%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP547-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 11:47:59 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 60 RR)
% Number of literals : 60 ( 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 : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(identity,divide(u,v)),divide(divide(v,w),u)),w),
file('GRP547-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(identity,v)),multiply(u,v)),
file('GRP547-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(identity,u),inverse(u)),
file('GRP547-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP547-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP547-1.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(divide(u,v)),divide(divide(v,w),u)),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(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(27,plain,
equal(divide(inverse(divide(u,inverse(divide(v,w)))),divide(x,u)),divide(divide(w,x),v)),
inference(spr,[status(thm),theory(equality)],[7]),
[iquote('0:SpR:7.0,7.0')] ).
cnf(29,plain,
equal(divide(inverse(divide(u,v)),divide(identity,u)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(31,plain,
equal(divide(inverse(divide(u,v)),divide(multiply(v,w),u)),inverse(w)),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(33,plain,
equal(divide(inverse(divide(divide(u,v),u)),identity),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(34,plain,
equal(divide(inverse(divide(inverse(u),v)),multiply(divide(v,w),u)),w),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(36,plain,
equal(divide(inverse(identity),divide(divide(u,v),u)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(37,plain,
equal(divide(inverse(inverse(u)),divide(divide(u,v),identity)),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(40,plain,
equal(multiply(inverse(divide(u,v)),u),v),
inference(rew,[status(thm),theory(equality)],[6,29,3]),
[iquote('0:Rew:6.0,29.0,3.0,29.0')] ).
cnf(41,plain,
equal(multiply(inverse(divide(divide(u,v),u)),identity),v),
inference(rew,[status(thm),theory(equality)],[15,33]),
[iquote('0:Rew:15.0,33.0')] ).
cnf(42,plain,
equal(inverse(divide(divide(u,v),u)),v),
inference(rew,[status(thm),theory(equality)],[3,36,9]),
[iquote('0:Rew:3.0,36.0,9.0,36.0')] ).
cnf(43,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[42,41]),
[iquote('0:Rew:42.0,41.0')] ).
cnf(44,plain,
equal(divide(u,identity),u),
inference(rew,[status(thm),theory(equality)],[43,15]),
[iquote('0:Rew:43.0,15.0')] ).
cnf(46,plain,
equal(divide(inverse(inverse(u)),divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[44,37]),
[iquote('0:Rew:44.0,37.0')] ).
cnf(53,plain,
equal(divide(inverse(multiply(u,divide(v,w))),divide(x,u)),divide(divide(w,x),v)),
inference(rew,[status(thm),theory(equality)],[6,27]),
[iquote('0:Rew:6.0,27.0')] ).
cnf(66,plain,
equal(inverse(divide(identity,u)),u),
inference(spr,[status(thm),theory(equality)],[40,43]),
[iquote('0:SpR:40.0,43.0')] ).
cnf(72,plain,
equal(multiply(inverse(u),inverse(divide(v,w))),divide(divide(w,u),v)),
inference(spr,[status(thm),theory(equality)],[7,40]),
[iquote('0:SpR:7.0,40.0')] ).
cnf(73,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[3,66]),
[iquote('0:Rew:3.0,66.0')] ).
cnf(75,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[73,46]),
[iquote('0:Rew:73.0,46.0')] ).
cnf(80,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[73,6]),
[iquote('0:SpR:73.0,6.0')] ).
cnf(83,plain,
equal(divide(inverse(u),divide(v,w)),divide(divide(w,u),v)),
inference(rew,[status(thm),theory(equality)],[80,72]),
[iquote('0:Rew:80.0,72.0')] ).
cnf(86,plain,
equal(divide(divide(u,multiply(u,divide(v,w))),x),divide(divide(w,x),v)),
inference(rew,[status(thm),theory(equality)],[83,53]),
[iquote('0:Rew:83.0,53.0')] ).
cnf(88,plain,
equal(divide(divide(u,divide(u,v)),multiply(v,w)),inverse(w)),
inference(rew,[status(thm),theory(equality)],[83,31]),
[iquote('0:Rew:83.0,31.0')] ).
cnf(94,plain,
equal(divide(u,multiply(u,v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[75,88]),
[iquote('0:Rew:75.0,88.0')] ).
cnf(96,plain,
equal(divide(inverse(divide(u,v)),w),divide(divide(v,w),u)),
inference(rew,[status(thm),theory(equality)],[94,86]),
[iquote('0:Rew:94.0,86.0')] ).
cnf(97,plain,
equal(divide(divide(u,multiply(divide(u,v),w)),inverse(w)),v),
inference(rew,[status(thm),theory(equality)],[96,34]),
[iquote('0:Rew:96.0,34.0')] ).
cnf(98,plain,
equal(multiply(divide(u,multiply(divide(u,v),w)),w),v),
inference(rew,[status(thm),theory(equality)],[6,97]),
[iquote('0:Rew:6.0,97.0')] ).
cnf(102,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[75,40]),
[iquote('0:SpR:75.0,40.0')] ).
cnf(121,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[75,42]),
[iquote('0:SpR:75.0,42.0')] ).
cnf(129,plain,
equal(divide(divide(u,v),w),divide(divide(u,w),v)),
inference(rew,[status(thm),theory(equality)],[121,96]),
[iquote('0:Rew:121.0,96.0')] ).
cnf(151,plain,
equal(divide(u,inverse(v)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[73,102]),
[iquote('0:SpR:73.0,102.0')] ).
cnf(153,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[6,151]),
[iquote('0:Rew:6.0,151.0')] ).
cnf(154,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[153,5]),
[iquote('0:Rew:153.0,5.0')] ).
cnf(156,plain,
equal(multiply(u,divide(v,multiply(divide(v,w),u))),w),
inference(rew,[status(thm),theory(equality)],[153,98]),
[iquote('0:Rew:153.0,98.0')] ).
cnf(232,plain,
equal(divide(divide(u,inverse(v)),w),multiply(divide(u,w),v)),
inference(spr,[status(thm),theory(equality)],[129,6]),
[iquote('0:SpR:129.0,6.0')] ).
cnf(256,plain,
equal(divide(divide(u,v),divide(u,w)),divide(w,v)),
inference(spr,[status(thm),theory(equality)],[75,129]),
[iquote('0:SpR:75.0,129.0')] ).
cnf(276,plain,
equal(divide(multiply(u,v),w),multiply(divide(u,w),v)),
inference(rew,[status(thm),theory(equality)],[6,232]),
[iquote('0:Rew:6.0,232.0')] ).
cnf(292,plain,
equal(divide(u,divide(v,w)),multiply(divide(w,v),u)),
inference(spr,[status(thm),theory(equality)],[121,102]),
[iquote('0:SpR:121.0,102.0')] ).
cnf(312,plain,
equal(multiply(divide(u,v),divide(v,w)),divide(u,w)),
inference(rew,[status(thm),theory(equality)],[292,256]),
[iquote('0:Rew:292.0,256.0')] ).
cnf(436,plain,
equal(multiply(u,divide(v,multiply(inverse(w),u))),multiply(v,w)),
inference(spr,[status(thm),theory(equality)],[94,156]),
[iquote('0:SpR:94.0,156.0')] ).
cnf(471,plain,
equal(multiply(u,divide(v,divide(u,w))),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[102,436]),
[iquote('0:Rew:102.0,436.0')] ).
cnf(472,plain,
equal(multiply(u,multiply(divide(v,u),w)),multiply(w,v)),
inference(rew,[status(thm),theory(equality)],[292,471]),
[iquote('0:Rew:292.0,471.0')] ).
cnf(709,plain,
equal(multiply(multiply(divide(u,divide(v,w)),x),v),multiply(w,multiply(x,u))),
inference(spr,[status(thm),theory(equality)],[472]),
[iquote('0:SpR:472.0,472.0')] ).
cnf(718,plain,
equal(multiply(u,multiply(multiply(divide(v,u),w),x)),multiply(x,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[276,472]),
[iquote('0:SpR:276.0,472.0')] ).
cnf(724,plain,
equal(multiply(divide(u,v),w),multiply(u,divide(w,v))),
inference(spr,[status(thm),theory(equality)],[312,472]),
[iquote('0:SpR:312.0,472.0')] ).
cnf(734,plain,
equal(divide(u,divide(v,w)),multiply(w,divide(u,v))),
inference(rew,[status(thm),theory(equality)],[724,292]),
[iquote('0:Rew:724.0,292.0')] ).
cnf(768,plain,
equal(multiply(u,multiply(divide(v,divide(u,w)),x)),multiply(w,multiply(x,v))),
inference(rew,[status(thm),theory(equality)],[153,709]),
[iquote('0:Rew:153.0,709.0')] ).
cnf(769,plain,
equal(multiply(u,multiply(multiply(v,divide(w,u)),x)),multiply(v,multiply(x,w))),
inference(rew,[status(thm),theory(equality)],[734,768]),
[iquote('0:Rew:734.0,768.0')] ).
cnf(771,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[769,718,724]),
[iquote('0:Rew:769.0,718.0,724.0,718.0')] ).
cnf(772,plain,
~ equal(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[771,154]),
[iquote('0:Rew:771.0,154.0')] ).
cnf(773,plain,
~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[153,772]),
[iquote('0:Rew:153.0,772.0')] ).
cnf(774,plain,
$false,
inference(obv,[status(thm),theory(equality)],[773]),
[iquote('0:Obv:773.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP547-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n012.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 : Mon Jun 13 14:58:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.46
% 0.19/0.46 SPASS V 3.9
% 0.19/0.46 SPASS beiseite: Proof found.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 SPASS derived 446 clauses, backtracked 0 clauses, performed 0 splits and kept 122 clauses.
% 0.19/0.46 SPASS allocated 63734 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.11 on the problem.
% 0.19/0.46 0:00:00.03 for the input.
% 0.19/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.46 0:00:00.00 for inferences.
% 0.19/0.46 0:00:00.00 for the backtracking.
% 0.19/0.46 0:00:00.05 for the reduction.
% 0.19/0.46
% 0.19/0.46
% 0.19/0.46 Here is a proof with depth 3, length 60 :
% 0.19/0.46 % SZS output start Refutation
% See solution above
% 0.19/0.46 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_3
% 0.19/0.46
%------------------------------------------------------------------------------