TSTP Solution File: KLE139+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE139+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 02:28:41 EDT 2022
% Result : Theorem 2.33s 2.55s
% Output : Refutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of clauses : 40 ( 35 unt; 0 nHn; 40 RR)
% Number of literals : 45 ( 0 equ; 11 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(u,zero),u),
file('KLE139+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE139+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE139+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(zero,u),zero),
file('KLE139+1.p',unknown),
[] ).
cnf(6,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE139+1.p',unknown),
[] ).
cnf(7,axiom,
equal(addition(one,multiplication(u,star(u))),star(u)),
file('KLE139+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(one,multiplication(star(u),u)),star(u)),
file('KLE139+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE139+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE139+1.p',unknown),
[] ).
cnf(12,axiom,
~ equal(addition(multiplication(strong_iteration(skc1),skc1),one),strong_iteration(skc1)),
file('KLE139+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(star(u),multiplication(strong_iteration(u),zero)),strong_iteration(u)),
file('KLE139+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE139+1.p',unknown),
[] ).
cnf(15,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE139+1.p',unknown),
[] ).
cnf(16,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE139+1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE139+1.p',unknown),
[] ).
cnf(22,plain,
~ equal(addition(one,multiplication(strong_iteration(skc1),skc1)),strong_iteration(skc1)),
inference(rew,[status(thm),theory(equality)],[6,12]),
[iquote('0:Rew:6.0,12.0')] ).
cnf(31,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(80,plain,
( ~ equal(u,u)
| leq(zero,u) ),
inference(spl,[status(thm),theory(equality)],[31,11]),
[iquote('0:SpL:31.0,11.0')] ).
cnf(87,plain,
leq(zero,u),
inference(obv,[status(thm),theory(equality)],[80]),
[iquote('0:Obv:80.0')] ).
cnf(169,plain,
equal(addition(one,addition(multiplication(u,star(u)),v)),addition(star(u),v)),
inference(spr,[status(thm),theory(equality)],[7,14]),
[iquote('0:SpR:7.0,14.0')] ).
cnf(172,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(239,plain,
equal(addition(multiplication(one,u),multiplication(multiplication(v,star(v)),u)),multiplication(star(v),u)),
inference(spr,[status(thm),theory(equality)],[7,17]),
[iquote('0:SpR:7.0,17.0')] ).
cnf(240,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(251,plain,
equal(addition(u,multiplication(v,multiplication(star(v),u))),multiplication(star(v),u)),
inference(rew,[status(thm),theory(equality)],[4,239,15]),
[iquote('0:Rew:4.0,239.0,15.0,239.0')] ).
cnf(252,plain,
equal(addition(multiplication(strong_iteration(u),zero),multiplication(star(u),v)),multiplication(strong_iteration(u),v)),
inference(rew,[status(thm),theory(equality)],[6,240,5,15]),
[iquote('0:Rew:6.0,240.0,5.0,240.0,15.0,240.0')] ).
cnf(304,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(306,plain,
( ~ leq(u,v)
| equal(addition(multiplication(w,u),multiplication(w,v)),multiplication(w,v)) ),
inference(spr,[status(thm),theory(equality)],[10,16]),
[iquote('0:SpR:10.1,16.0')] ).
cnf(312,plain,
equal(addition(multiplication(u,one),multiplication(u,multiplication(star(v),v))),multiplication(u,star(v))),
inference(spr,[status(thm),theory(equality)],[8,16]),
[iquote('0:SpR:8.0,16.0')] ).
cnf(327,plain,
equal(addition(u,multiplication(u,multiplication(star(v),v))),multiplication(u,star(v))),
inference(rew,[status(thm),theory(equality)],[3,312]),
[iquote('0:Rew:3.0,312.0')] ).
cnf(601,plain,
equal(addition(u,multiplication(u,zero)),u),
inference(spr,[status(thm),theory(equality)],[3,304]),
[iquote('0:SpR:3.0,304.0')] ).
cnf(2429,plain,
equal(multiplication(star(u),u),multiplication(u,star(u))),
inference(spr,[status(thm),theory(equality)],[327,251]),
[iquote('0:SpR:327.0,251.0')] ).
cnf(7081,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)],[306,172]),
[iquote('0:SpR:306.1,172.0')] ).
cnf(7119,plain,
equal(addition(star(u),multiplication(strong_iteration(u),v)),addition(strong_iteration(u),multiplication(strong_iteration(u),v))),
inference(mrr,[status(thm)],[7081,87]),
[iquote('0:MRR:7081.0,87.0')] ).
cnf(13010,plain,
equal(addition(multiplication(strong_iteration(u),zero),multiplication(u,star(u))),multiplication(strong_iteration(u),u)),
inference(spr,[status(thm),theory(equality)],[2429,252]),
[iquote('0:SpR:2429.0,252.0')] ).
cnf(13162,plain,
equal(addition(multiplication(u,star(u)),multiplication(strong_iteration(u),zero)),multiplication(strong_iteration(u),u)),
inference(rew,[status(thm),theory(equality)],[6,13010]),
[iquote('0:Rew:6.0,13010.0')] ).
cnf(13163,plain,
~ equal(addition(one,addition(multiplication(skc1,star(skc1)),multiplication(strong_iteration(skc1),zero))),strong_iteration(skc1)),
inference(rew,[status(thm),theory(equality)],[13162,22]),
[iquote('0:Rew:13162.0,22.0')] ).
cnf(13171,plain,
~ equal(addition(star(skc1),multiplication(strong_iteration(skc1),zero)),strong_iteration(skc1)),
inference(rew,[status(thm),theory(equality)],[169,13163]),
[iquote('0:Rew:169.0,13163.0')] ).
cnf(13172,plain,
~ equal(addition(strong_iteration(skc1),multiplication(strong_iteration(skc1),zero)),strong_iteration(skc1)),
inference(rew,[status(thm),theory(equality)],[7119,13171]),
[iquote('0:Rew:7119.0,13171.0')] ).
cnf(13173,plain,
~ equal(strong_iteration(skc1),strong_iteration(skc1)),
inference(rew,[status(thm),theory(equality)],[601,13172]),
[iquote('0:Rew:601.0,13172.0')] ).
cnf(13174,plain,
$false,
inference(obv,[status(thm),theory(equality)],[13173]),
[iquote('0:Obv:13173.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE139+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 09:23:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.33/2.55
% 2.33/2.55 SPASS V 3.9
% 2.33/2.55 SPASS beiseite: Proof found.
% 2.33/2.55 % SZS status Theorem
% 2.33/2.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.33/2.55 SPASS derived 9510 clauses, backtracked 0 clauses, performed 0 splits and kept 2166 clauses.
% 2.33/2.55 SPASS allocated 97174 KBytes.
% 2.33/2.55 SPASS spent 0:00:02.15 on the problem.
% 2.33/2.55 0:00:00.04 for the input.
% 2.33/2.55 0:00:00.03 for the FLOTTER CNF translation.
% 2.33/2.55 0:00:00.06 for inferences.
% 2.33/2.55 0:00:00.00 for the backtracking.
% 2.33/2.55 0:00:01.99 for the reduction.
% 2.33/2.55
% 2.33/2.55
% 2.33/2.55 Here is a proof with depth 3, length 40 :
% 2.33/2.55 % SZS output start Refutation
% See solution above
% 2.33/2.55 Formulae used in the proof : additive_identity multiplicative_right_identity multiplicative_left_identity left_annihilation additive_commutativity star_unfold1 star_unfold2 order goals isolation additive_associativity multiplicative_associativity distributivity1 distributivity2
% 2.33/2.55
%------------------------------------------------------------------------------