TSTP Solution File: KLE145+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE145+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 : Sun Jul 17 02:28:45 EDT 2022
% Result : Theorem 165.56s 165.81s
% Output : Refutation 167.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 19
% Syntax : Number of clauses : 106 ( 75 unt; 0 nHn; 106 RR)
% Number of literals : 140 ( 0 equ; 37 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(u,zero),u),
file('KLE145+2.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,u),u),
file('KLE145+2.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE145+2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE145+2.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(zero,u),zero),
file('KLE145+2.p',unknown),
[] ).
cnf(6,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE145+2.p',unknown),
[] ).
cnf(7,axiom,
equal(addition(one,multiplication(u,star(u))),star(u)),
file('KLE145+2.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(one,multiplication(star(u),u)),star(u)),
file('KLE145+2.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(multiplication(u,strong_iteration(u)),one),strong_iteration(u)),
file('KLE145+2.p',unknown),
[] ).
cnf(10,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE145+2.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE145+2.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(star(u),multiplication(strong_iteration(u),zero)),strong_iteration(u)),
file('KLE145+2.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE145+2.p',unknown),
[] ).
cnf(14,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE145+2.p',unknown),
[] ).
cnf(15,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE145+2.p',unknown),
[] ).
cnf(16,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE145+2.p',unknown),
[] ).
cnf(17,axiom,
( ~ leq(strong_iteration(skc3),star(strong_iteration(skc3)))
| ~ leq(star(strong_iteration(skc2)),strong_iteration(skc2)) ),
file('KLE145+2.p',unknown),
[] ).
cnf(18,axiom,
( ~ leq(addition(multiplication(u,v),w),v)
| leq(multiplication(star(u),w),v) ),
file('KLE145+2.p',unknown),
[] ).
cnf(19,axiom,
( ~ leq(addition(multiplication(u,v),w),u)
| leq(multiplication(w,star(v)),u) ),
file('KLE145+2.p',unknown),
[] ).
cnf(21,plain,
equal(addition(one,multiplication(u,strong_iteration(u))),strong_iteration(u)),
inference(rew,[status(thm),theory(equality)],[6,9]),
[iquote('0:Rew:6.0,9.0')] ).
cnf(30,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(65,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[10,6]),
[iquote('0:SpR:10.1,6.0')] ).
cnf(71,plain,
( ~ leq(one,multiplication(u,star(u)))
| equal(multiplication(u,star(u)),star(u)) ),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.1,7.0')] ).
cnf(75,plain,
( ~ equal(u,u)
| leq(u,u) ),
inference(spl,[status(thm),theory(equality)],[2,11]),
[iquote('0:SpL:2.0,11.0')] ).
cnf(79,plain,
( ~ equal(u,u)
| leq(zero,u) ),
inference(spl,[status(thm),theory(equality)],[30,11]),
[iquote('0:SpL:30.0,11.0')] ).
cnf(85,plain,
leq(u,u),
inference(obv,[status(thm),theory(equality)],[75]),
[iquote('0:Obv:75.0')] ).
cnf(86,plain,
leq(zero,u),
inference(obv,[status(thm),theory(equality)],[79]),
[iquote('0:Obv:79.0')] ).
cnf(115,plain,
( ~ leq(u,v)
| ~ leq(v,u)
| equal(v,u) ),
inference(spr,[status(thm),theory(equality)],[65,10]),
[iquote('0:SpR:65.1,10.1')] ).
cnf(125,plain,
( ~ leq(u,v)
| ~ equal(v,u)
| leq(v,u) ),
inference(spl,[status(thm),theory(equality)],[65,11]),
[iquote('0:SpL:65.1,11.0')] ).
cnf(150,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[2,13]),
[iquote('0:SpR:2.0,13.0')] ).
cnf(152,plain,
equal(addition(addition(u,v),w),addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[6,13]),
[iquote('0:SpR:6.0,13.0')] ).
cnf(158,plain,
equal(addition(one,addition(multiplication(u,star(u)),v)),addition(star(u),v)),
inference(spr,[status(thm),theory(equality)],[7,13]),
[iquote('0:SpR:7.0,13.0')] ).
cnf(161,plain,
equal(addition(star(u),addition(multiplication(strong_iteration(u),zero),v)),addition(strong_iteration(u),v)),
inference(spr,[status(thm),theory(equality)],[12,13]),
[iquote('0:SpR:12.0,13.0')] ).
cnf(166,plain,
equal(addition(u,addition(v,w)),addition(v,addition(u,w))),
inference(rew,[status(thm),theory(equality)],[13,152]),
[iquote('0:Rew:13.0,152.0')] ).
cnf(192,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[150,11]),
[iquote('0:SpL:150.0,11.0')] ).
cnf(197,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[192]),
[iquote('0:Obv:192.0')] ).
cnf(203,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[6,197]),
[iquote('0:SpR:6.0,197.0')] ).
cnf(208,plain,
leq(one,star(u)),
inference(spr,[status(thm),theory(equality)],[8,197]),
[iquote('0:SpR:8.0,197.0')] ).
cnf(226,plain,
equal(addition(multiplication(one,u),multiplication(multiplication(star(v),v),u)),multiplication(star(v),u)),
inference(spr,[status(thm),theory(equality)],[8,16]),
[iquote('0:SpR:8.0,16.0')] ).
cnf(227,plain,
equal(addition(multiplication(one,u),multiplication(multiplication(v,strong_iteration(v)),u)),multiplication(strong_iteration(v),u)),
inference(spr,[status(thm),theory(equality)],[21,16]),
[iquote('0:SpR:21.0,16.0')] ).
cnf(228,plain,
equal(addition(multiplication(one,u),multiplication(multiplication(v,star(v)),u)),multiplication(star(v),u)),
inference(spr,[status(thm),theory(equality)],[7,16]),
[iquote('0:SpR:7.0,16.0')] ).
cnf(229,plain,
equal(addition(multiplication(star(u),v),multiplication(multiplication(strong_iteration(u),zero),v)),multiplication(strong_iteration(u),v)),
inference(spr,[status(thm),theory(equality)],[12,16]),
[iquote('0:SpR:12.0,16.0')] ).
cnf(237,plain,
equal(addition(u,multiplication(star(v),multiplication(v,u))),multiplication(star(v),u)),
inference(rew,[status(thm),theory(equality)],[4,226,14]),
[iquote('0:Rew:4.0,226.0,14.0,226.0')] ).
cnf(238,plain,
equal(addition(u,multiplication(v,multiplication(strong_iteration(v),u))),multiplication(strong_iteration(v),u)),
inference(rew,[status(thm),theory(equality)],[4,227,14]),
[iquote('0:Rew:4.0,227.0,14.0,227.0')] ).
cnf(239,plain,
equal(addition(u,multiplication(v,multiplication(star(v),u))),multiplication(star(v),u)),
inference(rew,[status(thm),theory(equality)],[4,228,14]),
[iquote('0:Rew:4.0,228.0,14.0,228.0')] ).
cnf(240,plain,
equal(addition(multiplication(strong_iteration(u),zero),multiplication(star(u),v)),multiplication(strong_iteration(u),v)),
inference(rew,[status(thm),theory(equality)],[6,229,5,14]),
[iquote('0:Rew:6.0,229.0,5.0,229.0,14.0,229.0')] ).
cnf(257,plain,
leq(multiplication(u,strong_iteration(u)),strong_iteration(u)),
inference(spr,[status(thm),theory(equality)],[21,203]),
[iquote('0:SpR:21.0,203.0')] ).
cnf(258,plain,
leq(multiplication(u,star(u)),star(u)),
inference(spr,[status(thm),theory(equality)],[7,203]),
[iquote('0:SpR:7.0,203.0')] ).
cnf(260,plain,
leq(u,addition(v,addition(w,u))),
inference(spr,[status(thm),theory(equality)],[13,203]),
[iquote('0:SpR:13.0,203.0')] ).
cnf(268,plain,
equal(addition(multiplication(u,v),multiplication(u,zero)),multiplication(u,v)),
inference(spr,[status(thm),theory(equality)],[1,15]),
[iquote('0:SpR:1.0,15.0')] ).
cnf(270,plain,
( ~ leq(u,v)
| equal(addition(multiplication(w,u),multiplication(w,v)),multiplication(w,v)) ),
inference(spr,[status(thm),theory(equality)],[10,15]),
[iquote('0:SpR:10.1,15.0')] ).
cnf(276,plain,
equal(addition(multiplication(u,one),multiplication(u,multiplication(star(v),v))),multiplication(u,star(v))),
inference(spr,[status(thm),theory(equality)],[8,15]),
[iquote('0:SpR:8.0,15.0')] ).
cnf(277,plain,
equal(addition(multiplication(u,one),multiplication(u,multiplication(v,strong_iteration(v)))),multiplication(u,strong_iteration(v))),
inference(spr,[status(thm),theory(equality)],[21,15]),
[iquote('0:SpR:21.0,15.0')] ).
cnf(279,plain,
equal(addition(multiplication(u,star(v)),multiplication(u,multiplication(strong_iteration(v),zero))),multiplication(u,strong_iteration(v))),
inference(spr,[status(thm),theory(equality)],[12,15]),
[iquote('0:SpR:12.0,15.0')] ).
cnf(286,plain,
equal(addition(u,multiplication(u,multiplication(star(v),v))),multiplication(u,star(v))),
inference(rew,[status(thm),theory(equality)],[3,276]),
[iquote('0:Rew:3.0,276.0')] ).
cnf(287,plain,
equal(addition(u,multiplication(u,multiplication(v,strong_iteration(v)))),multiplication(u,strong_iteration(v))),
inference(rew,[status(thm),theory(equality)],[3,277]),
[iquote('0:Rew:3.0,277.0')] ).
cnf(352,plain,
leq(u,addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[6,260]),
[iquote('0:SpR:6.0,260.0')] ).
cnf(382,plain,
leq(one,addition(u,star(v))),
inference(spr,[status(thm),theory(equality)],[8,352]),
[iquote('0:SpR:8.0,352.0')] ).
cnf(407,plain,
( ~ leq(multiplication(u,v),w)
| ~ leq(w,v)
| leq(multiplication(star(u),w),v) ),
inference(spl,[status(thm),theory(equality)],[10,18]),
[iquote('0:SpL:10.1,18.0')] ).
cnf(420,plain,
leq(one,addition(star(u),v)),
inference(spr,[status(thm),theory(equality)],[6,382]),
[iquote('0:SpR:6.0,382.0')] ).
cnf(461,plain,
( ~ leq(addition(u,multiplication(v,w)),v)
| leq(multiplication(u,star(w)),v) ),
inference(spl,[status(thm),theory(equality)],[6,19]),
[iquote('0:SpL:6.0,19.0')] ).
cnf(630,plain,
equal(addition(u,multiplication(u,zero)),u),
inference(spr,[status(thm),theory(equality)],[3,268]),
[iquote('0:SpR:3.0,268.0')] ).
cnf(971,plain,
equal(addition(one,addition(u,multiplication(v,star(v)))),addition(u,star(v))),
inference(spr,[status(thm),theory(equality)],[7,166]),
[iquote('0:SpR:7.0,166.0')] ).
cnf(1946,plain,
( ~ leq(multiplication(u,star(u)),v)
| equal(addition(star(u),v),addition(one,v)) ),
inference(spr,[status(thm),theory(equality)],[10,158]),
[iquote('0:SpR:10.1,158.0')] ).
cnf(2086,plain,
leq(u,addition(v,multiplication(star(w),u))),
inference(spr,[status(thm),theory(equality)],[237,352]),
[iquote('0:SpR:237.0,352.0')] ).
cnf(2091,plain,
leq(one,multiplication(star(u),star(v))),
inference(spr,[status(thm),theory(equality)],[237,420]),
[iquote('0:SpR:237.0,420.0')] ).
cnf(2172,plain,
equal(multiplication(u,multiplication(strong_iteration(u),zero)),multiplication(strong_iteration(u),zero)),
inference(spr,[status(thm),theory(equality)],[238,30]),
[iquote('0:SpR:238.0,30.0')] ).
cnf(2323,plain,
leq(u,star(u)),
inference(spr,[status(thm),theory(equality)],[8,2086]),
[iquote('0:SpR:8.0,2086.0')] ).
cnf(2336,plain,
~ leq(star(strong_iteration(skc2)),strong_iteration(skc2)),
inference(mrr,[status(thm)],[17,2323]),
[iquote('0:MRR:17.0,2323.0')] ).
cnf(2362,plain,
equal(multiplication(star(u),u),multiplication(u,star(u))),
inference(spr,[status(thm),theory(equality)],[286,239]),
[iquote('0:SpR:286.0,239.0')] ).
cnf(3404,plain,
equal(multiplication(star(u),star(star(u))),star(star(u))),
inference(res,[status(thm),theory(equality)],[2091,71]),
[iquote('0:Res:2091.0,71.0')] ).
cnf(3797,plain,
equal(multiplication(star(u),multiplication(strong_iteration(u),zero)),multiplication(strong_iteration(u),multiplication(u,multiplication(strong_iteration(u),zero)))),
inference(spr,[status(thm),theory(equality)],[240,237]),
[iquote('0:SpR:240.0,237.0')] ).
cnf(3832,plain,
equal(multiplication(star(u),multiplication(strong_iteration(u),zero)),multiplication(strong_iteration(u),multiplication(strong_iteration(u),zero))),
inference(rew,[status(thm),theory(equality)],[2172,3797]),
[iquote('0:Rew:2172.0,3797.0')] ).
cnf(4344,plain,
( ~ leq(multiplication(u,strong_iteration(v)),u)
| leq(multiplication(u,star(multiplication(v,strong_iteration(v)))),u) ),
inference(spl,[status(thm),theory(equality)],[287,461]),
[iquote('0:SpL:287.0,461.0')] ).
cnf(6769,plain,
( ~ leq(zero,u)
| equal(addition(star(v),multiplication(strong_iteration(v),u)),addition(strong_iteration(v),multiplication(strong_iteration(v),u))) ),
inference(spr,[status(thm),theory(equality)],[270,161]),
[iquote('0:SpR:270.1,161.0')] ).
cnf(6782,plain,
( ~ leq(one,u)
| equal(addition(v,multiplication(v,u)),multiplication(v,u)) ),
inference(spr,[status(thm),theory(equality)],[3,270]),
[iquote('0:SpR:3.0,270.1')] ).
cnf(6810,plain,
equal(addition(star(u),multiplication(strong_iteration(u),v)),addition(strong_iteration(u),multiplication(strong_iteration(u),v))),
inference(mrr,[status(thm)],[6769,86]),
[iquote('0:MRR:6769.0,86.0')] ).
cnf(7289,plain,
( ~ leq(strong_iteration(u),strong_iteration(u))
| leq(multiplication(star(u),strong_iteration(u)),strong_iteration(u)) ),
inference(res,[status(thm),theory(equality)],[257,407]),
[iquote('0:Res:257.0,407.0')] ).
cnf(7293,plain,
( ~ leq(star(u),star(u))
| leq(multiplication(star(u),star(u)),star(u)) ),
inference(res,[status(thm),theory(equality)],[258,407]),
[iquote('0:Res:258.0,407.0')] ).
cnf(7326,plain,
leq(multiplication(star(u),strong_iteration(u)),strong_iteration(u)),
inference(mrr,[status(thm)],[7289,85]),
[iquote('0:MRR:7289.0,85.0')] ).
cnf(7327,plain,
leq(multiplication(star(u),star(u)),star(u)),
inference(mrr,[status(thm)],[7293,85]),
[iquote('0:MRR:7293.0,85.0')] ).
cnf(7431,plain,
( ~ leq(star(u),star(u))
| leq(multiplication(star(star(u)),star(u)),star(u)) ),
inference(res,[status(thm),theory(equality)],[7327,407]),
[iquote('0:Res:7327.0,407.0')] ).
cnf(7444,plain,
( ~ leq(star(u),star(u))
| leq(star(star(u)),star(u)) ),
inference(rew,[status(thm),theory(equality)],[3404,7431,2362]),
[iquote('0:Rew:3404.0,7431.1,2362.0,7431.1')] ).
cnf(7445,plain,
leq(star(star(u)),star(u)),
inference(mrr,[status(thm)],[7444,85]),
[iquote('0:MRR:7444.0,85.0')] ).
cnf(9736,plain,
equal(addition(multiplication(star(u),star(star(u))),multiplication(star(star(u)),multiplication(strong_iteration(u),zero))),multiplication(star(star(u)),strong_iteration(u))),
inference(spr,[status(thm),theory(equality)],[2362,279]),
[iquote('0:SpR:2362.0,279.0')] ).
cnf(9878,plain,
equal(addition(star(star(u)),multiplication(star(star(u)),multiplication(strong_iteration(u),zero))),multiplication(star(star(u)),strong_iteration(u))),
inference(rew,[status(thm),theory(equality)],[3404,9736]),
[iquote('0:Rew:3404.0,9736.0')] ).
cnf(21553,plain,
( ~ leq(star(u),star(star(u)))
| equal(star(star(u)),star(u)) ),
inference(res,[status(thm),theory(equality)],[7445,115]),
[iquote('0:Res:7445.0,115.0')] ).
cnf(21602,plain,
( ~ leq(strong_iteration(u),multiplication(star(u),strong_iteration(u)))
| equal(multiplication(star(u),strong_iteration(u)),strong_iteration(u)) ),
inference(res,[status(thm),theory(equality)],[7326,115]),
[iquote('0:Res:7326.0,115.0')] ).
cnf(21628,plain,
equal(star(star(u)),star(u)),
inference(mrr,[status(thm)],[21553,2323]),
[iquote('0:MRR:21553.0,2323.0')] ).
cnf(21673,plain,
equal(addition(star(u),multiplication(star(u),multiplication(strong_iteration(u),zero))),multiplication(star(u),strong_iteration(u))),
inference(rew,[status(thm),theory(equality)],[21628,9878]),
[iquote('0:Rew:21628.0,9878.0')] ).
cnf(21705,plain,
equal(multiplication(star(u),strong_iteration(u)),addition(strong_iteration(u),multiplication(strong_iteration(u),multiplication(strong_iteration(u),zero)))),
inference(rew,[status(thm),theory(equality)],[6810,21673,3832]),
[iquote('0:Rew:6810.0,21673.0,3832.0,21673.0')] ).
cnf(21711,plain,
( ~ leq(strong_iteration(u),addition(strong_iteration(u),multiplication(strong_iteration(u),multiplication(strong_iteration(u),zero))))
| equal(addition(strong_iteration(u),multiplication(strong_iteration(u),multiplication(strong_iteration(u),zero))),strong_iteration(u)) ),
inference(rew,[status(thm),theory(equality)],[21705,21602]),
[iquote('0:Rew:21705.0,21602.1,21705.0,21602.0')] ).
cnf(21712,plain,
equal(addition(strong_iteration(u),multiplication(strong_iteration(u),multiplication(strong_iteration(u),zero))),strong_iteration(u)),
inference(mrr,[status(thm)],[21711,197]),
[iquote('0:MRR:21711.0,197.0')] ).
cnf(21713,plain,
equal(multiplication(star(u),strong_iteration(u)),strong_iteration(u)),
inference(rew,[status(thm),theory(equality)],[21712,21705]),
[iquote('0:Rew:21712.0,21705.0')] ).
cnf(22139,plain,
( ~ equal(star(u),u)
| leq(star(u),u) ),
inference(res,[status(thm),theory(equality)],[2323,125]),
[iquote('0:Res:2323.0,125.0')] ).
cnf(22856,plain,
equal(multiplication(strong_iteration(u),strong_iteration(u)),addition(multiplication(strong_iteration(u),zero),strong_iteration(u))),
inference(spr,[status(thm),theory(equality)],[21713,240]),
[iquote('0:SpR:21713.0,240.0')] ).
cnf(22949,plain,
equal(multiplication(strong_iteration(u),strong_iteration(u)),strong_iteration(u)),
inference(rew,[status(thm),theory(equality)],[630,22856,6]),
[iquote('0:Rew:630.0,22856.0,6.0,22856.0')] ).
cnf(25125,plain,
~ equal(star(strong_iteration(skc2)),strong_iteration(skc2)),
inference(res,[status(thm),theory(equality)],[22139,2336]),
[iquote('0:Res:22139.1,2336.0')] ).
cnf(33138,plain,
( ~ leq(one,star(u))
| equal(addition(one,multiplication(u,star(u))),addition(u,star(u))) ),
inference(spr,[status(thm),theory(equality)],[6782,971]),
[iquote('0:SpR:6782.1,971.0')] ).
cnf(33301,plain,
( ~ leq(one,star(u))
| equal(addition(u,star(u)),star(u)) ),
inference(rew,[status(thm),theory(equality)],[7,33138]),
[iquote('0:Rew:7.0,33138.1')] ).
cnf(33302,plain,
equal(addition(u,star(u)),star(u)),
inference(mrr,[status(thm)],[33301,208]),
[iquote('0:MRR:33301.0,208.0')] ).
cnf(121712,plain,
( ~ leq(multiplication(multiplication(u,strong_iteration(u)),strong_iteration(u)),multiplication(u,strong_iteration(u)))
| equal(addition(star(multiplication(u,strong_iteration(u))),multiplication(u,strong_iteration(u))),addition(one,multiplication(u,strong_iteration(u)))) ),
inference(res,[status(thm),theory(equality)],[4344,1946]),
[iquote('0:Res:4344.1,1946.0')] ).
cnf(121769,plain,
( ~ leq(multiplication(u,strong_iteration(u)),multiplication(u,strong_iteration(u)))
| equal(star(multiplication(u,strong_iteration(u))),strong_iteration(u)) ),
inference(rew,[status(thm),theory(equality)],[33302,121712,6,21,22949,14]),
[iquote('0:Rew:33302.0,121712.1,6.0,121712.1,21.0,121712.1,22949.0,121712.0,14.0,121712.0')] ).
cnf(121770,plain,
equal(star(multiplication(u,strong_iteration(u))),strong_iteration(u)),
inference(mrr,[status(thm)],[121769,85]),
[iquote('0:MRR:121769.0,85.0')] ).
cnf(121954,plain,
equal(star(strong_iteration(u)),strong_iteration(u)),
inference(spr,[status(thm),theory(equality)],[121770,21628]),
[iquote('0:SpR:121770.0,21628.0')] ).
cnf(122274,plain,
$false,
inference(unc,[status(thm)],[121954,25125]),
[iquote('0:UnC:121954.0,25125.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE145+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n015.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 : Thu Jun 16 08:02:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 165.56/165.81
% 165.56/165.81 SPASS V 3.9
% 165.56/165.81 SPASS beiseite: Proof found.
% 165.56/165.81 % SZS status Theorem
% 165.56/165.81 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 165.56/165.81 SPASS derived 88959 clauses, backtracked 0 clauses, performed 0 splits and kept 18421 clauses.
% 165.56/165.81 SPASS allocated 168980 KBytes.
% 165.56/165.81 SPASS spent 0:2:45.31 on the problem.
% 165.56/165.81 0:00:00.04 for the input.
% 165.56/165.81 0:00:00.03 for the FLOTTER CNF translation.
% 165.56/165.81 0:00:00.71 for inferences.
% 165.56/165.81 0:00:00.00 for the backtracking.
% 165.56/165.81 0:2:44.17 for the reduction.
% 165.56/165.81
% 165.56/165.81
% 165.56/165.81 Here is a proof with depth 9, length 106 :
% 165.56/165.81 % SZS output start Refutation
% See solution above
% 167.16/167.37 Formulae used in the proof : additive_identity idempotence multiplicative_right_identity multiplicative_left_identity left_annihilation additive_commutativity star_unfold1 star_unfold2 infty_unfold1 order isolation additive_associativity multiplicative_associativity distributivity1 distributivity2 goals star_induction1 star_induction2
% 167.16/167.37
%------------------------------------------------------------------------------