TSTP Solution File: KLE167+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE167+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 02:28:53 EDT 2022
% Result : Theorem 0.53s 0.76s
% Output : Refutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 25 ( 18 unt; 0 nHn; 25 RR)
% Number of literals : 32 ( 0 equ; 10 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiplication(skc5,skc4),zero),
file('KLE167+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,zero),u),
file('KLE167+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE167+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE167+1.p',unknown),
[] ).
cnf(7,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE167+1.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(one,multiplication(star(u),u)),star(u)),
file('KLE167+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE167+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE167+1.p',unknown),
[] ).
cnf(16,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE167+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ leq(skc6,multiplication(skc6,star(skc7)))
| ~ leq(multiplication(skc5,star(skc4)),skc5) ),
file('KLE167+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ leq(addition(multiplication(u,v),w),u)
| leq(multiplication(w,star(v)),u) ),
file('KLE167+1.p',unknown),
[] ).
cnf(32,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[7,2]),
[iquote('0:SpR:7.0,2.0')] ).
cnf(77,plain,
( ~ equal(u,u)
| leq(u,u) ),
inference(spl,[status(thm),theory(equality)],[3,12]),
[iquote('0:SpL:3.0,12.0')] ).
cnf(87,plain,
leq(u,u),
inference(obv,[status(thm),theory(equality)],[77]),
[iquote('0:Obv:77.0')] ).
cnf(143,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[3,14]),
[iquote('0:SpR:3.0,14.0')] ).
cnf(233,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[143,12]),
[iquote('0:SpL:143.0,12.0')] ).
cnf(237,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[233]),
[iquote('0:Obv:233.0')] ).
cnf(272,plain,
equal(addition(multiplication(u,one),multiplication(u,multiplication(star(v),v))),multiplication(u,star(v))),
inference(spr,[status(thm),theory(equality)],[9,16]),
[iquote('0:SpR:9.0,16.0')] ).
cnf(283,plain,
equal(addition(u,multiplication(u,multiplication(star(v),v))),multiplication(u,star(v))),
inference(rew,[status(thm),theory(equality)],[4,272]),
[iquote('0:Rew:4.0,272.0')] ).
cnf(452,plain,
( ~ leq(addition(zero,u),skc5)
| leq(multiplication(u,star(skc4)),skc5) ),
inference(spl,[status(thm),theory(equality)],[1,20]),
[iquote('0:SpL:1.0,20.0')] ).
cnf(468,plain,
( ~ leq(u,skc5)
| leq(multiplication(u,star(skc4)),skc5) ),
inference(rew,[status(thm),theory(equality)],[32,452]),
[iquote('0:Rew:32.0,452.0')] ).
cnf(2474,plain,
leq(u,multiplication(u,star(v))),
inference(spr,[status(thm),theory(equality)],[283,237]),
[iquote('0:SpR:283.0,237.0')] ).
cnf(2515,plain,
~ leq(multiplication(skc5,star(skc4)),skc5),
inference(mrr,[status(thm)],[18,2474]),
[iquote('0:MRR:18.0,2474.0')] ).
cnf(2618,plain,
~ leq(skc5,skc5),
inference(res,[status(thm),theory(equality)],[468,2515]),
[iquote('0:Res:468.1,2515.0')] ).
cnf(2619,plain,
$false,
inference(mrr,[status(thm)],[2618,87]),
[iquote('0:MRR:2618.0,87.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE167+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 14:51:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.53/0.76
% 0.53/0.76 SPASS V 3.9
% 0.53/0.76 SPASS beiseite: Proof found.
% 0.53/0.76 % SZS status Theorem
% 0.53/0.76 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.53/0.76 SPASS derived 1935 clauses, backtracked 0 clauses, performed 0 splits and kept 635 clauses.
% 0.53/0.76 SPASS allocated 87477 KBytes.
% 0.53/0.76 SPASS spent 0:00:00.40 on the problem.
% 0.53/0.76 0:00:00.04 for the input.
% 0.53/0.76 0:00:00.03 for the FLOTTER CNF translation.
% 0.53/0.76 0:00:00.02 for inferences.
% 0.53/0.76 0:00:00.00 for the backtracking.
% 0.53/0.76 0:00:00.28 for the reduction.
% 0.53/0.76
% 0.53/0.76
% 0.53/0.76 Here is a proof with depth 3, length 25 :
% 0.53/0.76 % SZS output start Refutation
% See solution above
% 0.53/0.76 Formulae used in the proof : goals left_annihilation additive_identity idempotence multiplicative_right_identity additive_commutativity star_unfold2 order additive_associativity distributivity1 star_induction2
% 0.53/0.76
%------------------------------------------------------------------------------