%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP099-1 : 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 11:45:17 EDT 2022
% Result : Unsatisfiable 0.12s 0.42s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 5
% Syntax : Number of clauses : 90 ( 81 unt; 0 nHn; 90 RR)
% Number of literals : 109 ( 0 equ; 30 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 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(identity,w))),double_divide(identity,identity)),v),
file('GRP099-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP099-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP099-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP099-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(multiply(identity,a2),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(a1),a1),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
file('GRP099-1.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)),double_divide(identity,w))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew: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(14,plain,
( ~ equal(multiply(identity,a2),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(inverse(identity),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[12,5]),
[iquote('0:Rew:12.0,5.2')] ).
cnf(15,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(inverse(identity),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[13,14]),
[iquote('0:Rew:13.0,14.0')] ).
cnf(21,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(u,inverse(identity))),identity)),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(22,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(u,identity)),inverse(identity))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(23,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,identity),double_divide(identity,inverse(u)))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(25,plain,
equal(double_divide(double_divide(u,multiply(double_divide(u,inverse(identity)),v)),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[6,21,3]),
[iquote('0:Rew:6.0,21.0,3.0,21.0')] ).
cnf(26,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,inverse(u)),inverse(identity))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,22]),
[iquote('0:Rew:3.0,22.0')] ).
cnf(27,plain,
equal(double_divide(double_divide(u,double_divide(inverse(v),double_divide(identity,inverse(u)))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,23]),
[iquote('0:Rew:3.0,23.0')] ).
cnf(70,plain,
equal(double_divide(double_divide(identity,multiply(identity,u)),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,25]),
[iquote('0:SpR:4.0,25.0')] ).
cnf(72,plain,
equal(double_divide(double_divide(identity,inverse(inverse(u))),inverse(identity)),u),
inference(rew,[status(thm),theory(equality)],[13,70]),
[iquote('0:Rew:13.0,70.0')] ).
cnf(76,plain,
equal(double_divide(double_divide(double_divide(identity,inverse(inverse(u))),multiply(u,v)),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[72,25]),
[iquote('0:SpR:72.0,25.0')] ).
cnf(77,plain,
equal(multiply(inverse(identity),double_divide(identity,inverse(inverse(u)))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[72,6]),
[iquote('0:SpR:72.0,6.0')] ).
cnf(127,plain,
equal(double_divide(double_divide(double_divide(u,v),double_divide(double_divide(w,multiply(v,u)),inverse(identity))),inverse(identity)),w),
inference(spr,[status(thm),theory(equality)],[6,26]),
[iquote('0:SpR:6.0,26.0')] ).
cnf(128,plain,
equal(double_divide(double_divide(u,double_divide(identity,inverse(identity))),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,26]),
[iquote('0:SpR:4.0,26.0')] ).
cnf(129,plain,
equal(double_divide(u,double_divide(double_divide(v,double_divide(u,w)),double_divide(identity,w))),double_divide(double_divide(identity,double_divide(v,inverse(identity))),inverse(identity))),
inference(spr,[status(thm),theory(equality)],[7,26]),
[iquote('0:SpR:7.0,26.0')] ).
cnf(130,plain,
equal(double_divide(double_divide(identity,double_divide(u,inverse(identity))),inverse(identity)),double_divide(v,multiply(double_divide(v,inverse(identity)),u))),
inference(spr,[status(thm),theory(equality)],[25,26]),
[iquote('0:SpR:25.0,26.0')] ).
cnf(131,plain,
equal(double_divide(double_divide(identity,double_divide(u,inverse(identity))),inverse(identity)),double_divide(identity,inverse(inverse(u)))),
inference(spr,[status(thm),theory(equality)],[72,26]),
[iquote('0:SpR:72.0,26.0')] ).
cnf(133,plain,
equal(double_divide(double_divide(inverse(u),u),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[72,26]),
[iquote('0:SpR:72.0,26.0')] ).
cnf(135,plain,
equal(double_divide(inverse(u),inverse(identity)),u),
inference(rew,[status(thm),theory(equality)],[3,128,4]),
[iquote('0:Rew:3.0,128.0,4.0,128.0')] ).
cnf(138,plain,
equal(double_divide(u,multiply(double_divide(u,inverse(identity)),v)),double_divide(identity,inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[131,130]),
[iquote('0:Rew:131.0,130.0')] ).
cnf(148,plain,
equal(double_divide(u,double_divide(double_divide(v,double_divide(u,w)),double_divide(identity,w))),double_divide(identity,inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[131,129]),
[iquote('0:Rew:131.0,129.0')] ).
cnf(158,plain,
equal(double_divide(multiply(u,v),inverse(identity)),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[6,135]),
[iquote('0:SpR:6.0,135.0')] ).
cnf(175,plain,
equal(double_divide(inverse(inverse(identity)),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[3,133]),
[iquote('0:SpR:3.0,133.0')] ).
cnf(177,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[135,175]),
[iquote('0:Rew:135.0,175.0')] ).
cnf(180,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(identity,identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[177,15]),
[iquote('0:Rew:177.0,15.2')] ).
cnf(182,plain,
equal(multiply(identity,double_divide(identity,inverse(inverse(u)))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[177,77]),
[iquote('0:Rew:177.0,77.0')] ).
cnf(185,plain,
equal(double_divide(inverse(u),identity),u),
inference(rew,[status(thm),theory(equality)],[177,135]),
[iquote('0:Rew:177.0,135.0')] ).
cnf(188,plain,
equal(double_divide(double_divide(u,double_divide(inverse(v),double_divide(identity,inverse(u)))),identity),v),
inference(rew,[status(thm),theory(equality)],[177,27]),
[iquote('0:Rew:177.0,27.0')] ).
cnf(190,plain,
equal(double_divide(u,multiply(double_divide(u,identity),v)),double_divide(identity,inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[177,138]),
[iquote('0:Rew:177.0,138.0')] ).
cnf(191,plain,
equal(double_divide(double_divide(double_divide(identity,inverse(inverse(u))),multiply(u,v)),identity),v),
inference(rew,[status(thm),theory(equality)],[177,76]),
[iquote('0:Rew:177.0,76.0')] ).
cnf(195,plain,
equal(double_divide(double_divide(double_divide(u,v),double_divide(double_divide(w,multiply(v,u)),identity)),identity),w),
inference(rew,[status(thm),theory(equality)],[177,127]),
[iquote('0:Rew:177.0,127.0')] ).
cnf(197,plain,
equal(double_divide(multiply(u,v),identity),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[177,158]),
[iquote('0:Rew:177.0,158.0')] ).
cnf(199,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[3,185]),
[iquote('0:Rew:3.0,185.0')] ).
cnf(200,plain,
equal(multiply(identity,u),u),
inference(rew,[status(thm),theory(equality)],[199,13]),
[iquote('0:Rew:199.0,13.0')] ).
cnf(201,plain,
equal(double_divide(u,double_divide(double_divide(v,double_divide(u,w)),double_divide(identity,w))),double_divide(identity,v)),
inference(rew,[status(thm),theory(equality)],[199,148]),
[iquote('0:Rew:199.0,148.0')] ).
cnf(205,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[3,197]),
[iquote('0:Rew:3.0,197.0')] ).
cnf(207,plain,
equal(double_divide(identity,u),inverse(u)),
inference(rew,[status(thm),theory(equality)],[200,182,199]),
[iquote('0:Rew:200.0,182.0,199.0,182.0')] ).
cnf(216,plain,
equal(multiply(double_divide(inverse(u),double_divide(identity,inverse(v))),v),u),
inference(rew,[status(thm),theory(equality)],[6,188,3]),
[iquote('0:Rew:6.0,188.0,3.0,188.0')] ).
cnf(217,plain,
equal(multiply(double_divide(inverse(u),v),v),u),
inference(rew,[status(thm),theory(equality)],[199,216,207]),
[iquote('0:Rew:199.0,216.0,207.0,216.0')] ).
cnf(218,plain,
equal(double_divide(u,multiply(inverse(u),v)),double_divide(identity,inverse(inverse(v)))),
inference(rew,[status(thm),theory(equality)],[3,190]),
[iquote('0:Rew:3.0,190.0')] ).
cnf(219,plain,
equal(double_divide(u,multiply(inverse(u),v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[207,218,199]),
[iquote('0:Rew:207.0,218.0,199.0,218.0')] ).
cnf(220,plain,
equal(multiply(multiply(u,v),double_divide(identity,inverse(inverse(u)))),v),
inference(rew,[status(thm),theory(equality)],[6,191,3]),
[iquote('0:Rew:6.0,191.0,3.0,191.0')] ).
cnf(221,plain,
equal(multiply(multiply(u,v),inverse(u)),v),
inference(rew,[status(thm),theory(equality)],[207,220,199]),
[iquote('0:Rew:207.0,220.0,199.0,220.0')] ).
cnf(226,plain,
equal(multiply(multiply(multiply(u,v),w),double_divide(v,u)),w),
inference(rew,[status(thm),theory(equality)],[6,195,3]),
[iquote('0:Rew:6.0,195.0,3.0,195.0,6.0,195.0,3.0,195.0')] ).
cnf(227,plain,
equal(double_divide(u,double_divide(double_divide(v,double_divide(u,w)),inverse(w))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[207,201]),
[iquote('0:Rew:207.0,201.0,207.0,201.0')] ).
cnf(232,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[180]),
[iquote('0:Obv:180.2')] ).
cnf(233,plain,
( ~ equal(a2,a2)
| ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[199,232]),
[iquote('0:Rew:199.0,232.0')] ).
cnf(234,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[233]),
[iquote('0:Obv:233.0')] ).
cnf(262,plain,
equal(multiply(double_divide(u,v),v),inverse(u)),
inference(spr,[status(thm),theory(equality)],[199,217]),
[iquote('0:SpR:199.0,217.0')] ).
cnf(334,plain,
equal(multiply(u,inverse(multiply(v,u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[221]),
[iquote('0:SpR:221.0,221.0')] ).
cnf(348,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[205,334]),
[iquote('0:Rew:205.0,334.0')] ).
cnf(356,plain,
equal(multiply(inverse(u),inverse(double_divide(u,v))),v),
inference(spr,[status(thm),theory(equality)],[262,221]),
[iquote('0:SpR:262.0,221.0')] ).
cnf(367,plain,
equal(multiply(inverse(u),multiply(v,u)),v),
inference(rew,[status(thm),theory(equality)],[6,356]),
[iquote('0:Rew:6.0,356.0')] ).
cnf(461,plain,
equal(multiply(inverse(u),inverse(v)),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[348,221]),
[iquote('0:SpR:348.0,221.0')] ).
cnf(463,plain,
equal(inverse(double_divide(inverse(u),v)),double_divide(u,inverse(v))),
inference(spr,[status(thm),theory(equality)],[348,219]),
[iquote('0:SpR:348.0,219.0')] ).
cnf(477,plain,
equal(double_divide(u,inverse(v)),multiply(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[6,463]),
[iquote('0:Rew:6.0,463.0')] ).
cnf(480,plain,
equal(double_divide(u,multiply(v,inverse(double_divide(w,double_divide(u,v))))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[477,227]),
[iquote('0:Rew:477.0,227.0')] ).
cnf(484,plain,
equal(double_divide(u,multiply(v,multiply(double_divide(u,v),w))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[6,480]),
[iquote('0:Rew:6.0,480.0')] ).
cnf(504,plain,
equal(multiply(u,multiply(v,inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[199,367]),
[iquote('0:SpR:199.0,367.0')] ).
cnf(786,plain,
equal(multiply(double_divide(u,v),inverse(w)),double_divide(w,multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[205,461]),
[iquote('0:SpR:205.0,461.0')] ).
cnf(826,plain,
equal(inverse(multiply(u,inverse(double_divide(v,w)))),double_divide(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[504,484]),
[iquote('0:SpR:504.0,484.0')] ).
cnf(830,plain,
equal(double_divide(u,double_divide(u,v)),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[504,484]),
[iquote('0:SpR:504.0,484.0')] ).
cnf(831,plain,
equal(double_divide(u,double_divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[199,830]),
[iquote('0:Rew:199.0,830.0')] ).
cnf(854,plain,
equal(double_divide(multiply(u,v),w),double_divide(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[205,826,6]),
[iquote('0:Rew:205.0,826.0,6.0,826.0')] ).
cnf(896,plain,
equal(inverse(double_divide(u,v)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[831,348]),
[iquote('0:SpR:831.0,348.0')] ).
cnf(922,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[6,896]),
[iquote('0:Rew:6.0,896.0')] ).
cnf(925,plain,
equal(multiply(double_divide(u,v),multiply(multiply(v,u),w)),w),
inference(rew,[status(thm),theory(equality)],[922,226]),
[iquote('0:Rew:922.0,226.0')] ).
cnf(926,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[922,234]),
[iquote('0:Rew:922.0,234.1')] ).
cnf(949,plain,
( ~ equal(multiply(a4,b4),multiply(a4,b4))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[922,926]),
[iquote('0:Rew:922.0,926.0')] ).
cnf(950,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(obv,[status(thm),theory(equality)],[949]),
[iquote('0:Obv:949.0')] ).
cnf(1210,plain,
equal(multiply(double_divide(u,v),inverse(w)),double_divide(multiply(v,u),w)),
inference(spr,[status(thm),theory(equality)],[348,925]),
[iquote('0:SpR:348.0,925.0')] ).
cnf(1256,plain,
equal(double_divide(u,multiply(v,w)),double_divide(w,multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[786,1210,854]),
[iquote('0:Rew:786.0,1210.0,854.0,1210.0')] ).
cnf(1764,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(w,multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[854,6]),
[iquote('0:SpR:854.0,6.0')] ).
cnf(1811,plain,
equal(multiply(multiply(u,v),w),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[6,1764]),
[iquote('0:Rew:6.0,1764.0')] ).
cnf(1915,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(multiply(v,u),w)),
inference(spr,[status(thm),theory(equality)],[1256,6]),
[iquote('0:SpR:1256.0,6.0')] ).
cnf(1977,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(u,w),v)),
inference(rew,[status(thm),theory(equality)],[6,1915]),
[iquote('0:Rew:6.0,1915.0')] ).
cnf(1978,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[1811,1977]),
[iquote('0:Rew:1811.0,1977.0,1811.0,1977.0')] ).
cnf(1980,plain,
~ equal(multiply(b3,multiply(a3,c3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[1978,950]),
[iquote('0:Rew:1978.0,950.0')] ).
cnf(2188,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[922,1811]),
[iquote('0:SpR:922.0,1811.0')] ).
cnf(2202,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[1811,2188]),
[iquote('0:Rew:1811.0,2188.0')] ).
cnf(2203,plain,
$false,
inference(unc,[status(thm)],[2202,1980]),
[iquote('0:UnC:2202.0,1980.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : GRP099-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.04/0.08 % 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 12:53:11 EDT 2022
% 0.07/0.27 % CPUTime :
% 0.12/0.42
% 0.12/0.42 SPASS V 3.9
% 0.12/0.42 SPASS beiseite: Proof found.
% 0.12/0.42 % SZS status Theorem
% 0.12/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.42 SPASS derived 1150 clauses, backtracked 0 clauses, performed 0 splits and kept 166 clauses.
% 0.12/0.42 SPASS allocated 64799 KBytes.
% 0.12/0.42 SPASS spent 0:00:00.14 on the problem.
% 0.12/0.42 0:00:00.03 for the input.
% 0.12/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.42 0:00:00.01 for inferences.
% 0.12/0.42 0:00:00.00 for the backtracking.
% 0.12/0.42 0:00:00.09 for the reduction.
% 0.12/0.42
% 0.12/0.42
% 0.12/0.42 Here is a proof with depth 8, length 90 :
% 0.12/0.42 % SZS output start Refutation
% See solution above
% 0.12/0.43 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms
% 0.12/0.43
%------------------------------------------------------------------------------