_divide(u,multiply(v,double_divide(identity,double_divide(inverse(u),identity)))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(53,plain,
equal(double_divide(u,inverse(inverse(double_divide(identity,double_divide(inverse(u),double_divide(identity,v)))))),v),
inference(spr,[status(thm),theory(equality)],[13,7]),
[iquote('0:SpR:13.0,7.0')] ).
cnf(54,plain,
equal(double_divide(u,multiply(v,double_divide(identity,inverse(inverse(u))))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[3,49]),
[iquote('0:Rew:3.0,49.0')] ).
cnf(55,plain,
equal(double_divide(u,inverse(multiply(double_divide(inverse(u),double_divide(identity,v)),identity))),v),
inference(rew,[status(thm),theory(equality)],[6,53]),
[iquote('0:Rew:6.0,53.0')] ).
cnf(60,plain,
equal(multiply(multiply(u,double_divide(identity,inverse(inverse(v)))),v),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[54,6]),
[iquote('0:SpR:54.0,6.0')] ).
cnf(67,plain,
equal(double_divide(u,inverse(inverse(double_divide(identity,inverse(inverse(u)))))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[13,54]),
[iquote('0:SpR:13.0,54.0')] ).
cnf(68,plain,
equal(inverse(multiply(inverse(inverse(u)),identity)),double_divide(u,inverse(identity))),
inference(spr,[status(thm),theory(equality)],[15,54]),
[iquote('0:SpR:15.0,54.0')] ).
cnf(70,plain,
equal(double_divide(u,inverse(multiply(inverse(inverse(u)),identity))),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[6,67]),
[iquote('0:Rew:6.0,67.0')] ).
cnf(71,plain,
equal(double_divide(u,double_divide(u,inverse(identity))),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[68,70]),
[iquote('0:Rew:68.0,70.0')] ).
cnf(79,plain,
equal(double_divide(u,multiply(inverse(u),double_divide(identity,inverse(identity)))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[71,7]),
[iquote('0:SpR:71.0,7.0')] ).
cnf(84,plain,
equal(double_divide(u,multiply(inverse(u),identity)),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[4,79]),
[iquote('0:Rew:4.0,79.0')] ).
cnf(101,plain,
equal(double_divide(u,multiply(v,double_divide(identity,double_divide(inverse(u),inverse(identity))))),multiply(inverse(v),identity)),
inference(spr,[status(thm),theory(equality)],[84,7]),
[iquote('0:SpR:84.0,7.0')] ).
cnf(103,plain,
equal(double_divide(identity,inverse(identity)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[12,84]),
[iquote('0:SpR:12.0,84.0')] ).
cnf(104,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[4,103]),
[iquote('0:Rew:4.0,103.0')] ).
cnf(109,plain,
equal(inverse(multiply(inverse(inverse(u)),identity)),double_divide(u,identity)),
inference(rew,[status(thm),theory(equality)],[104,68]),
[iquote('0:Rew:104.0,68.0')] ).
cnf(115,plain,
equal(inverse(multiply(inverse(inverse(u)),identity)),inverse(u)),
inference(rew,[status(thm),theory(equality)],[3,109]),
[iquote('0:Rew:3.0,109.0')] ).
cnf(122,plain,
equal(double_divide(u,multiply(v,double_divide(identity,double_divide(inverse(u),identity)))),multiply(inverse(v),identity)),
inference(rew,[status(thm),theory(equality)],[104,101]),
[iquote('0:Rew:104.0,101.0')] ).
cnf(123,plain,
equal(multiply(inverse(u),identity),inverse(u)),
inference(rew,[status(thm),theory(equality)],[54,122,3]),
[iquote('0:Rew:54.0,122.0,3.0,122.0')] ).
cnf(124,plain,
equal(inverse(inverse(inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[123,115]),
[iquote('0:Rew:123.0,115.0')] ).
cnf(128,plain,
equal(double_divide(identity,multiply(u,double_divide(identity,inverse(identity)))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[104,54]),
[iquote('0:SpR:104.0,54.0')] ).
cnf(130,plain,
equal(double_divide(identity,multiply(u,double_divide(identity,double_divide(identity,double_divide(u,v))))),v),
inference(spr,[status(thm),theory(equality)],[104,7]),
[iquote('0:SpR:104.0,7.0')] ).
cnf(134,plain,
equal(double_divide(identity,multiply(u,identity)),inverse(u)),
inference(rew,[status(thm),theory(equality)],[104,128,3]),
[iquote('0:Rew:104.0,128.0,3.0,128.0,104.0,128.0')] ).
cnf(147,plain,
equal(multiply(multiply(u,v),identity),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[6,123]),
[iquote('0:SpR:6.0,123.0')] ).
cnf(162,plain,
equal(inverse(inverse(multiply(u,v))),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[6,124]),
[iquote('0:SpR:6.0,124.0')] ).
cnf(165,plain,
equal(multiply(multiply(u,identity),identity),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[134,6]),
[iquote('0:SpR:134.0,6.0')] ).
cnf(171,plain,
equal(double_divide(identity,inverse(u)),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[123,134]),
[iquote('0:SpR:123.0,134.0')] ).
cnf(174,plain,
equal(double_divide(u,multiply(v,inverse(inverse(inverse(u))))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[171,54]),
[iquote('0:Rew:171.0,54.0')] ).
cnf(181,plain,
equal(multiply(multiply(u,inverse(inverse(inverse(v)))),v),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[171,60]),
[iquote('0:Rew:171.0,60.0')] ).
cnf(184,plain,
equal(multiply(u,identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[147,165]),
[iquote('0:Rew:147.0,165.0')] ).
cnf(188,plain,
equal(double_divide(u,inverse(inverse(inverse(double_divide(inverse(u),double_divide(identity,v)))))),v),
inference(rew,[status(thm),theory(equality)],[184,55]),
[iquote('0:Rew:184.0,55.0')] ).
cnf(192,plain,
equal(double_divide(u,multiply(v,inverse(u))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[124,174]),
[iquote('0:Rew:124.0,174.0')] ).
cnf(194,plain,
equal(multiply(multiply(u,inverse(v)),v),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[124,181]),
[iquote('0:Rew:124.0,181.0')] ).
cnf(195,plain,
equal(double_divide(u,inverse(inverse(multiply(double_divide(identity,v),inverse(u))))),v),
inference(rew,[status(thm),theory(equality)],[6,188]),
[iquote('0:Rew:6.0,188.0')] ).
cnf(196,plain,
equal(inverse(double_divide(identity,u)),u),
inference(rew,[status(thm),theory(equality)],[192,195,162]),
[iquote('0:Rew:192.0,195.0,162.0,195.0')] ).
cnf(197,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[6,196]),
[iquote('0:Rew:6.0,196.0')] ).
cnf(198,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[184,197]),
[iquote('0:Rew:184.0,197.0')] ).
cnf(202,plain,
equal(double_divide(identity,inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[198,171]),
[iquote('0:Rew:198.0,171.0')] ).
cnf(204,plain,
equal(multiply(multiply(u,inverse(v)),v),u),
inference(rew,[status(thm),theory(equality)],[198,194]),
[iquote('0:Rew:198.0,194.0')] ).
cnf(213,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[6,198]),
[iquote('0:SpR:6.0,198.0')] ).
cnf(237,plain,
equal(double_divide(identity,u),inverse(u)),
inference(spr,[status(thm),theory(equality)],[198,202]),
[iquote('0:SpR:198.0,202.0')] ).
cnf(240,plain,
equal(double_divide(u,multiply(v,inverse(double_divide(inverse(u),double_divide(v,w))))),w),
inference(rew,[status(thm),theory(equality)],[237,7]),
[iquote('0:Rew:237.0,7.0')] ).
cnf(241,plain,
equal(double_divide(identity,multiply(u,double_divide(identity,inverse(double_divide(u,v))))),v),
inference(rew,[status(thm),theory(equality)],[237,130]),
[iquote('0:Rew:237.0,130.0')] ).
cnf(245,plain,
equal(double_divide(u,multiply(v,inverse(double_divide(inverse(u),w)))),multiply(x,double_divide(identity,double_divide(inverse(v),double_divide(x,w))))),
inference(rew,[status(thm),theory(equality)],[237,48]),
[iquote('0:Rew:237.0,48.0')] ).
cnf(256,plain,
equal(double_divide(identity,multiply(u,double_divide(identity,multiply(v,u)))),v),
inference(rew,[status(thm),theory(equality)],[6,241]),
[iquote('0:Rew:6.0,241.0')] ).
cnf(257,plain,
equal(double_divide(double_divide(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[213,256,237]),
[iquote('0:Rew:213.0,256.0,237.0,256.0,213.0,256.0,237.0,256.0')] ).
cnf(261,plain,
equal(double_divide(u,multiply(v,multiply(double_divide(v,w),inverse(u)))),w),
inference(rew,[status(thm),theory(equality)],[6,240]),
[iquote('0:Rew:6.0,240.0')] ).
cnf(266,plain,
equal(double_divide(u,multiply(v,multiply(w,inverse(u)))),multiply(x,double_divide(identity,double_divide(inverse(v),double_divide(x,w))))),
inference(rew,[status(thm),theory(equality)],[6,245]),
[iquote('0:Rew:6.0,245.0')] ).
cnf(267,plain,
equal(double_divide(u,multiply(v,multiply(w,inverse(u)))),multiply(x,inverse(double_divide(inverse(v),double_divide(x,w))))),
inference(rew,[status(thm),theory(equality)],[237,266]),
[iquote('0:Rew:237.0,266.0')] ).
cnf(268,plain,
equal(double_divide(u,multiply(v,multiply(w,inverse(u)))),multiply(x,multiply(double_divide(x,w),inverse(v)))),
inference(rew,[status(thm),theory(equality)],[6,267]),
[iquote('0:Rew:6.0,267.0')] ).
cnf(324,plain,
equal(multiply(u,multiply(double_divide(u,v),inverse(w))),double_divide(v,w)),
inference(spr,[status(thm),theory(equality)],[261,257]),
[iquote('0:SpR:261.0,257.0')] ).
cnf(334,plain,
equal(double_divide(u,multiply(v,multiply(w,inverse(u)))),double_divide(w,v)),
inference(rew,[status(thm),theory(equality)],[324,268]),
[iquote('0:Rew:324.0,268.0')] ).
cnf(363,plain,
equal(multiply(multiply(u,v),inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[198,204]),
[iquote('0:SpR:198.0,204.0')] ).
cnf(711,plain,
equal(double_divide(multiply(u,v),w),double_divide(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[363,334]),
[iquote('0:SpR:363.0,334.0')] ).
cnf(1547,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[711,6]),
[iquote('0:SpR:711.0,6.0')] ).
cnf(1587,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[6,1547]),
[iquote('0:Rew:6.0,1547.0')] ).
cnf(1588,plain,
$false,
inference(unc,[status(thm)],[1587,5]),
[iquote('0:UnC:1587.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : GRP489-1 : TPTP v8.1.0. Released v2.6.0.
% 0.02/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n009.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 : Tue Jun 14 10:27:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.50
% 0.18/0.50 SPASS V 3.9
% 0.18/0.50 SPASS beiseite: Proof found.
% 0.18/0.50 % SZS status Theorem
% 0.18/0.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.50 SPASS derived 817 clauses, backtracked 0 clauses, performed 0 splits and kept 131 clauses.
% 0.18/0.50 SPASS allocated 64544 KBytes.
% 0.18/0.50 SPASS spent 0:00:00.15 on the problem.
% 0.18/0.50 0:00:00.03 for the input.
% 0.18/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.50 0:00:00.01 for inferences.
% 0.18/0.50 0:00:00.00 for the backtracking.
% 0.18/0.50 0:00:00.09 for the reduction.
% 0.18/0.50
% 0.18/0.50
% 0.18/0.50 Here is a proof with depth 7, length 67 :
% 0.18/0.50 % SZS output start Refutation
% See solution above
% 0.18/0.50 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_3
% 0.18/0.50
%------------------------------------------------------------------------------