TSTP Solution File: KLE144+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE144+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 02:28:44 EDT 2022
% Result : Theorem 0.50s 0.66s
% Output : Refutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 28 ( 23 unt; 0 nHn; 28 RR)
% Number of literals : 33 ( 0 equ; 7 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('KLE144+2.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE144+2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE144+2.p',unknown),
[] ).
cnf(6,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE144+2.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(one,multiplication(star(u),u)),star(u)),
file('KLE144+2.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE144+2.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE144+2.p',unknown),
[] ).
cnf(14,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE144+2.p',unknown),
[] ).
cnf(16,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE144+2.p',unknown),
[] ).
cnf(17,axiom,
( ~ leq(strong_iteration(one),strong_iteration(star(skc3)))
| ~ leq(strong_iteration(star(skc2)),strong_iteration(one)) ),
file('KLE144+2.p',unknown),
[] ).
cnf(20,axiom,
( ~ leq(u,addition(multiplication(v,u),w))
| leq(u,multiplication(strong_iteration(v),w)) ),
file('KLE144+2.p',unknown),
[] ).
cnf(150,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[2,13]),
[iquote('0:SpR:2.0,13.0')] ).
cnf(192,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[150,11]),
[iquote('0:SpL:150.0,11.0')] ).
cnf(196,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[192]),
[iquote('0:Obv:192.0')] ).
cnf(202,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[6,196]),
[iquote('0:SpR:6.0,196.0')] ).
cnf(225,plain,
equal(addition(multiplication(one,u),multiplication(multiplication(star(v),v),u)),multiplication(star(v),u)),
inference(spr,[status(thm),theory(equality)],[8,16]),
[iquote('0:SpR:8.0,16.0')] ).
cnf(236,plain,
equal(addition(u,multiplication(star(v),multiplication(v,u))),multiplication(star(v),u)),
inference(rew,[status(thm),theory(equality)],[4,225,14]),
[iquote('0:Rew:4.0,225.0,14.0,225.0')] ).
cnf(259,plain,
leq(u,addition(v,addition(w,u))),
inference(spr,[status(thm),theory(equality)],[13,202]),
[iquote('0:SpR:13.0,202.0')] ).
cnf(351,plain,
leq(u,addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[6,259]),
[iquote('0:SpR:6.0,259.0')] ).
cnf(524,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(549,plain,
leq(u,multiplication(strong_iteration(one),v)),
inference(mrr,[status(thm)],[524,196]),
[iquote('0:MRR:524.0,196.0')] ).
cnf(557,plain,
leq(u,strong_iteration(one)),
inference(spr,[status(thm),theory(equality)],[3,549]),
[iquote('0:SpR:3.0,549.0')] ).
cnf(562,plain,
~ leq(strong_iteration(one),strong_iteration(star(skc3))),
inference(mrr,[status(thm)],[17,557]),
[iquote('0:MRR:17.1,557.0')] ).
cnf(1928,plain,
leq(u,addition(v,multiplication(star(w),u))),
inference(spr,[status(thm),theory(equality)],[236,351]),
[iquote('0:SpR:236.0,351.0')] ).
cnf(2138,plain,
leq(u,addition(multiplication(star(v),u),w)),
inference(spr,[status(thm),theory(equality)],[6,1928]),
[iquote('0:SpR:6.0,1928.0')] ).
cnf(2278,plain,
leq(u,multiplication(strong_iteration(star(v)),w)),
inference(res,[status(thm),theory(equality)],[2138,20]),
[iquote('0:Res:2138.0,20.0')] ).
cnf(2437,plain,
leq(u,strong_iteration(star(v))),
inference(spr,[status(thm),theory(equality)],[3,2278]),
[iquote('0:SpR:3.0,2278.0')] ).
cnf(2446,plain,
$false,
inference(unc,[status(thm)],[2437,562]),
[iquote('0:UnC:2437.0,562.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE144+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n018.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 08:22:00 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.50/0.66
% 0.50/0.66 SPASS V 3.9
% 0.50/0.66 SPASS beiseite: Proof found.
% 0.50/0.66 % SZS status Theorem
% 0.50/0.66 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.50/0.66 SPASS derived 1798 clauses, backtracked 0 clauses, performed 0 splits and kept 592 clauses.
% 0.50/0.66 SPASS allocated 87345 KBytes.
% 0.50/0.66 SPASS spent 0:00:00.30 on the problem.
% 0.50/0.66 0:00:00.04 for the input.
% 0.50/0.66 0:00:00.03 for the FLOTTER CNF translation.
% 0.50/0.66 0:00:00.02 for inferences.
% 0.50/0.66 0:00:00.00 for the backtracking.
% 0.50/0.66 0:00:00.20 for the reduction.
% 0.50/0.66
% 0.50/0.66
% 0.50/0.66 Here is a proof with depth 9, length 28 :
% 0.50/0.66 % SZS output start Refutation
% See solution above
% 0.50/0.66 Formulae used in the proof : idempotence multiplicative_right_identity multiplicative_left_identity additive_commutativity star_unfold2 order additive_associativity multiplicative_associativity distributivity2 goals infty_coinduction
% 0.50/0.66
%------------------------------------------------------------------------------