TSTP Solution File: KLE040+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE040+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 02:28:12 EDT 2022
% Result : Theorem 6.60s 6.83s
% Output : Refutation 6.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of clauses : 60 ( 32 unt; 0 nHn; 60 RR)
% Number of literals : 92 ( 0 equ; 33 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(addition(u,u),u),
file('KLE040+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE040+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE040+1.p',unknown),
[] ).
cnf(7,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE040+1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(multiplication(star(skc1),star(skc1)),star(skc1)),
file('KLE040+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE040+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE040+1.p',unknown),
[] ).
cnf(11,axiom,
leq(addition(one,multiplication(u,star(u))),star(u)),
file('KLE040+1.p',unknown),
[] ).
cnf(12,axiom,
leq(addition(one,multiplication(star(u),u)),star(u)),
file('KLE040+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE040+1.p',unknown),
[] ).
cnf(15,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE040+1.p',unknown),
[] ).
cnf(16,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE040+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ leq(addition(multiplication(u,v),w),v)
| leq(multiplication(star(u),w),v) ),
file('KLE040+1.p',unknown),
[] ).
cnf(51,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.1,7.0')] ).
cnf(59,plain,
( ~ equal(u,u)
| leq(u,u) ),
inference(spl,[status(thm),theory(equality)],[2,10]),
[iquote('0:SpL:2.0,10.0')] ).
cnf(64,plain,
leq(u,u),
inference(obv,[status(thm),theory(equality)],[59]),
[iquote('0:Obv:59.0')] ).
cnf(88,plain,
( ~ leq(u,v)
| ~ leq(v,u)
| equal(v,u) ),
inference(spr,[status(thm),theory(equality)],[51,9]),
[iquote('0:SpR:51.1,9.1')] ).
cnf(108,plain,
( ~ leq(addition(u,v),w)
| equal(addition(u,addition(v,w)),w) ),
inference(spr,[status(thm),theory(equality)],[13,9]),
[iquote('0:SpR:13.0,9.1')] ).
cnf(114,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(116,plain,
equal(addition(addition(u,v),w),addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[7,13]),
[iquote('0:SpR:7.0,13.0')] ).
cnf(124,plain,
equal(addition(u,addition(v,w)),addition(v,addition(u,w))),
inference(rew,[status(thm),theory(equality)],[13,116]),
[iquote('0:Rew:13.0,116.0')] ).
cnf(142,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[114,10]),
[iquote('0:SpL:114.0,10.0')] ).
cnf(146,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[142]),
[iquote('0:Obv:142.0')] ).
cnf(152,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[7,146]),
[iquote('0:SpR:7.0,146.0')] ).
cnf(166,plain,
leq(u,addition(v,addition(w,u))),
inference(spr,[status(thm),theory(equality)],[13,152]),
[iquote('0:SpR:13.0,152.0')] ).
cnf(170,plain,
leq(u,addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[7,166]),
[iquote('0:SpR:7.0,166.0')] ).
cnf(180,plain,
( ~ leq(addition(u,v),w)
| leq(v,w) ),
inference(spr,[status(thm),theory(equality)],[51,166]),
[iquote('0:SpR:51.1,166.0')] ).
cnf(193,plain,
( ~ leq(u,v)
| equal(addition(multiplication(u,w),multiplication(v,w)),multiplication(v,w)) ),
inference(spr,[status(thm),theory(equality)],[9,16]),
[iquote('0:SpR:9.1,16.0')] ).
cnf(222,plain,
( ~ leq(addition(u,v),w)
| leq(u,w) ),
inference(spr,[status(thm),theory(equality)],[51,170]),
[iquote('0:SpR:51.1,170.0')] ).
cnf(333,plain,
( ~ leq(u,v)
| equal(addition(multiplication(w,u),multiplication(w,v)),multiplication(w,v)) ),
inference(spr,[status(thm),theory(equality)],[9,15]),
[iquote('0:SpR:9.1,15.0')] ).
cnf(378,plain,
( ~ leq(multiplication(u,v),w)
| ~ leq(w,v)
| leq(multiplication(star(u),w),v) ),
inference(spl,[status(thm),theory(equality)],[9,17]),
[iquote('0:SpL:9.1,17.0')] ).
cnf(437,plain,
leq(multiplication(u,star(u)),star(u)),
inference(res,[status(thm),theory(equality)],[11,180]),
[iquote('0:Res:11.0,180.0')] ).
cnf(516,plain,
leq(one,star(u)),
inference(res,[status(thm),theory(equality)],[12,222]),
[iquote('0:Res:12.0,222.0')] ).
cnf(1694,plain,
( ~ leq(addition(u,v),w)
| equal(addition(u,w),w) ),
inference(spr,[status(thm),theory(equality)],[108,114]),
[iquote('0:SpR:108.1,114.0')] ).
cnf(1706,plain,
( ~ leq(addition(u,v),w)
| equal(addition(v,addition(u,w)),w) ),
inference(spr,[status(thm),theory(equality)],[108,124]),
[iquote('0:SpR:108.1,124.0')] ).
cnf(1784,plain,
( ~ leq(addition(u,v),w)
| equal(addition(v,w),w) ),
inference(rew,[status(thm),theory(equality)],[1694,1706]),
[iquote('0:Rew:1694.1,1706.1')] ).
cnf(3243,plain,
( ~ leq(one,u)
| equal(addition(v,multiplication(u,v)),multiplication(u,v)) ),
inference(spr,[status(thm),theory(equality)],[4,193]),
[iquote('0:SpR:4.0,193.1')] ).
cnf(3432,plain,
( ~ leq(one,u)
| equal(addition(v,multiplication(v,u)),multiplication(v,u)) ),
inference(spr,[status(thm),theory(equality)],[3,333]),
[iquote('0:SpR:3.0,333.1')] ).
cnf(3612,plain,
( ~ leq(star(u),star(u))
| leq(multiplication(star(u),star(u)),star(u)) ),
inference(res,[status(thm),theory(equality)],[437,378]),
[iquote('0:Res:437.0,378.0')] ).
cnf(3630,plain,
leq(multiplication(star(u),star(u)),star(u)),
inference(mrr,[status(thm)],[3612,64]),
[iquote('0:MRR:3612.0,64.0')] ).
cnf(3662,plain,
( ~ leq(star(u),star(u))
| leq(multiplication(star(star(u)),star(u)),star(u)) ),
inference(res,[status(thm),theory(equality)],[3630,378]),
[iquote('0:Res:3630.0,378.0')] ).
cnf(3677,plain,
leq(multiplication(star(star(u)),star(u)),star(u)),
inference(mrr,[status(thm)],[3662,64]),
[iquote('0:MRR:3662.0,64.0')] ).
cnf(10726,plain,
equal(addition(one,star(u)),star(u)),
inference(res,[status(thm),theory(equality)],[12,1694]),
[iquote('0:Res:12.0,1694.0')] ).
cnf(10770,plain,
equal(addition(multiplication(one,u),multiplication(star(v),u)),multiplication(star(v),u)),
inference(spr,[status(thm),theory(equality)],[10726,16]),
[iquote('0:SpR:10726.0,16.0')] ).
cnf(10816,plain,
( ~ leq(star(u),v)
| leq(one,v) ),
inference(spl,[status(thm),theory(equality)],[10726,222]),
[iquote('0:SpL:10726.0,222.0')] ).
cnf(10872,plain,
equal(addition(u,multiplication(star(v),u)),multiplication(star(v),u)),
inference(rew,[status(thm),theory(equality)],[4,10770]),
[iquote('0:Rew:4.0,10770.0')] ).
cnf(10993,plain,
equal(addition(multiplication(star(u),u),star(u)),star(u)),
inference(res,[status(thm),theory(equality)],[12,1784]),
[iquote('0:Res:12.0,1784.0')] ).
cnf(11015,plain,
equal(addition(star(u),multiplication(star(u),u)),star(u)),
inference(rew,[status(thm),theory(equality)],[7,10993]),
[iquote('0:Rew:7.0,10993.0')] ).
cnf(12018,plain,
( ~ leq(one,u)
| leq(v,multiplication(u,v)) ),
inference(spr,[status(thm),theory(equality)],[3243,146]),
[iquote('0:SpR:3243.1,146.0')] ).
cnf(14642,plain,
( ~ leq(one,u)
| equal(multiplication(star(u),u),star(u)) ),
inference(spr,[status(thm),theory(equality)],[11015,3432]),
[iquote('0:SpR:11015.0,3432.1')] ).
cnf(23288,plain,
( ~ leq(one,u)
| ~ leq(one,star(u))
| leq(u,star(u)) ),
inference(spr,[status(thm),theory(equality)],[14642,12018]),
[iquote('0:SpR:14642.1,12018.1')] ).
cnf(23290,plain,
( ~ leq(one,star(u))
| leq(star(star(u)),star(u)) ),
inference(spr,[status(thm),theory(equality)],[14642,3677]),
[iquote('0:SpR:14642.1,3677.0')] ).
cnf(23334,plain,
leq(star(star(u)),star(u)),
inference(mrr,[status(thm)],[23290,516]),
[iquote('0:MRR:23290.0,516.0')] ).
cnf(23337,plain,
( ~ leq(one,u)
| leq(u,star(u)) ),
inference(mrr,[status(thm)],[23288,516]),
[iquote('0:MRR:23288.1,516.0')] ).
cnf(24459,plain,
( ~ leq(one,u)
| ~ leq(star(u),u)
| equal(star(u),u) ),
inference(res,[status(thm),theory(equality)],[23337,88]),
[iquote('0:Res:23337.1,88.0')] ).
cnf(24492,plain,
( ~ leq(star(u),u)
| equal(star(u),u) ),
inference(mrr,[status(thm)],[24459,10816]),
[iquote('0:MRR:24459.0,10816.1')] ).
cnf(24505,plain,
equal(star(star(u)),star(u)),
inference(res,[status(thm),theory(equality)],[23334,24492]),
[iquote('0:Res:23334.0,24492.0')] ).
cnf(24641,plain,
equal(addition(star(u),multiplication(star(u),star(u))),star(u)),
inference(spr,[status(thm),theory(equality)],[24505,11015]),
[iquote('0:SpR:24505.0,11015.0')] ).
cnf(24734,plain,
equal(multiplication(star(u),star(u)),star(u)),
inference(rew,[status(thm),theory(equality)],[10872,24641]),
[iquote('0:Rew:10872.0,24641.0')] ).
cnf(24735,plain,
$false,
inference(unc,[status(thm)],[24734,8]),
[iquote('0:UnC:24734.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE040+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n011.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 : Thu Jun 16 16:26:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 6.60/6.83
% 6.60/6.83 SPASS V 3.9
% 6.60/6.83 SPASS beiseite: Proof found.
% 6.60/6.83 % SZS status Theorem
% 6.60/6.83 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.60/6.83 SPASS derived 18052 clauses, backtracked 0 clauses, performed 0 splits and kept 3731 clauses.
% 6.60/6.83 SPASS allocated 101866 KBytes.
% 6.60/6.83 SPASS spent 0:00:06.31 on the problem.
% 6.60/6.83 0:00:00.03 for the input.
% 6.60/6.83 0:00:00.03 for the FLOTTER CNF translation.
% 6.60/6.83 0:00:00.13 for inferences.
% 6.60/6.83 0:00:00.00 for the backtracking.
% 6.60/6.83 0:00:06.09 for the reduction.
% 6.60/6.83
% 6.60/6.83
% 6.60/6.83 Here is a proof with depth 11, length 60 :
% 6.60/6.83 % SZS output start Refutation
% See solution above
% 6.60/6.83 Formulae used in the proof : additive_idempotence multiplicative_right_identity multiplicative_left_identity additive_commutativity goals order star_unfold_right star_unfold_left additive_associativity right_distributivity left_distributivity star_induction_left
% 6.60/6.83
%------------------------------------------------------------------------------