TSTP Solution File: KLE143+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE143+1 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Jul 17 02:28:43 EDT 2022
% Result : Theorem 6.44s 6.66s
% Output : Refutation 6.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 18
% Syntax : Number of clauses : 83 ( 64 unt; 0 nHn; 83 RR)
% Number of literals : 104 ( 0 equ; 22 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(u,zero),u),
file('KLE143+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,u),u),
file('KLE143+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE143+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE143+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(zero,u),zero),
file('KLE143+1.p',unknown),
[] ).
cnf(6,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE143+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(multiplication(strong_iteration(skc1),strong_iteration(skc1)),strong_iteration(skc1)),
file('KLE143+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(one,multiplication(u,star(u))),star(u)),
file('KLE143+1.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(one,multiplication(star(u),u)),star(u)),
file('KLE143+1.p',unknown),
[] ).
cnf(10,axiom,
equal(addition(multiplication(u,strong_iteration(u)),one),strong_iteration(u)),
file('KLE143+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE143+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE143+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(star(u),multiplication(strong_iteration(u),zero)),strong_iteration(u)),
file('KLE143+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE143+1.p',unknown),
[] ).
cnf(15,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE143+1.p',unknown),
[] ).
cnf(16,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE143+1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE143+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ leq(addition(multiplication(u,v),w),v)
| leq(multiplication(star(u),w),v) ),
file('KLE143+1.p',unknown),
[] ).
cnf(21,plain,
equal(addition(one,multiplication(u,strong_iteration(u))),strong_iteration(u)),
inference(rew,[status(thm),theory(equality)],[6,10]),
[iquote('0:Rew:6.0,10.0')] ).
cnf(30,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(60,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[11,6]),
[iquote('0:SpR:11.1,6.0')] ).
cnf(66,plain,
( ~ leq(one,multiplication(u,star(u)))
| equal(multiplication(u,star(u)),star(u)) ),
inference(spr,[status(thm),theory(equality)],[11,8]),
[iquote('0:SpR:11.1,8.0')] ).
cnf(75,plain,
( ~ equal(u,u)
| leq(u,u) ),
inference(spl,[status(thm),theory(equality)],[2,12]),
[iquote('0:SpL:2.0,12.0')] ).
cnf(79,plain,
( ~ equal(u,u)
| leq(zero,u) ),
inference(spl,[status(thm),theory(equality)],[30,12]),
[iquote('0:SpL:30.0,12.0')] ).
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)],[60,11]),
[iquote('0:SpR:60.1,11.1')] ).
cnf(135,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[2,14]),
[iquote('0:SpR:2.0,14.0')] ).
cnf(146,plain,
equal(addition(star(u),addition(multiplication(strong_iteration(u),zero),v)),addition(strong_iteration(u),v)),
inference(spr,[status(thm),theory(equality)],[13,14]),
[iquote('0:SpR:13.0,14.0')] ).
cnf(192,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[135,12]),
[iquote('0:SpL:135.0,12.0')] ).
cnf(197,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[192]),
[iquote('0:Obv:192.0')] ).
cnf(213,plain,
equal(addition(multiplication(one,u),multiplication(multiplication(star(v),v),u)),multiplication(star(v),u)),
inference(spr,[status(thm),theory(equality)],[9,17]),
[iquote('0:SpR:9.0,17.0')] ).
cnf(214,plain,
equal(addition(multiplication(one,u),multiplication(multiplication(v,strong_iteration(v)),u)),multiplication(strong_iteration(v),u)),
inference(spr,[status(thm),theory(equality)],[21,17]),
[iquote('0:SpR:21.0,17.0')] ).
cnf(215,plain,
equal(addition(multiplication(one,u),multiplication(multiplication(v,star(v)),u)),multiplication(star(v),u)),
inference(spr,[status(thm),theory(equality)],[8,17]),
[iquote('0:SpR:8.0,17.0')] ).
cnf(216,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)],[13,17]),
[iquote('0:SpR:13.0,17.0')] ).
cnf(224,plain,
equal(addition(u,multiplication(star(v),multiplication(v,u))),multiplication(star(v),u)),
inference(rew,[status(thm),theory(equality)],[4,213,15]),
[iquote('0:Rew:4.0,213.0,15.0,213.0')] ).
cnf(225,plain,
equal(addition(u,multiplication(v,multiplication(strong_iteration(v),u))),multiplication(strong_iteration(v),u)),
inference(rew,[status(thm),theory(equality)],[4,214,15]),
[iquote('0:Rew:4.0,214.0,15.0,214.0')] ).
cnf(226,plain,
equal(addition(u,multiplication(v,multiplication(star(v),u))),multiplication(star(v),u)),
inference(rew,[status(thm),theory(equality)],[4,215,15]),
[iquote('0:Rew:4.0,215.0,15.0,215.0')] ).
cnf(227,plain,
equal(addition(multiplication(strong_iteration(u),zero),multiplication(star(u),v)),multiplication(strong_iteration(u),v)),
inference(rew,[status(thm),theory(equality)],[6,216,5,15]),
[iquote('0:Rew:6.0,216.0,5.0,216.0,15.0,216.0')] ).
cnf(233,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[6,197]),
[iquote('0:SpR:6.0,197.0')] ).
cnf(255,plain,
equal(addition(multiplication(u,v),multiplication(u,zero)),multiplication(u,v)),
inference(spr,[status(thm),theory(equality)],[1,16]),
[iquote('0:SpR:1.0,16.0')] ).
cnf(257,plain,
( ~ leq(u,v)
| equal(addition(multiplication(w,u),multiplication(w,v)),multiplication(w,v)) ),
inference(spr,[status(thm),theory(equality)],[11,16]),
[iquote('0:SpR:11.1,16.0')] ).
cnf(263,plain,
equal(addition(multiplication(u,one),multiplication(u,multiplication(star(v),v))),multiplication(u,star(v))),
inference(spr,[status(thm),theory(equality)],[9,16]),
[iquote('0:SpR:9.0,16.0')] ).
cnf(266,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)],[13,16]),
[iquote('0:SpR:13.0,16.0')] ).
cnf(273,plain,
equal(addition(u,multiplication(u,multiplication(star(v),v))),multiplication(u,star(v))),
inference(rew,[status(thm),theory(equality)],[3,263]),
[iquote('0:Rew:3.0,263.0')] ).
cnf(289,plain,
leq(multiplication(u,strong_iteration(u)),strong_iteration(u)),
inference(spr,[status(thm),theory(equality)],[21,233]),
[iquote('0:SpR:21.0,233.0')] ).
cnf(290,plain,
leq(multiplication(u,star(u)),star(u)),
inference(spr,[status(thm),theory(equality)],[8,233]),
[iquote('0:SpR:8.0,233.0')] ).
cnf(292,plain,
leq(u,addition(v,addition(w,u))),
inference(spr,[status(thm),theory(equality)],[14,233]),
[iquote('0:SpR:14.0,233.0')] ).
cnf(335,plain,
( ~ leq(multiplication(u,v),w)
| ~ leq(w,v)
| leq(multiplication(star(u),w),v) ),
inference(spl,[status(thm),theory(equality)],[11,18]),
[iquote('0:SpL:11.1,18.0')] ).
cnf(370,plain,
leq(u,addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[6,292]),
[iquote('0:SpR:6.0,292.0')] ).
cnf(421,plain,
leq(one,addition(u,star(v))),
inference(spr,[status(thm),theory(equality)],[9,370]),
[iquote('0:SpR:9.0,370.0')] ).
cnf(441,plain,
leq(one,addition(star(u),v)),
inference(spr,[status(thm),theory(equality)],[6,421]),
[iquote('0:SpR:6.0,421.0')] ).
cnf(565,plain,
equal(addition(u,multiplication(u,zero)),u),
inference(spr,[status(thm),theory(equality)],[3,255]),
[iquote('0:SpR:3.0,255.0')] ).
cnf(2090,plain,
leq(u,addition(v,multiplication(star(w),u))),
inference(spr,[status(thm),theory(equality)],[224,370]),
[iquote('0:SpR:224.0,370.0')] ).
cnf(2095,plain,
leq(one,multiplication(star(u),star(v))),
inference(spr,[status(thm),theory(equality)],[224,441]),
[iquote('0:SpR:224.0,441.0')] ).
cnf(2176,plain,
equal(multiplication(u,multiplication(strong_iteration(u),zero)),multiplication(strong_iteration(u),zero)),
inference(spr,[status(thm),theory(equality)],[225,30]),
[iquote('0:SpR:225.0,30.0')] ).
cnf(2265,plain,
leq(u,star(u)),
inference(spr,[status(thm),theory(equality)],[9,2090]),
[iquote('0:SpR:9.0,2090.0')] ).
cnf(2410,plain,
equal(multiplication(star(u),u),multiplication(u,star(u))),
inference(spr,[status(thm),theory(equality)],[273,226]),
[iquote('0:SpR:273.0,226.0')] ).
cnf(3455,plain,
equal(multiplication(star(u),star(star(u))),star(star(u))),
inference(res,[status(thm),theory(equality)],[2095,66]),
[iquote('0:Res:2095.0,66.0')] ).
cnf(3842,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)],[227,224]),
[iquote('0:SpR:227.0,224.0')] ).
cnf(3878,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)],[2176,3842]),
[iquote('0:Rew:2176.0,3842.0')] ).
cnf(6805,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)],[257,146]),
[iquote('0:SpR:257.1,146.0')] ).
cnf(6846,plain,
equal(addition(star(u),multiplication(strong_iteration(u),v)),addition(strong_iteration(u),multiplication(strong_iteration(u),v))),
inference(mrr,[status(thm)],[6805,86]),
[iquote('0:MRR:6805.0,86.0')] ).
cnf(7348,plain,
( ~ leq(strong_iteration(u),strong_iteration(u))
| leq(multiplication(star(u),strong_iteration(u)),strong_iteration(u)) ),
inference(res,[status(thm),theory(equality)],[289,335]),
[iquote('0:Res:289.0,335.0')] ).
cnf(7350,plain,
( ~ leq(star(u),star(u))
| leq(multiplication(star(u),star(u)),star(u)) ),
inference(res,[status(thm),theory(equality)],[290,335]),
[iquote('0:Res:290.0,335.0')] ).
cnf(7387,plain,
leq(multiplication(star(u),strong_iteration(u)),strong_iteration(u)),
inference(mrr,[status(thm)],[7348,85]),
[iquote('0:MRR:7348.0,85.0')] ).
cnf(7388,plain,
leq(multiplication(star(u),star(u)),star(u)),
inference(mrr,[status(thm)],[7350,85]),
[iquote('0:MRR:7350.0,85.0')] ).
cnf(7494,plain,
( ~ leq(star(u),star(u))
| leq(multiplication(star(star(u)),star(u)),star(u)) ),
inference(res,[status(thm),theory(equality)],[7388,335]),
[iquote('0:Res:7388.0,335.0')] ).
cnf(7507,plain,
( ~ leq(star(u),star(u))
| leq(star(star(u)),star(u)) ),
inference(rew,[status(thm),theory(equality)],[3455,7494,2410]),
[iquote('0:Rew:3455.0,7494.1,2410.0,7494.1')] ).
cnf(7508,plain,
leq(star(star(u)),star(u)),
inference(mrr,[status(thm)],[7507,85]),
[iquote('0:MRR:7507.0,85.0')] ).
cnf(9693,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)],[2410,266]),
[iquote('0:SpR:2410.0,266.0')] ).
cnf(9835,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)],[3455,9693]),
[iquote('0:Rew:3455.0,9693.0')] ).
cnf(22672,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)],[7387,115]),
[iquote('0:Res:7387.0,115.0')] ).
cnf(22692,plain,
( ~ leq(star(u),star(star(u)))
| equal(star(star(u)),star(u)) ),
inference(res,[status(thm),theory(equality)],[7508,115]),
[iquote('0:Res:7508.0,115.0')] ).
cnf(22720,plain,
equal(star(star(u)),star(u)),
inference(mrr,[status(thm)],[22692,2265]),
[iquote('0:MRR:22692.0,2265.0')] ).
cnf(22776,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)],[22720,9835]),
[iquote('0:Rew:22720.0,9835.0')] ).
cnf(22815,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)],[6846,22776,3878]),
[iquote('0:Rew:6846.0,22776.0,3878.0,22776.0')] ).
cnf(22822,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)],[22815,22672]),
[iquote('0:Rew:22815.0,22672.1,22815.0,22672.0')] ).
cnf(22823,plain,
equal(addition(strong_iteration(u),multiplication(strong_iteration(u),multiplication(strong_iteration(u),zero))),strong_iteration(u)),
inference(mrr,[status(thm)],[22822,197]),
[iquote('0:MRR:22822.0,197.0')] ).
cnf(22824,plain,
equal(multiplication(star(u),strong_iteration(u)),strong_iteration(u)),
inference(rew,[status(thm),theory(equality)],[22823,22815]),
[iquote('0:Rew:22823.0,22815.0')] ).
cnf(25761,plain,
equal(multiplication(strong_iteration(u),strong_iteration(u)),addition(multiplication(strong_iteration(u),zero),strong_iteration(u))),
inference(spr,[status(thm),theory(equality)],[22824,227]),
[iquote('0:SpR:22824.0,227.0')] ).
cnf(25852,plain,
equal(multiplication(strong_iteration(u),strong_iteration(u)),strong_iteration(u)),
inference(rew,[status(thm),theory(equality)],[565,25761,6]),
[iquote('0:Rew:565.0,25761.0,6.0,25761.0')] ).
cnf(25853,plain,
$false,
inference(unc,[status(thm)],[25852,7]),
[iquote('0:UnC:25852.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KLE143+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 12:25:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 6.44/6.66
% 6.44/6.66 SPASS V 3.9
% 6.44/6.66 SPASS beiseite: Proof found.
% 6.44/6.66 % SZS status Theorem
% 6.44/6.66 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.44/6.66 SPASS derived 19059 clauses, backtracked 0 clauses, performed 0 splits and kept 4111 clauses.
% 6.44/6.66 SPASS allocated 105117 KBytes.
% 6.44/6.66 SPASS spent 0:00:06.28 on the problem.
% 6.44/6.66 0:00:00.04 for the input.
% 6.44/6.66 0:00:00.03 for the FLOTTER CNF translation.
% 6.44/6.66 0:00:00.13 for inferences.
% 6.44/6.66 0:00:00.00 for the backtracking.
% 6.44/6.66 0:00:06.04 for the reduction.
% 6.44/6.66
% 6.44/6.66
% 6.44/6.66 Here is a proof with depth 9, length 83 :
% 6.44/6.66 % SZS output start Refutation
% See solution above
% 6.54/6.79 Formulae used in the proof : additive_identity idempotence multiplicative_right_identity multiplicative_left_identity left_annihilation additive_commutativity goals star_unfold1 star_unfold2 infty_unfold1 order isolation additive_associativity multiplicative_associativity distributivity1 distributivity2 star_induction1
% 6.54/6.79
%------------------------------------------------------------------------------