%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE038+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 13.28s 13.49s
% Output : Refutation 13.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 29 ( 22 unt; 0 nHn; 29 RR)
% Number of literals : 36 ( 0 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 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(skc1,star(skc1)),
file('KLE038+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE038+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE038+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE038+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE038+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE038+1.p',unknown),
[] ).
cnf(12,axiom,
leq(addition(one,multiplication(star(u),u)),star(u)),
file('KLE038+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE038+1.p',unknown),
[] ).
cnf(16,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE038+1.p',unknown),
[] ).
cnf(109,plain,
( ~ leq(addition(u,v),w)
| equal(addition(u,addition(v,w)),w) ),
inference(spr,[status(thm),theory(equality)],[13,9]),
[iquote('0:SpR:13.0,9.1')] ).
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(117,plain,
equal(addition(addition(u,v),w),addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[8,13]),
[iquote('0:SpR:8.0,13.0')] ).
cnf(125,plain,
equal(addition(u,addition(v,w)),addition(v,addition(u,w))),
inference(rew,[status(thm),theory(equality)],[13,117]),
[iquote('0:Rew:13.0,117.0')] ).
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(1726,plain,
( ~ leq(addition(u,v),w)
| equal(addition(u,w),w) ),
inference(spr,[status(thm),theory(equality)],[109,115]),
[iquote('0:SpR:109.1,115.0')] ).
cnf(1738,plain,
( ~ leq(addition(u,v),w)
| equal(addition(v,addition(u,w)),w) ),
inference(spr,[status(thm),theory(equality)],[109,125]),
[iquote('0:SpR:109.1,125.0')] ).
cnf(1815,plain,
( ~ leq(addition(u,v),w)
| equal(addition(v,w),w) ),
inference(rew,[status(thm),theory(equality)],[1726,1738]),
[iquote('0:Rew:1726.1,1738.1')] ).
cnf(10796,plain,
equal(addition(one,star(u)),star(u)),
inference(res,[status(thm),theory(equality)],[12,1726]),
[iquote('0:Res:12.0,1726.0')] ).
cnf(10840,plain,
equal(addition(multiplication(one,u),multiplication(star(v),u)),multiplication(star(v),u)),
inference(spr,[status(thm),theory(equality)],[10796,16]),
[iquote('0:SpR:10796.0,16.0')] ).
cnf(10943,plain,
equal(addition(u,multiplication(star(v),u)),multiplication(star(v),u)),
inference(rew,[status(thm),theory(equality)],[5,10840]),
[iquote('0:Rew:5.0,10840.0')] ).
cnf(11064,plain,
equal(addition(multiplication(star(u),u),star(u)),star(u)),
inference(res,[status(thm),theory(equality)],[12,1815]),
[iquote('0:Res:12.0,1815.0')] ).
cnf(11086,plain,
equal(addition(star(u),multiplication(star(u),u)),star(u)),
inference(rew,[status(thm),theory(equality)],[8,11064]),
[iquote('0:Rew:8.0,11064.0')] ).
cnf(35082,plain,
leq(u,addition(v,multiplication(star(w),u))),
inference(spr,[status(thm),theory(equality)],[10943,171]),
[iquote('0:SpR:10943.0,171.0')] ).
cnf(35659,plain,
leq(u,star(u)),
inference(spr,[status(thm),theory(equality)],[11086,35082]),
[iquote('0:SpR:11086.0,35082.0')] ).
cnf(35701,plain,
$false,
inference(unc,[status(thm)],[35659,1]),
[iquote('0:UnC:35659.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE038+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % 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 09:07:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 13.28/13.49
% 13.28/13.49 SPASS V 3.9
% 13.28/13.49 SPASS beiseite: Proof found.
% 13.28/13.49 % SZS status Theorem
% 13.28/13.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.28/13.49 SPASS derived 25778 clauses, backtracked 0 clauses, performed 0 splits and kept 5174 clauses.
% 13.28/13.49 SPASS allocated 108159 KBytes.
% 13.28/13.49 SPASS spent 0:0:12.84 on the problem.
% 13.28/13.49 0:00:00.03 for the input.
% 13.28/13.49 0:00:00.03 for the FLOTTER CNF translation.
% 13.28/13.49 0:00:00.18 for inferences.
% 13.28/13.49 0:00:00.00 for the backtracking.
% 13.28/13.49 0:0:12.56 for the reduction.
% 13.28/13.49
% 13.28/13.49
% 13.28/13.49 Here is a proof with depth 7, length 29 :
% 13.28/13.49 % SZS output start Refutation
% See solution above
% 13.28/13.49 Formulae used in the proof : goals additive_idempotence multiplicative_left_identity additive_commutativity order star_unfold_left additive_associativity left_distributivity
% 13.28/13.49
%------------------------------------------------------------------------------