TSTP Solution File: KLE148+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE148+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 02:28:46 EDT 2022
% Result : Theorem 0.52s 0.67s
% Output : Refutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of clauses : 29 ( 25 unt; 0 nHn; 29 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiplication(skc5,skc4),zero),
file('KLE148+2.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,zero),u),
file('KLE148+2.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE148+2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE148+2.p',unknown),
[] ).
cnf(6,axiom,
equal(multiplication(zero,u),zero),
file('KLE148+2.p',unknown),
[] ).
cnf(7,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE148+2.p',unknown),
[] ).
cnf(10,axiom,
equal(addition(multiplication(u,strong_iteration(u)),one),strong_iteration(u)),
file('KLE148+2.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE148+2.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE148+2.p',unknown),
[] ).
cnf(15,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE148+2.p',unknown),
[] ).
cnf(16,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE148+2.p',unknown),
[] ).
cnf(18,axiom,
( ~ leq(skc6,multiplication(skc6,strong_iteration(skc7)))
| ~ leq(multiplication(skc5,strong_iteration(skc4)),skc5) ),
file('KLE148+2.p',unknown),
[] ).
cnf(22,plain,
equal(addition(one,multiplication(u,strong_iteration(u))),strong_iteration(u)),
inference(rew,[status(thm),theory(equality)],[7,10]),
[iquote('0:Rew:7.0,10.0')] ).
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(106,plain,
equal(multiplication(skc5,multiplication(skc4,u)),multiplication(zero,u)),
inference(spr,[status(thm),theory(equality)],[1,15]),
[iquote('0:SpR:1.0,15.0')] ).
cnf(111,plain,
equal(multiplication(skc5,multiplication(skc4,u)),zero),
inference(rew,[status(thm),theory(equality)],[6,106]),
[iquote('0:Rew:6.0,106.0')] ).
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(238,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[233]),
[iquote('0:Obv:233.0')] ).
cnf(274,plain,
equal(addition(multiplication(u,one),multiplication(u,multiplication(v,strong_iteration(v)))),multiplication(u,strong_iteration(v))),
inference(spr,[status(thm),theory(equality)],[22,16]),
[iquote('0:SpR:22.0,16.0')] ).
cnf(285,plain,
equal(addition(u,multiplication(u,multiplication(v,strong_iteration(v)))),multiplication(u,strong_iteration(v))),
inference(rew,[status(thm),theory(equality)],[4,274]),
[iquote('0:Rew:4.0,274.0')] ).
cnf(2597,plain,
leq(u,multiplication(u,strong_iteration(v))),
inference(spr,[status(thm),theory(equality)],[285,238]),
[iquote('0:SpR:285.0,238.0')] ).
cnf(2630,plain,
equal(multiplication(skc5,strong_iteration(skc4)),addition(skc5,zero)),
inference(spr,[status(thm),theory(equality)],[111,285]),
[iquote('0:SpR:111.0,285.0')] ).
cnf(2641,plain,
~ leq(multiplication(skc5,strong_iteration(skc4)),skc5),
inference(mrr,[status(thm)],[18,2597]),
[iquote('0:MRR:18.0,2597.0')] ).
cnf(2643,plain,
equal(multiplication(skc5,strong_iteration(skc4)),skc5),
inference(rew,[status(thm),theory(equality)],[32,2630,7]),
[iquote('0:Rew:32.0,2630.0,7.0,2630.0')] ).
cnf(2644,plain,
~ leq(skc5,skc5),
inference(rew,[status(thm),theory(equality)],[2643,2641]),
[iquote('0:Rew:2643.0,2641.0')] ).
cnf(2645,plain,
$false,
inference(mrr,[status(thm)],[2644,87]),
[iquote('0:MRR:2644.0,87.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE148+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.14/0.33 % Computer : n009.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Thu Jun 16 13:38:22 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.52/0.67
% 0.52/0.67 SPASS V 3.9
% 0.52/0.67 SPASS beiseite: Proof found.
% 0.52/0.67 % SZS status Theorem
% 0.52/0.67 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.52/0.67 SPASS derived 2006 clauses, backtracked 0 clauses, performed 0 splits and kept 656 clauses.
% 0.52/0.67 SPASS allocated 87470 KBytes.
% 0.52/0.67 SPASS spent 0:00:00.31 on the problem.
% 0.52/0.67 0:00:00.03 for the input.
% 0.52/0.67 0:00:00.03 for the FLOTTER CNF translation.
% 0.52/0.67 0:00:00.02 for inferences.
% 0.52/0.67 0:00:00.00 for the backtracking.
% 0.52/0.67 0:00:00.21 for the reduction.
% 0.52/0.67
% 0.52/0.67
% 0.52/0.67 Here is a proof with depth 3, length 29 :
% 0.52/0.67 % SZS output start Refutation
% See solution above
% 0.52/0.67 Formulae used in the proof : goals left_annihilation additive_identity idempotence multiplicative_right_identity additive_commutativity infty_unfold1 order additive_associativity multiplicative_associativity distributivity1
% 0.52/0.67
%------------------------------------------------------------------------------