TSTP Solution File: KLE037+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE037+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 02:28:11 EDT 2022
% Result : Theorem 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of clauses : 17 ( 12 unt; 0 nHn; 17 RR)
% Number of literals : 22 ( 0 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ leq(one,star(skc1)),
file('KLE037+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE037+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE037+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE037+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE037+1.p',unknown),
[] ).
cnf(12,axiom,
leq(addition(one,multiplication(star(u),u)),star(u)),
file('KLE037+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE037+1.p',unknown),
[] ).
cnf(52,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[9,8]),
[iquote('0:SpR:9.1,8.0')] ).
cnf(115,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[3,13]),
[iquote('0:SpR:3.0,13.0')] ).
cnf(143,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[115,10]),
[iquote('0:SpL:115.0,10.0')] ).
cnf(147,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[143]),
[iquote('0:Obv:143.0')] ).
cnf(153,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[8,147]),
[iquote('0:SpR:8.0,147.0')] ).
cnf(167,plain,
leq(u,addition(v,addition(w,u))),
inference(spr,[status(thm),theory(equality)],[13,153]),
[iquote('0:SpR:13.0,153.0')] ).
cnf(171,plain,
leq(u,addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[8,167]),
[iquote('0:SpR:8.0,167.0')] ).
cnf(223,plain,
( ~ leq(addition(u,v),w)
| leq(u,w) ),
inference(spr,[status(thm),theory(equality)],[52,171]),
[iquote('0:SpR:52.1,171.0')] ).
cnf(518,plain,
leq(one,star(u)),
inference(res,[status(thm),theory(equality)],[12,223]),
[iquote('0:Res:12.0,223.0')] ).
cnf(531,plain,
$false,
inference(unc,[status(thm)],[518,1]),
[iquote('0:UnC:518.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE037+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n010.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 09:19:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 421 clauses, backtracked 0 clauses, performed 0 splits and kept 139 clauses.
% 0.19/0.47 SPASS allocated 85504 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.19/0.47 0:00:00.04 for the input.
% 0.19/0.47 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.00 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.03 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 7, length 17 :
% 0.19/0.47 % SZS output start Refutation
% See solution above
% 0.19/0.47 Formulae used in the proof : goals additive_idempotence additive_commutativity order star_unfold_left additive_associativity
% 0.19/0.47
%------------------------------------------------------------------------------