TSTP Solution File: KLE143+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE143+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 02:28:44 EDT 2022
% Result : Theorem 5.44s 5.62s
% Output : Refutation 5.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 19
% Syntax : Number of clauses : 87 ( 66 unt; 0 nHn; 87 RR)
% Number of literals : 110 ( 0 equ; 26 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('KLE143+2.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,u),u),
file('KLE143+2.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE143+2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE143+2.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(zero,u),zero),
file('KLE143+2.p',unknown),
[] ).
cnf(6,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE143+2.p',unknown),
[] ).
cnf(7,axiom,
equal(addition(one,multiplication(u,star(u))),star(u)),
file('KLE143+2.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(one,multiplication(star(u),u)),star(u)),
file('KLE143+2.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(multiplication(u,strong_iteration(u)),one),strong_iteration(u)),
file('KLE143+2.p',unknown),
[] ).
cnf(10,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE143+2.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE143+2.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(star(u),multiplication(strong_iteration(u),zero)),strong_iteration(u)),
file('KLE143+2.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE143+2.p',unknown),
[] ).
cnf(14,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE143+2.p',unknown),
[] ).
cnf(15,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE143+2.p',unknown),
[] ).
cnf(16,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE143+2.p',unknown),
[] ).
cnf(17,axiom,
( ~ leq(addition(multiplication(u,v),w),v)
| leq(multiplication(star(u),w),v) ),
file('KLE143+2.p',unknown),
[] ).
cnf(19,axiom,
( ~ leq(u,addition(multiplication(v,u),w))
| leq(u,multiplication(strong_iteration(v),w)) ),
file('KLE143+2.p',unknown),
[] ).
cnf(20,axiom,
( ~ leq(strong_iteration(skc3),multiplication(strong_iteration(skc3),strong_iteration(skc3)))
| ~ leq(multiplication(strong_iteration(skc2),strong_iteration(skc2)),strong_iteration(skc2)) ),
file('KLE143+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(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(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(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(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(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(341,plain,
( ~ leq(multiplication(u,v),w)
| ~ leq(w,v)
| leq(multiplication(star(u),w),v) ),
inference(spl,[status(thm),theory(equality)],[10,17]),
[iquote('0:SpL:10.1,17.0')] ).
cnf(370,plain,
leq(u,addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[6,260]),
[iquote('0:SpR:6.0,260.0')] ).
cnf(400,plain,
leq(one,addition(u,star(v))),
inference(spr,[status(thm),theory(equality)],[8,370]),
[iquote('0:SpR:8.0,370.0')] ).
cnf(441,plain,
leq(one,addition(star(u),v)),
inference(spr,[status(thm),theory(equality)],[6,400]),
[iquote('0:SpR:6.0,400.0')] ).
cnf(486,plain,
leq(u,multiplication(strong_iteration(v),u)),
inference(res,[status(thm),theory(equality)],[203,19]),
[iquote('0:Res:203.0,19.0')] ).
cnf(492,plain,
~ leq(multiplication(strong_iteration(skc2),strong_iteration(skc2)),strong_iteration(skc2)),
inference(mrr,[status(thm)],[20,486]),
[iquote('0:MRR:20.0,486.0')] ).
cnf(614,plain,
equal(addition(u,multiplication(u,zero)),u),
inference(spr,[status(thm),theory(equality)],[3,268]),
[iquote('0:SpR:3.0,268.0')] ).
cnf(1943,plain,
leq(u,addition(v,multiplication(star(w),u))),
inference(spr,[status(thm),theory(equality)],[237,370]),
[iquote('0:SpR:237.0,370.0')] ).
cnf(1948,plain,
leq(one,multiplication(star(u),star(v))),
inference(spr,[status(thm),theory(equality)],[237,441]),
[iquote('0:SpR:237.0,441.0')] ).
cnf(2031,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(2126,plain,
leq(u,star(u)),
inference(spr,[status(thm),theory(equality)],[8,1943]),
[iquote('0:SpR:8.0,1943.0')] ).
cnf(2275,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(3329,plain,
equal(multiplication(star(u),star(star(u))),star(star(u))),
inference(res,[status(thm),theory(equality)],[1948,71]),
[iquote('0:Res:1948.0,71.0')] ).
cnf(3735,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(3771,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)],[2031,3735]),
[iquote('0:Rew:2031.0,3735.0')] ).
cnf(6699,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(6737,plain,
equal(addition(star(u),multiplication(strong_iteration(u),v)),addition(strong_iteration(u),multiplication(strong_iteration(u),v))),
inference(mrr,[status(thm)],[6699,86]),
[iquote('0:MRR:6699.0,86.0')] ).
cnf(7345,plain,
( ~ leq(strong_iteration(u),strong_iteration(u))
| leq(multiplication(star(u),strong_iteration(u)),strong_iteration(u)) ),
inference(res,[status(thm),theory(equality)],[257,341]),
[iquote('0:Res:257.0,341.0')] ).
cnf(7347,plain,
( ~ leq(star(u),star(u))
| leq(multiplication(star(u),star(u)),star(u)) ),
inference(res,[status(thm),theory(equality)],[258,341]),
[iquote('0:Res:258.0,341.0')] ).
cnf(7385,plain,
leq(multiplication(star(u),strong_iteration(u)),strong_iteration(u)),
inference(mrr,[status(thm)],[7345,85]),
[iquote('0:MRR:7345.0,85.0')] ).
cnf(7386,plain,
leq(multiplication(star(u),star(u)),star(u)),
inference(mrr,[status(thm)],[7347,85]),
[iquote('0:MRR:7347.0,85.0')] ).
cnf(7646,plain,
( ~ leq(star(u),star(u))
| leq(multiplication(star(star(u)),star(u)),star(u)) ),
inference(res,[status(thm),theory(equality)],[7386,341]),
[iquote('0:Res:7386.0,341.0')] ).
cnf(7663,plain,
( ~ leq(star(u),star(u))
| leq(star(star(u)),star(u)) ),
inference(rew,[status(thm),theory(equality)],[3329,7646,2275]),
[iquote('0:Rew:3329.0,7646.1,2275.0,7646.1')] ).
cnf(7664,plain,
leq(star(star(u)),star(u)),
inference(mrr,[status(thm)],[7663,85]),
[iquote('0:MRR:7663.0,85.0')] ).
cnf(9757,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)],[2275,279]),
[iquote('0:SpR:2275.0,279.0')] ).
cnf(9901,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)],[3329,9757]),
[iquote('0:Rew:3329.0,9757.0')] ).
cnf(22847,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)],[7385,115]),
[iquote('0:Res:7385.0,115.0')] ).
cnf(22876,plain,
( ~ leq(star(u),star(star(u)))
| equal(star(star(u)),star(u)) ),
inference(res,[status(thm),theory(equality)],[7664,115]),
[iquote('0:Res:7664.0,115.0')] ).
cnf(22903,plain,
equal(star(star(u)),star(u)),
inference(mrr,[status(thm)],[22876,2126]),
[iquote('0:MRR:22876.0,2126.0')] ).
cnf(22960,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)],[22903,9901]),
[iquote('0:Rew:22903.0,9901.0')] ).
cnf(23001,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)],[6737,22960,3771]),
[iquote('0:Rew:6737.0,22960.0,3771.0,22960.0')] ).
cnf(23008,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)],[23001,22847]),
[iquote('0:Rew:23001.0,22847.1,23001.0,22847.0')] ).
cnf(23009,plain,
equal(addition(strong_iteration(u),multiplication(strong_iteration(u),multiplication(strong_iteration(u),zero))),strong_iteration(u)),
inference(mrr,[status(thm)],[23008,197]),
[iquote('0:MRR:23008.0,197.0')] ).
cnf(23010,plain,
equal(multiplication(star(u),strong_iteration(u)),strong_iteration(u)),
inference(rew,[status(thm),theory(equality)],[23009,23001]),
[iquote('0:Rew:23009.0,23001.0')] ).
cnf(23410,plain,
equal(multiplication(strong_iteration(u),strong_iteration(u)),addition(multiplication(strong_iteration(u),zero),strong_iteration(u))),
inference(spr,[status(thm),theory(equality)],[23010,240]),
[iquote('0:SpR:23010.0,240.0')] ).
cnf(23502,plain,
equal(multiplication(strong_iteration(u),strong_iteration(u)),strong_iteration(u)),
inference(rew,[status(thm),theory(equality)],[614,23410,6]),
[iquote('0:Rew:614.0,23410.0,6.0,23410.0')] ).
cnf(23503,plain,
~ leq(strong_iteration(skc2),strong_iteration(skc2)),
inference(rew,[status(thm),theory(equality)],[23502,492]),
[iquote('0:Rew:23502.0,492.0')] ).
cnf(23510,plain,
$false,
inference(mrr,[status(thm)],[23503,85]),
[iquote('0:MRR:23503.0,85.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE143+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n008.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 07:14:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 5.44/5.62
% 5.44/5.62 SPASS V 3.9
% 5.44/5.62 SPASS beiseite: Proof found.
% 5.44/5.62 % SZS status Theorem
% 5.44/5.62 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.44/5.62 SPASS derived 17251 clauses, backtracked 0 clauses, performed 0 splits and kept 3755 clauses.
% 5.44/5.62 SPASS allocated 103910 KBytes.
% 5.44/5.62 SPASS spent 0:00:05.26 on the problem.
% 5.44/5.62 0:00:00.03 for the input.
% 5.44/5.62 0:00:00.03 for the FLOTTER CNF translation.
% 5.44/5.62 0:00:00.11 for inferences.
% 5.44/5.62 0:00:00.00 for the backtracking.
% 5.44/5.62 0:00:05.05 for the reduction.
% 5.44/5.62
% 5.44/5.62
% 5.44/5.62 Here is a proof with depth 9, length 87 :
% 5.44/5.62 % SZS output start Refutation
% See solution above
% 5.52/5.73 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 star_induction1 infty_coinduction goals
% 5.52/5.73
%------------------------------------------------------------------------------