TSTP Solution File: KLE139+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE139+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 02:28:42 EDT 2022
% Result : Theorem 1.44s 1.69s
% Output : Refutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of clauses : 45 ( 31 unt; 0 nHn; 45 RR)
% Number of literals : 59 ( 0 equ; 22 neg)
% Maximal clause size : 2 ( 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('KLE139+2.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,u),u),
file('KLE139+2.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE139+2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE139+2.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(zero,u),zero),
file('KLE139+2.p',unknown),
[] ).
cnf(6,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE139+2.p',unknown),
[] ).
cnf(7,axiom,
equal(addition(one,multiplication(u,star(u))),star(u)),
file('KLE139+2.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(one,multiplication(star(u),u)),star(u)),
file('KLE139+2.p',unknown),
[] ).
cnf(10,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE139+2.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE139+2.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(star(u),multiplication(strong_iteration(u),zero)),strong_iteration(u)),
file('KLE139+2.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE139+2.p',unknown),
[] ).
cnf(14,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE139+2.p',unknown),
[] ).
cnf(15,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE139+2.p',unknown),
[] ).
cnf(16,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE139+2.p',unknown),
[] ).
cnf(20,axiom,
( ~ leq(strong_iteration(skc2),addition(multiplication(strong_iteration(skc2),skc2),one))
| ~ leq(addition(multiplication(strong_iteration(skc3),skc3),one),strong_iteration(skc3)) ),
file('KLE139+2.p',unknown),
[] ).
cnf(22,plain,
( ~ leq(strong_iteration(skc2),addition(one,multiplication(strong_iteration(skc2),skc2)))
| ~ leq(addition(one,multiplication(strong_iteration(skc3),skc3)),strong_iteration(skc3)) ),
inference(rew,[status(thm),theory(equality)],[6,20]),
[iquote('0:Rew:6.0,20.1,6.0,20.0')] ).
cnf(31,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(76,plain,
( ~ equal(u,u)
| leq(u,u) ),
inference(spl,[status(thm),theory(equality)],[2,11]),
[iquote('0:SpL:2.0,11.0')] ).
cnf(80,plain,
( ~ equal(u,u)
| leq(zero,u) ),
inference(spl,[status(thm),theory(equality)],[31,11]),
[iquote('0:SpL:31.0,11.0')] ).
cnf(86,plain,
leq(u,u),
inference(obv,[status(thm),theory(equality)],[76]),
[iquote('0:Obv:76.0')] ).
cnf(87,plain,
leq(zero,u),
inference(obv,[status(thm),theory(equality)],[80]),
[iquote('0:Obv:80.0')] ).
cnf(159,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(162,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(229,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(230,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(240,plain,
equal(addition(u,multiplication(v,multiplication(star(v),u))),multiplication(star(v),u)),
inference(rew,[status(thm),theory(equality)],[4,229,14]),
[iquote('0:Rew:4.0,229.0,14.0,229.0')] ).
cnf(241,plain,
equal(addition(multiplication(strong_iteration(u),zero),multiplication(star(u),v)),multiplication(strong_iteration(u),v)),
inference(rew,[status(thm),theory(equality)],[6,230,5,14]),
[iquote('0:Rew:6.0,230.0,5.0,230.0,14.0,230.0')] ).
cnf(269,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(271,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(277,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(287,plain,
equal(addition(u,multiplication(u,multiplication(star(v),v))),multiplication(u,star(v))),
inference(rew,[status(thm),theory(equality)],[3,277]),
[iquote('0:Rew:3.0,277.0')] ).
cnf(617,plain,
equal(addition(u,multiplication(u,zero)),u),
inference(spr,[status(thm),theory(equality)],[3,269]),
[iquote('0:SpR:3.0,269.0')] ).
cnf(2284,plain,
equal(multiplication(star(u),u),multiplication(u,star(u))),
inference(spr,[status(thm),theory(equality)],[287,240]),
[iquote('0:SpR:287.0,240.0')] ).
cnf(6708,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)],[271,162]),
[iquote('0:SpR:271.1,162.0')] ).
cnf(6746,plain,
equal(addition(star(u),multiplication(strong_iteration(u),v)),addition(strong_iteration(u),multiplication(strong_iteration(u),v))),
inference(mrr,[status(thm)],[6708,87]),
[iquote('0:MRR:6708.0,87.0')] ).
cnf(9782,plain,
equal(addition(multiplication(strong_iteration(u),zero),multiplication(u,star(u))),multiplication(strong_iteration(u),u)),
inference(spr,[status(thm),theory(equality)],[2284,241]),
[iquote('0:SpR:2284.0,241.0')] ).
cnf(9899,plain,
equal(addition(multiplication(u,star(u)),multiplication(strong_iteration(u),zero)),multiplication(strong_iteration(u),u)),
inference(rew,[status(thm),theory(equality)],[6,9782]),
[iquote('0:Rew:6.0,9782.0')] ).
cnf(9900,plain,
( ~ leq(strong_iteration(skc2),addition(one,multiplication(strong_iteration(skc2),skc2)))
| ~ leq(addition(one,addition(multiplication(skc3,star(skc3)),multiplication(strong_iteration(skc3),zero))),strong_iteration(skc3)) ),
inference(rew,[status(thm),theory(equality)],[9899,22]),
[iquote('0:Rew:9899.0,22.1')] ).
cnf(9953,plain,
( ~ leq(strong_iteration(skc2),addition(one,multiplication(strong_iteration(skc2),skc2)))
| ~ leq(addition(star(skc3),multiplication(strong_iteration(skc3),zero)),strong_iteration(skc3)) ),
inference(rew,[status(thm),theory(equality)],[159,9900]),
[iquote('0:Rew:159.0,9900.1')] ).
cnf(9954,plain,
( ~ leq(strong_iteration(skc2),addition(one,addition(multiplication(skc2,star(skc2)),multiplication(strong_iteration(skc2),zero))))
| ~ leq(addition(strong_iteration(skc3),multiplication(strong_iteration(skc3),zero)),strong_iteration(skc3)) ),
inference(rew,[status(thm),theory(equality)],[6746,9953,9899]),
[iquote('0:Rew:6746.0,9953.1,9899.0,9953.0')] ).
cnf(9955,plain,
( ~ leq(strong_iteration(skc2),addition(star(skc2),multiplication(strong_iteration(skc2),zero)))
| ~ leq(strong_iteration(skc3),strong_iteration(skc3)) ),
inference(rew,[status(thm),theory(equality)],[617,9954,159]),
[iquote('0:Rew:617.0,9954.1,159.0,9954.0')] ).
cnf(9956,plain,
( ~ leq(strong_iteration(skc2),addition(strong_iteration(skc2),multiplication(strong_iteration(skc2),zero)))
| ~ leq(strong_iteration(skc3),strong_iteration(skc3)) ),
inference(rew,[status(thm),theory(equality)],[6746,9955]),
[iquote('0:Rew:6746.0,9955.0')] ).
cnf(9957,plain,
( ~ leq(strong_iteration(skc2),strong_iteration(skc2))
| ~ leq(strong_iteration(skc3),strong_iteration(skc3)) ),
inference(rew,[status(thm),theory(equality)],[617,9956]),
[iquote('0:Rew:617.0,9956.0')] ).
cnf(9958,plain,
$false,
inference(mrr,[status(thm)],[9957,86]),
[iquote('0:MRR:9957.0,9957.1,86.0,86.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07 % Problem : KLE139+2 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.07 % Command : run_spass %d %s
% 0.06/0.25 % Computer : n009.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 600
% 0.06/0.25 % DateTime : Thu Jun 16 12:01:52 EDT 2022
% 0.06/0.25 % CPUTime :
% 1.44/1.69
% 1.44/1.69 SPASS V 3.9
% 1.44/1.69 SPASS beiseite: Proof found.
% 1.44/1.69 % SZS status Theorem
% 1.44/1.69 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.44/1.69 SPASS derived 7224 clauses, backtracked 0 clauses, performed 0 splits and kept 1705 clauses.
% 1.44/1.69 SPASS allocated 93259 KBytes.
% 1.44/1.69 SPASS spent 0:00:01.40 on the problem.
% 1.44/1.69 0:00:00.02 for the input.
% 1.44/1.69 0:00:00.02 for the FLOTTER CNF translation.
% 1.44/1.69 0:00:00.05 for inferences.
% 1.44/1.69 0:00:00.00 for the backtracking.
% 1.44/1.69 0:00:01.28 for the reduction.
% 1.44/1.69
% 1.44/1.69
% 1.44/1.69 Here is a proof with depth 3, length 45 :
% 1.44/1.69 % SZS output start Refutation
% See solution above
% 1.44/1.69 Formulae used in the proof : additive_identity idempotence multiplicative_right_identity multiplicative_left_identity left_annihilation additive_commutativity star_unfold1 star_unfold2 order isolation additive_associativity multiplicative_associativity distributivity1 distributivity2 goals
% 1.44/1.69
%------------------------------------------------------------------------------