TSTP Solution File: KLE140+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE140+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 02:28:42 EDT 2022
% Result : Theorem 244.61s 244.82s
% Output : Refutation 244.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of clauses : 66 ( 52 unt; 0 nHn; 66 RR)
% Number of literals : 80 ( 0 equ; 15 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,
leq(skc2,skc3),
file('KLE140+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,zero),u),
file('KLE140+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE140+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE140+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE140+1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiplication(zero,u),zero),
file('KLE140+1.p',unknown),
[] ).
cnf(7,axiom,
~ leq(strong_iteration(skc2),strong_iteration(skc3)),
file('KLE140+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE140+1.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(one,multiplication(u,star(u))),star(u)),
file('KLE140+1.p',unknown),
[] ).
cnf(10,axiom,
equal(addition(one,multiplication(star(u),u)),star(u)),
file('KLE140+1.p',unknown),
[] ).
cnf(11,axiom,
equal(addition(multiplication(u,strong_iteration(u)),one),strong_iteration(u)),
file('KLE140+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE140+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE140+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(star(u),multiplication(strong_iteration(u),zero)),strong_iteration(u)),
file('KLE140+1.p',unknown),
[] ).
cnf(15,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE140+1.p',unknown),
[] ).
cnf(16,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE140+1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE140+1.p',unknown),
[] ).
cnf(18,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE140+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ leq(u,addition(multiplication(v,u),w))
| leq(u,multiplication(strong_iteration(v),w)) ),
file('KLE140+1.p',unknown),
[] ).
cnf(22,plain,
equal(addition(one,multiplication(u,strong_iteration(u))),strong_iteration(u)),
inference(rew,[status(thm),theory(equality)],[8,11]),
[iquote('0:Rew:8.0,11.0')] ).
cnf(23,plain,
equal(addition(skc2,skc3),skc3),
inference(res,[status(thm),theory(equality)],[1,12]),
[iquote('0:Res:1.0,12.0')] ).
cnf(34,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[8,2]),
[iquote('0:SpR:8.0,2.0')] ).
cnf(70,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[12,8]),
[iquote('0:SpR:12.1,8.0')] ).
cnf(81,plain,
( ~ equal(u,u)
| leq(u,u) ),
inference(spl,[status(thm),theory(equality)],[3,13]),
[iquote('0:SpL:3.0,13.0')] ).
cnf(92,plain,
leq(u,u),
inference(obv,[status(thm),theory(equality)],[81]),
[iquote('0:Obv:81.0')] ).
cnf(161,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[3,15]),
[iquote('0:SpR:3.0,15.0')] ).
cnf(162,plain,
( ~ leq(u,v)
| equal(addition(u,addition(v,w)),addition(v,w)) ),
inference(spr,[status(thm),theory(equality)],[12,15]),
[iquote('0:SpR:12.1,15.0')] ).
cnf(163,plain,
equal(addition(addition(u,v),w),addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[8,15]),
[iquote('0:SpR:8.0,15.0')] ).
cnf(168,plain,
equal(addition(one,addition(multiplication(u,strong_iteration(u)),v)),addition(strong_iteration(u),v)),
inference(spr,[status(thm),theory(equality)],[22,15]),
[iquote('0:SpR:22.0,15.0')] ).
cnf(177,plain,
equal(addition(u,addition(v,w)),addition(v,addition(u,w))),
inference(rew,[status(thm),theory(equality)],[15,163]),
[iquote('0:Rew:15.0,163.0')] ).
cnf(207,plain,
equal(addition(multiplication(skc2,u),multiplication(skc3,u)),multiplication(skc3,u)),
inference(spr,[status(thm),theory(equality)],[23,18]),
[iquote('0:SpR:23.0,18.0')] ).
cnf(217,plain,
equal(addition(multiplication(one,u),multiplication(multiplication(v,strong_iteration(v)),u)),multiplication(strong_iteration(v),u)),
inference(spr,[status(thm),theory(equality)],[22,18]),
[iquote('0:SpR:22.0,18.0')] ).
cnf(218,plain,
equal(addition(multiplication(one,u),multiplication(multiplication(v,star(v)),u)),multiplication(star(v),u)),
inference(spr,[status(thm),theory(equality)],[9,18]),
[iquote('0:SpR:9.0,18.0')] ).
cnf(221,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)],[14,18]),
[iquote('0:SpR:14.0,18.0')] ).
cnf(232,plain,
equal(addition(u,multiplication(v,multiplication(strong_iteration(v),u))),multiplication(strong_iteration(v),u)),
inference(rew,[status(thm),theory(equality)],[5,217,16]),
[iquote('0:Rew:5.0,217.0,16.0,217.0')] ).
cnf(233,plain,
equal(addition(u,multiplication(v,multiplication(star(v),u))),multiplication(star(v),u)),
inference(rew,[status(thm),theory(equality)],[5,218,16]),
[iquote('0:Rew:5.0,218.0,16.0,218.0')] ).
cnf(234,plain,
equal(addition(multiplication(strong_iteration(u),zero),multiplication(star(u),v)),multiplication(strong_iteration(u),v)),
inference(rew,[status(thm),theory(equality)],[8,221,6,16]),
[iquote('0:Rew:8.0,221.0,6.0,221.0,16.0,221.0')] ).
cnf(266,plain,
equal(addition(multiplication(u,one),multiplication(u,multiplication(star(v),v))),multiplication(u,star(v))),
inference(spr,[status(thm),theory(equality)],[10,17]),
[iquote('0:SpR:10.0,17.0')] ).
cnf(267,plain,
equal(addition(multiplication(u,one),multiplication(u,multiplication(v,strong_iteration(v)))),multiplication(u,strong_iteration(v))),
inference(spr,[status(thm),theory(equality)],[22,17]),
[iquote('0:SpR:22.0,17.0')] ).
cnf(271,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)],[14,17]),
[iquote('0:SpR:14.0,17.0')] ).
cnf(280,plain,
equal(addition(u,multiplication(u,multiplication(star(v),v))),multiplication(u,star(v))),
inference(rew,[status(thm),theory(equality)],[4,266]),
[iquote('0:Rew:4.0,266.0')] ).
cnf(281,plain,
equal(addition(u,multiplication(u,multiplication(v,strong_iteration(v)))),multiplication(u,strong_iteration(v))),
inference(rew,[status(thm),theory(equality)],[4,267]),
[iquote('0:Rew:4.0,267.0')] ).
cnf(533,plain,
( ~ leq(u,addition(v,multiplication(w,u)))
| leq(u,multiplication(strong_iteration(w),v)) ),
inference(spl,[status(thm),theory(equality)],[8,21]),
[iquote('0:SpL:8.0,21.0')] ).
cnf(643,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[161,13]),
[iquote('0:SpL:161.0,13.0')] ).
cnf(653,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[643]),
[iquote('0:Obv:643.0')] ).
cnf(1313,plain,
equal(addition(one,addition(u,multiplication(v,strong_iteration(v)))),addition(u,strong_iteration(v))),
inference(spr,[status(thm),theory(equality)],[22,177]),
[iquote('0:SpR:22.0,177.0')] ).
cnf(2094,plain,
( ~ leq(u,multiplication(v,strong_iteration(v)))
| equal(addition(one,multiplication(v,strong_iteration(v))),addition(strong_iteration(v),u)) ),
inference(spr,[status(thm),theory(equality)],[70,168]),
[iquote('0:SpR:70.1,168.0')] ).
cnf(2125,plain,
( ~ leq(u,multiplication(v,strong_iteration(v)))
| equal(addition(strong_iteration(v),u),strong_iteration(v)) ),
inference(rew,[status(thm),theory(equality)],[22,2094]),
[iquote('0:Rew:22.0,2094.1')] ).
cnf(2454,plain,
equal(multiplication(u,multiplication(strong_iteration(u),zero)),multiplication(strong_iteration(u),zero)),
inference(spr,[status(thm),theory(equality)],[232,34]),
[iquote('0:SpR:232.0,34.0')] ).
cnf(2709,plain,
equal(multiplication(star(u),u),multiplication(u,star(u))),
inference(spr,[status(thm),theory(equality)],[280,233]),
[iquote('0:SpR:280.0,233.0')] ).
cnf(3363,plain,
( ~ leq(u,one)
| equal(addition(u,addition(strong_iteration(v),w)),addition(strong_iteration(v),w)) ),
inference(spr,[status(thm),theory(equality)],[168,162]),
[iquote('0:SpR:168.0,162.1')] ).
cnf(4950,plain,
( ~ leq(multiplication(u,strong_iteration(u)),multiplication(v,strong_iteration(u)))
| leq(multiplication(u,strong_iteration(u)),multiplication(strong_iteration(v),v)) ),
inference(spl,[status(thm),theory(equality)],[281,533]),
[iquote('0:SpL:281.0,533.0')] ).
cnf(11370,plain,
equal(addition(multiplication(strong_iteration(u),zero),multiplication(u,star(u))),multiplication(strong_iteration(u),u)),
inference(spr,[status(thm),theory(equality)],[2709,234]),
[iquote('0:SpR:2709.0,234.0')] ).
cnf(11529,plain,
equal(addition(multiplication(u,star(u)),multiplication(strong_iteration(u),zero)),multiplication(strong_iteration(u),u)),
inference(rew,[status(thm),theory(equality)],[8,11370]),
[iquote('0:Rew:8.0,11370.0')] ).
cnf(16007,plain,
leq(multiplication(skc2,u),multiplication(skc3,u)),
inference(spr,[status(thm),theory(equality)],[207,653]),
[iquote('0:SpR:207.0,653.0')] ).
cnf(16381,plain,
equal(addition(multiplication(u,star(u)),multiplication(strong_iteration(u),zero)),multiplication(u,strong_iteration(u))),
inference(spr,[status(thm),theory(equality)],[2454,271]),
[iquote('0:SpR:2454.0,271.0')] ).
cnf(16469,plain,
equal(multiplication(strong_iteration(u),u),multiplication(u,strong_iteration(u))),
inference(rew,[status(thm),theory(equality)],[16381,11529]),
[iquote('0:Rew:16381.0,11529.0')] ).
cnf(16470,plain,
( ~ leq(multiplication(u,strong_iteration(u)),multiplication(v,strong_iteration(u)))
| leq(multiplication(u,strong_iteration(u)),multiplication(v,strong_iteration(v))) ),
inference(rew,[status(thm),theory(equality)],[16469,4950]),
[iquote('0:Rew:16469.0,4950.1')] ).
cnf(43409,plain,
( ~ leq(one,one)
| equal(addition(strong_iteration(u),multiplication(v,strong_iteration(v))),addition(strong_iteration(u),strong_iteration(v))) ),
inference(spr,[status(thm),theory(equality)],[3363,1313]),
[iquote('0:SpR:3363.1,1313.0')] ).
cnf(43579,plain,
equal(addition(strong_iteration(u),multiplication(v,strong_iteration(v))),addition(strong_iteration(u),strong_iteration(v))),
inference(mrr,[status(thm)],[43409,92]),
[iquote('0:MRR:43409.0,92.0')] ).
cnf(166583,plain,
leq(multiplication(skc2,strong_iteration(skc2)),multiplication(skc3,strong_iteration(skc3))),
inference(res,[status(thm),theory(equality)],[16007,16470]),
[iquote('0:Res:16007.0,16470.0')] ).
cnf(166823,plain,
equal(addition(strong_iteration(skc3),multiplication(skc2,strong_iteration(skc2))),strong_iteration(skc3)),
inference(res,[status(thm),theory(equality)],[166583,2125]),
[iquote('0:Res:166583.0,2125.0')] ).
cnf(166832,plain,
equal(addition(strong_iteration(skc3),strong_iteration(skc2)),strong_iteration(skc3)),
inference(rew,[status(thm),theory(equality)],[43579,166823]),
[iquote('0:Rew:43579.0,166823.0')] ).
cnf(166833,plain,
equal(addition(strong_iteration(skc2),strong_iteration(skc3)),strong_iteration(skc3)),
inference(rew,[status(thm),theory(equality)],[8,166832]),
[iquote('0:Rew:8.0,166832.0')] ).
cnf(166962,plain,
leq(strong_iteration(skc2),strong_iteration(skc3)),
inference(spr,[status(thm),theory(equality)],[166833,653]),
[iquote('0:SpR:166833.0,653.0')] ).
cnf(167162,plain,
$false,
inference(mrr,[status(thm)],[166962,7]),
[iquote('0:MRR:166962.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE140+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n011.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Thu Jun 16 13:24:36 EDT 2022
% 0.15/0.36 % CPUTime :
% 244.61/244.82
% 244.61/244.82 SPASS V 3.9
% 244.61/244.82 SPASS beiseite: Proof found.
% 244.61/244.82 % SZS status Theorem
% 244.61/244.82 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 244.61/244.82 SPASS derived 121378 clauses, backtracked 0 clauses, performed 0 splits and kept 30009 clauses.
% 244.61/244.82 SPASS allocated 206104 KBytes.
% 244.61/244.82 SPASS spent 0:04:02.10 on the problem.
% 244.61/244.82 0:00:00.03 for the input.
% 244.61/244.82 0:00:00.03 for the FLOTTER CNF translation.
% 244.61/244.82 0:00:01.03 for inferences.
% 244.61/244.82 0:00:00.00 for the backtracking.
% 244.61/244.82 0:04:00.37 for the reduction.
% 244.61/244.82
% 244.61/244.82
% 244.61/244.82 Here is a proof with depth 6, length 66 :
% 244.61/244.82 % SZS output start Refutation
% See solution above
% 244.61/244.82 Formulae used in the proof : goals 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 infty_coinduction
% 244.61/244.82
%------------------------------------------------------------------------------