%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP572-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 11:48:06 EDT 2022
% Result : Unsatisfiable 0.12s 0.38s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% 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 : 7 ( 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(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(u,w)),double_divide(w,identity))),double_divide(identity,identity)),v),
file('GRP572-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP572-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP572-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP572-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(b,a),multiply(a,b)),
file('GRP572-1.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(double_divide(u,double_divide(double_divide(v,double_divide(u,w)),inverse(w))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew: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(17,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(u,double_divide(w,x))),multiply(x,w))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(18,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,identity),inverse(inverse(u)))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(19,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,inverse(u)),inverse(identity))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(20,plain,
equal(double_divide(double_divide(u,double_divide(inverse(v),inverse(inverse(u)))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,18]),
[iquote('0:Rew:3.0,18.0')] ).
cnf(64,plain,
equal(double_divide(double_divide(u,identity),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,20]),
[iquote('0:SpR:4.0,20.0')] ).
cnf(65,plain,
equal(double_divide(inverse(u),inverse(identity)),u),
inference(rew,[status(thm),theory(equality)],[3,64]),
[iquote('0:Rew:3.0,64.0')] ).
cnf(70,plain,
equal(double_divide(double_divide(inverse(u),double_divide(double_divide(v,u),inverse(inverse(identity)))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[65,7]),
[iquote('0:SpR:65.0,7.0')] ).
cnf(117,plain,
equal(double_divide(double_divide(identity,double_divide(u,inverse(identity))),inverse(identity)),double_divide(v,double_divide(inverse(u),inverse(inverse(v))))),
inference(spr,[status(thm),theory(equality)],[20,19]),
[iquote('0:SpR:20.0,19.0')] ).
cnf(118,plain,
equal(double_divide(double_divide(identity,double_divide(u,inverse(identity))),inverse(identity)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[65,19]),
[iquote('0:SpR:65.0,19.0')] ).
cnf(124,plain,
equal(double_divide(u,double_divide(inverse(v),inverse(inverse(u)))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[118,117]),
[iquote('0:Rew:118.0,117.0')] ).
cnf(136,plain,
equal(multiply(double_divide(inverse(u),inverse(inverse(v))),v),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[124,6]),
[iquote('0:SpR:124.0,6.0')] ).
cnf(147,plain,
equal(multiply(inverse(identity),double_divide(identity,double_divide(u,inverse(identity)))),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[118,6]),
[iquote('0:SpR:118.0,6.0')] ).
cnf(152,plain,
equal(double_divide(double_divide(identity,identity),inverse(identity)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,118]),
[iquote('0:SpR:4.0,118.0')] ).
cnf(153,plain,
equal(double_divide(double_divide(identity,u),inverse(identity)),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[65,118]),
[iquote('0:SpR:65.0,118.0')] ).
cnf(155,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[65,152,3]),
[iquote('0:Rew:65.0,152.0,3.0,152.0')] ).
cnf(156,plain,
equal(multiply(inverse(u),u),identity),
inference(rew,[status(thm),theory(equality)],[155,12]),
[iquote('0:Rew:155.0,12.0')] ).
cnf(158,plain,
equal(double_divide(inverse(u),identity),u),
inference(rew,[status(thm),theory(equality)],[155,65]),
[iquote('0:Rew:155.0,65.0')] ).
cnf(163,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(u,double_divide(w,x))),multiply(x,w))),identity),v),
inference(rew,[status(thm),theory(equality)],[155,17]),
[iquote('0:Rew:155.0,17.0')] ).
cnf(164,plain,
equal(double_divide(double_divide(inverse(u),double_divide(double_divide(v,u),inverse(identity))),identity),v),
inference(rew,[status(thm),theory(equality)],[155,70]),
[iquote('0:Rew:155.0,70.0')] ).
cnf(168,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[3,158]),
[iquote('0:Rew:3.0,158.0')] ).
cnf(169,plain,
equal(multiply(identity,u),u),
inference(rew,[status(thm),theory(equality)],[168,13]),
[iquote('0:Rew:168.0,13.0')] ).
cnf(171,plain,
equal(multiply(double_divide(inverse(u),v),v),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[168,136]),
[iquote('0:Rew:168.0,136.0')] ).
cnf(175,plain,
equal(double_divide(double_divide(identity,u),identity),u),
inference(rew,[status(thm),theory(equality)],[155,153,168]),
[iquote('0:Rew:155.0,153.0,168.0,153.0')] ).
cnf(176,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[6,175,3]),
[iquote('0:Rew:6.0,175.0,3.0,175.0')] ).
cnf(178,plain,
equal(multiply(double_divide(inverse(u),v),v),u),
inference(rew,[status(thm),theory(equality)],[168,171]),
[iquote('0:Rew:168.0,171.0')] ).
cnf(180,plain,
equal(double_divide(identity,double_divide(u,identity)),u),
inference(rew,[status(thm),theory(equality)],[169,147,155,168]),
[iquote('0:Rew:169.0,147.0,155.0,147.0,168.0,147.0')] ).
cnf(181,plain,
equal(double_divide(identity,inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[3,180]),
[iquote('0:Rew:3.0,180.0')] ).
cnf(184,plain,
equal(multiply(double_divide(double_divide(u,v),inverse(identity)),inverse(v)),u),
inference(rew,[status(thm),theory(equality)],[6,164,3]),
[iquote('0:Rew:6.0,164.0,3.0,164.0')] ).
cnf(185,plain,
equal(multiply(double_divide(double_divide(u,v),identity),inverse(v)),u),
inference(rew,[status(thm),theory(equality)],[155,184]),
[iquote('0:Rew:155.0,184.0')] ).
cnf(186,plain,
equal(multiply(multiply(u,v),inverse(u)),v),
inference(rew,[status(thm),theory(equality)],[6,185,3]),
[iquote('0:Rew:6.0,185.0,3.0,185.0')] ).
cnf(199,plain,
equal(multiply(double_divide(double_divide(u,double_divide(v,double_divide(w,x))),multiply(x,w)),v),u),
inference(rew,[status(thm),theory(equality)],[6,163,3]),
[iquote('0:Rew:6.0,163.0,3.0,163.0')] ).
cnf(227,plain,
equal(double_divide(identity,u),inverse(u)),
inference(spr,[status(thm),theory(equality)],[168,181]),
[iquote('0:SpR:168.0,181.0')] ).
cnf(244,plain,
equal(double_divide(double_divide(u,double_divide(identity,double_divide(v,w))),multiply(w,v)),u),
inference(spr,[status(thm),theory(equality)],[199,176]),
[iquote('0:SpR:199.0,176.0')] ).
cnf(248,plain,
equal(multiply(double_divide(double_divide(u,double_divide(v,double_divide(w,inverse(w)))),identity),v),u),
inference(spr,[status(thm),theory(equality)],[156,199]),
[iquote('0:SpR:156.0,199.0')] ).
cnf(256,plain,
equal(double_divide(double_divide(u,inverse(double_divide(v,w))),multiply(w,v)),u),
inference(rew,[status(thm),theory(equality)],[227,244]),
[iquote('0:Rew:227.0,244.0')] ).
cnf(257,plain,
equal(double_divide(double_divide(u,multiply(v,w)),multiply(v,w)),u),
inference(rew,[status(thm),theory(equality)],[6,256]),
[iquote('0:Rew:6.0,256.0')] ).
cnf(260,plain,
equal(multiply(multiply(inverse(u),v),u),v),
inference(rew,[status(thm),theory(equality)],[6,248,3,4]),
[iquote('0:Rew:6.0,248.0,3.0,248.0,3.0,248.0,4.0,248.0')] ).
cnf(316,plain,
equal(multiply(double_divide(u,v),v),inverse(u)),
inference(spr,[status(thm),theory(equality)],[168,178]),
[iquote('0:SpR:168.0,178.0')] ).
cnf(374,plain,
equal(multiply(inverse(u),inverse(double_divide(u,v))),v),
inference(spr,[status(thm),theory(equality)],[316,186]),
[iquote('0:SpR:316.0,186.0')] ).
cnf(386,plain,
equal(multiply(inverse(u),multiply(v,u)),v),
inference(rew,[status(thm),theory(equality)],[6,374]),
[iquote('0:Rew:6.0,374.0')] ).
cnf(548,plain,
equal(multiply(u,multiply(v,inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[168,386]),
[iquote('0:SpR:168.0,386.0')] ).
cnf(1413,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[257,316]),
[iquote('0:SpR:257.0,316.0')] ).
cnf(1476,plain,
equal(multiply(multiply(u,v),w),multiply(w,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[6,1413]),
[iquote('0:Rew:6.0,1413.0')] ).
cnf(1480,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[1476,260]),
[iquote('0:Rew:1476.0,260.0')] ).
cnf(1527,plain,
equal(multiply(u,inverse(inverse(v))),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[548,1480]),
[iquote('0:SpR:548.0,1480.0')] ).
cnf(1537,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[168,1527]),
[iquote('0:Rew:168.0,1527.0')] ).
cnf(1538,plain,
$false,
inference(unc,[status(thm)],[1537,5]),
[iquote('0:UnC:1537.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.08 % Problem : GRP572-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.08 % Command : run_spass %d %s
% 0.07/0.27 % Computer : n032.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 600
% 0.07/0.27 % DateTime : Mon Jun 13 09:52:11 EDT 2022
% 0.07/0.27 % CPUTime :
% 0.12/0.38
% 0.12/0.38 SPASS V 3.9
% 0.12/0.38 SPASS beiseite: Proof found.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38 SPASS derived 889 clauses, backtracked 0 clauses, performed 0 splits and kept 128 clauses.
% 0.12/0.38 SPASS allocated 64409 KBytes.
% 0.12/0.38 SPASS spent 0:00:00.09 on the problem.
% 0.12/0.38 0:00:00.02 for the input.
% 0.12/0.38 0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.38 0:00:00.01 for inferences.
% 0.12/0.38 0:00:00.00 for the backtracking.
% 0.12/0.38 0:00:00.05 for the reduction.
% 0.12/0.38
% 0.12/0.38
% 0.12/0.38 Here is a proof with depth 7, length 56 :
% 0.12/0.38 % SZS output start Refutation
% See solution above
% 0.12/0.38 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_4
% 0.12/0.38
%------------------------------------------------------------------------------