TSTP Solution File: KLE002+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE002+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 02:27:56 EDT 2022
% Result : Theorem 0.46s 0.71s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 14 ( 11 unt; 0 nHn; 14 RR)
% Number of literals : 17 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
leq(skc3,skc4),
file('KLE002+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE002+1.p',unknown),
[] ).
cnf(9,axiom,
~ leq(multiplication(skc3,skc5),multiplication(skc4,skc5)),
file('KLE002+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE002+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE002+1.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE002+1.p',unknown),
[] ).
cnf(15,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE002+1.p',unknown),
[] ).
cnf(16,plain,
equal(addition(skc3,skc4),skc4),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(87,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[3,12]),
[iquote('0:SpR:3.0,12.0')] ).
cnf(127,plain,
equal(addition(multiplication(skc3,u),multiplication(skc4,u)),multiplication(skc4,u)),
inference(spr,[status(thm),theory(equality)],[16,15]),
[iquote('0:SpR:16.0,15.0')] ).
cnf(448,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[87,11]),
[iquote('0:SpL:87.0,11.0')] ).
cnf(453,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[448]),
[iquote('0:Obv:448.0')] ).
cnf(3061,plain,
leq(multiplication(skc3,u),multiplication(skc4,u)),
inference(spr,[status(thm),theory(equality)],[127,453]),
[iquote('0:SpR:127.0,453.0')] ).
cnf(3101,plain,
$false,
inference(unc,[status(thm)],[3061,9]),
[iquote('0:UnC:3061.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE002+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 13:10:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/0.71
% 0.46/0.71 SPASS V 3.9
% 0.46/0.71 SPASS beiseite: Proof found.
% 0.46/0.71 % SZS status Theorem
% 0.46/0.71 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.46/0.71 SPASS derived 2432 clauses, backtracked 0 clauses, performed 0 splits and kept 504 clauses.
% 0.46/0.71 SPASS allocated 87497 KBytes.
% 0.46/0.71 SPASS spent 0:00:00.35 on the problem.
% 0.46/0.71 0:00:00.04 for the input.
% 0.46/0.71 0:00:00.03 for the FLOTTER CNF translation.
% 0.46/0.71 0:00:00.02 for inferences.
% 0.46/0.71 0:00:00.00 for the backtracking.
% 0.46/0.71 0:00:00.25 for the reduction.
% 0.46/0.71
% 0.46/0.71
% 0.46/0.71 Here is a proof with depth 3, length 14 :
% 0.46/0.71 % SZS output start Refutation
% See solution above
% 0.46/0.71 Formulae used in the proof : goals additive_idempotence order additive_associativity left_distributivity
% 0.46/0.71
%------------------------------------------------------------------------------