TSTP Solution File: KLE141+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE141+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 02:28:42 EDT 2022
% Result : Theorem 0.18s 0.56s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of clauses : 41 ( 28 unt; 0 nHn; 41 RR)
% Number of literals : 54 ( 0 equ; 17 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(2,axiom,
equal(addition(u,u),u),
file('KLE141+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE141+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE141+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(zero,u),zero),
file('KLE141+1.p',unknown),
[] ).
cnf(6,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE141+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(multiplication(strong_iteration(one),skc1),strong_iteration(one)),
file('KLE141+1.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(one,multiplication(star(u),u)),star(u)),
file('KLE141+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE141+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE141+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(star(u),multiplication(strong_iteration(u),zero)),strong_iteration(u)),
file('KLE141+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE141+1.p',unknown),
[] ).
cnf(15,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE141+1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE141+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ leq(addition(multiplication(u,v),w),v)
| leq(multiplication(star(u),w),v) ),
file('KLE141+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ leq(u,addition(multiplication(v,u),w))
| leq(u,multiplication(strong_iteration(v),w)) ),
file('KLE141+1.p',unknown),
[] ).
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(75,plain,
( ~ equal(u,u)
| leq(u,u) ),
inference(spl,[status(thm),theory(equality)],[2,12]),
[iquote('0:SpL:2.0,12.0')] ).
cnf(85,plain,
leq(u,u),
inference(obv,[status(thm),theory(equality)],[75]),
[iquote('0:Obv:75.0')] ).
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(185,plain,
equal(addition(one,star(u)),star(u)),
inference(spr,[status(thm),theory(equality)],[9,135]),
[iquote('0:SpR:9.0,135.0')] ).
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(298,plain,
( ~ leq(star(u),one)
| equal(star(u),one) ),
inference(spr,[status(thm),theory(equality)],[185,60]),
[iquote('0:SpR:185.0,60.1')] ).
cnf(328,plain,
( ~ leq(addition(u,v),u)
| leq(multiplication(star(one),v),u) ),
inference(spl,[status(thm),theory(equality)],[4,18]),
[iquote('0:SpL:4.0,18.0')] ).
cnf(466,plain,
( ~ leq(u,addition(u,v))
| leq(u,multiplication(strong_iteration(one),v)) ),
inference(spl,[status(thm),theory(equality)],[4,20]),
[iquote('0:SpL:4.0,20.0')] ).
cnf(487,plain,
leq(u,multiplication(strong_iteration(one),v)),
inference(mrr,[status(thm)],[466,197]),
[iquote('0:MRR:466.0,197.0')] ).
cnf(499,plain,
leq(u,strong_iteration(one)),
inference(spr,[status(thm),theory(equality)],[3,487]),
[iquote('0:SpR:3.0,487.0')] ).
cnf(1289,plain,
( ~ leq(u,u)
| leq(multiplication(star(one),u),u) ),
inference(spl,[status(thm),theory(equality)],[2,328]),
[iquote('0:SpL:2.0,328.0')] ).
cnf(1314,plain,
leq(multiplication(star(one),u),u),
inference(mrr,[status(thm)],[1289,85]),
[iquote('0:MRR:1289.0,85.0')] ).
cnf(1378,plain,
leq(star(one),one),
inference(spr,[status(thm),theory(equality)],[3,1314]),
[iquote('0:SpR:3.0,1314.0')] ).
cnf(1643,plain,
equal(star(one),one),
inference(res,[status(thm),theory(equality)],[1378,298]),
[iquote('0:Res:1378.0,298.0')] ).
cnf(1803,plain,
equal(addition(one,multiplication(strong_iteration(one),zero)),strong_iteration(one)),
inference(spr,[status(thm),theory(equality)],[1643,13]),
[iquote('0:SpR:1643.0,13.0')] ).
cnf(1837,plain,
( ~ leq(one,multiplication(strong_iteration(one),zero))
| equal(multiplication(strong_iteration(one),zero),strong_iteration(one)) ),
inference(spr,[status(thm),theory(equality)],[1803,11]),
[iquote('0:SpR:1803.0,11.1')] ).
cnf(1840,plain,
equal(addition(multiplication(one,u),multiplication(multiplication(strong_iteration(one),zero),u)),multiplication(strong_iteration(one),u)),
inference(spr,[status(thm),theory(equality)],[1803,17]),
[iquote('0:SpR:1803.0,17.0')] ).
cnf(1859,plain,
equal(multiplication(strong_iteration(one),zero),strong_iteration(one)),
inference(mrr,[status(thm)],[1837,487]),
[iquote('0:MRR:1837.0,487.0')] ).
cnf(1865,plain,
equal(addition(u,multiplication(strong_iteration(one),zero)),multiplication(strong_iteration(one),u)),
inference(rew,[status(thm),theory(equality)],[4,1840,5,15]),
[iquote('0:Rew:4.0,1840.0,5.0,1840.0,15.0,1840.0')] ).
cnf(1866,plain,
equal(multiplication(strong_iteration(one),u),addition(u,strong_iteration(one))),
inference(rew,[status(thm),theory(equality)],[1859,1865]),
[iquote('0:Rew:1859.0,1865.0')] ).
cnf(1868,plain,
~ equal(addition(skc1,strong_iteration(one)),strong_iteration(one)),
inference(rew,[status(thm),theory(equality)],[1866,7]),
[iquote('0:Rew:1866.0,7.0')] ).
cnf(1876,plain,
( ~ leq(skc1,strong_iteration(one))
| ~ equal(strong_iteration(one),strong_iteration(one)) ),
inference(spl,[status(thm),theory(equality)],[11,1868]),
[iquote('0:SpL:11.1,1868.0')] ).
cnf(1878,plain,
~ leq(skc1,strong_iteration(one)),
inference(obv,[status(thm),theory(equality)],[1876]),
[iquote('0:Obv:1876.1')] ).
cnf(1879,plain,
$false,
inference(mrr,[status(thm)],[1878,499]),
[iquote('0:MRR:1878.0,499.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE141+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n012.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 12:56:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.56
% 0.18/0.56 SPASS V 3.9
% 0.18/0.56 SPASS beiseite: Proof found.
% 0.18/0.56 % SZS status Theorem
% 0.18/0.56 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.56 SPASS derived 1388 clauses, backtracked 0 clauses, performed 0 splits and kept 447 clauses.
% 0.18/0.56 SPASS allocated 86604 KBytes.
% 0.18/0.56 SPASS spent 0:00:00.21 on the problem.
% 0.18/0.56 0:00:00.04 for the input.
% 0.18/0.56 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.56 0:00:00.01 for inferences.
% 0.18/0.56 0:00:00.00 for the backtracking.
% 0.18/0.56 0:00:00.12 for the reduction.
% 0.18/0.56
% 0.18/0.56
% 0.18/0.56 Here is a proof with depth 6, length 41 :
% 0.18/0.56 % SZS output start Refutation
% See solution above
% 0.18/0.56 Formulae used in the proof : idempotence multiplicative_right_identity multiplicative_left_identity left_annihilation additive_commutativity goals star_unfold2 order isolation additive_associativity multiplicative_associativity distributivity2 star_induction1 infty_coinduction
% 0.18/0.56
%------------------------------------------------------------------------------