TSTP Solution File: KLE039+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE039+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 02:28:12 EDT 2022
% Result : Theorem 3.65s 3.82s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of clauses : 56 ( 28 unt; 0 nHn; 56 RR)
% Number of literals : 88 ( 0 equ; 33 neg)
% Maximal clause size : 3 ( 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(2,axiom,
equal(addition(u,u),u),
file('KLE039+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE039+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE039+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(star(star(skc1)),star(skc1)),
file('KLE039+1.p',unknown),
[] ).
cnf(8,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE039+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE039+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE039+1.p',unknown),
[] ).
cnf(11,axiom,
leq(addition(one,multiplication(u,star(u))),star(u)),
file('KLE039+1.p',unknown),
[] ).
cnf(12,axiom,
leq(addition(one,multiplication(star(u),u)),star(u)),
file('KLE039+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE039+1.p',unknown),
[] ).
cnf(15,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE039+1.p',unknown),
[] ).
cnf(16,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE039+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ leq(addition(multiplication(u,v),w),v)
| leq(multiplication(star(u),w),v) ),
file('KLE039+1.p',unknown),
[] ).
cnf(51,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(59,plain,
( ~ equal(u,u)
| leq(u,u) ),
inference(spl,[status(thm),theory(equality)],[2,10]),
[iquote('0:SpL:2.0,10.0')] ).
cnf(64,plain,
leq(u,u),
inference(obv,[status(thm),theory(equality)],[59]),
[iquote('0:Obv:59.0')] ).
cnf(88,plain,
( ~ leq(u,v)
| ~ leq(v,u)
| equal(v,u) ),
inference(spr,[status(thm),theory(equality)],[51,9]),
[iquote('0:SpR:51.1,9.1')] ).
cnf(108,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(114,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(116,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(124,plain,
equal(addition(u,addition(v,w)),addition(v,addition(u,w))),
inference(rew,[status(thm),theory(equality)],[13,116]),
[iquote('0:Rew:13.0,116.0')] ).
cnf(142,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[114,10]),
[iquote('0:SpL:114.0,10.0')] ).
cnf(146,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[142]),
[iquote('0:Obv:142.0')] ).
cnf(152,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[8,146]),
[iquote('0:SpR:8.0,146.0')] ).
cnf(166,plain,
leq(u,addition(v,addition(w,u))),
inference(spr,[status(thm),theory(equality)],[13,152]),
[iquote('0:SpR:13.0,152.0')] ).
cnf(170,plain,
leq(u,addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[8,166]),
[iquote('0:SpR:8.0,166.0')] ).
cnf(180,plain,
( ~ leq(addition(u,v),w)
| leq(v,w) ),
inference(spr,[status(thm),theory(equality)],[51,166]),
[iquote('0:SpR:51.1,166.0')] ).
cnf(193,plain,
( ~ leq(u,v)
| equal(addition(multiplication(u,w),multiplication(v,w)),multiplication(v,w)) ),
inference(spr,[status(thm),theory(equality)],[9,16]),
[iquote('0:SpR:9.1,16.0')] ).
cnf(222,plain,
( ~ leq(addition(u,v),w)
| leq(u,w) ),
inference(spr,[status(thm),theory(equality)],[51,170]),
[iquote('0:SpR:51.1,170.0')] ).
cnf(333,plain,
( ~ leq(u,v)
| equal(addition(multiplication(w,u),multiplication(w,v)),multiplication(w,v)) ),
inference(spr,[status(thm),theory(equality)],[9,15]),
[iquote('0:SpR:9.1,15.0')] ).
cnf(378,plain,
( ~ leq(multiplication(u,v),w)
| ~ leq(w,v)
| leq(multiplication(star(u),w),v) ),
inference(spl,[status(thm),theory(equality)],[9,17]),
[iquote('0:SpL:9.1,17.0')] ).
cnf(437,plain,
leq(multiplication(u,star(u)),star(u)),
inference(res,[status(thm),theory(equality)],[11,180]),
[iquote('0:Res:11.0,180.0')] ).
cnf(516,plain,
leq(one,star(u)),
inference(res,[status(thm),theory(equality)],[12,222]),
[iquote('0:Res:12.0,222.0')] ).
cnf(1549,plain,
( ~ leq(addition(u,v),w)
| equal(addition(u,w),w) ),
inference(spr,[status(thm),theory(equality)],[108,114]),
[iquote('0:SpR:108.1,114.0')] ).
cnf(1561,plain,
( ~ leq(addition(u,v),w)
| equal(addition(v,addition(u,w)),w) ),
inference(spr,[status(thm),theory(equality)],[108,124]),
[iquote('0:SpR:108.1,124.0')] ).
cnf(1635,plain,
( ~ leq(addition(u,v),w)
| equal(addition(v,w),w) ),
inference(rew,[status(thm),theory(equality)],[1549,1561]),
[iquote('0:Rew:1549.1,1561.1')] ).
cnf(2747,plain,
( ~ leq(one,u)
| equal(addition(v,multiplication(u,v)),multiplication(u,v)) ),
inference(spr,[status(thm),theory(equality)],[4,193]),
[iquote('0:SpR:4.0,193.1')] ).
cnf(3018,plain,
( ~ leq(one,u)
| equal(addition(v,multiplication(v,u)),multiplication(v,u)) ),
inference(spr,[status(thm),theory(equality)],[3,333]),
[iquote('0:SpR:3.0,333.1')] ).
cnf(3236,plain,
( ~ leq(star(u),star(u))
| leq(multiplication(star(u),star(u)),star(u)) ),
inference(res,[status(thm),theory(equality)],[437,378]),
[iquote('0:Res:437.0,378.0')] ).
cnf(3254,plain,
leq(multiplication(star(u),star(u)),star(u)),
inference(mrr,[status(thm)],[3236,64]),
[iquote('0:MRR:3236.0,64.0')] ).
cnf(3285,plain,
( ~ leq(star(u),star(u))
| leq(multiplication(star(star(u)),star(u)),star(u)) ),
inference(res,[status(thm),theory(equality)],[3254,378]),
[iquote('0:Res:3254.0,378.0')] ).
cnf(3298,plain,
leq(multiplication(star(star(u)),star(u)),star(u)),
inference(mrr,[status(thm)],[3285,64]),
[iquote('0:MRR:3285.0,64.0')] ).
cnf(9148,plain,
equal(addition(one,star(u)),star(u)),
inference(res,[status(thm),theory(equality)],[12,1549]),
[iquote('0:Res:12.0,1549.0')] ).
cnf(9246,plain,
( ~ leq(star(u),v)
| leq(one,v) ),
inference(spl,[status(thm),theory(equality)],[9148,222]),
[iquote('0:SpL:9148.0,222.0')] ).
cnf(9429,plain,
equal(addition(multiplication(star(u),u),star(u)),star(u)),
inference(res,[status(thm),theory(equality)],[12,1635]),
[iquote('0:Res:12.0,1635.0')] ).
cnf(9453,plain,
equal(addition(star(u),multiplication(star(u),u)),star(u)),
inference(rew,[status(thm),theory(equality)],[8,9429]),
[iquote('0:Rew:8.0,9429.0')] ).
cnf(10602,plain,
( ~ leq(one,u)
| leq(v,multiplication(u,v)) ),
inference(spr,[status(thm),theory(equality)],[2747,146]),
[iquote('0:SpR:2747.1,146.0')] ).
cnf(11062,plain,
( ~ leq(one,u)
| equal(multiplication(star(u),u),star(u)) ),
inference(spr,[status(thm),theory(equality)],[3018,9453]),
[iquote('0:SpR:3018.1,9453.0')] ).
cnf(18380,plain,
( ~ leq(one,u)
| ~ leq(one,star(u))
| leq(u,star(u)) ),
inference(spr,[status(thm),theory(equality)],[11062,10602]),
[iquote('0:SpR:11062.1,10602.1')] ).
cnf(18391,plain,
( ~ leq(one,star(u))
| leq(star(star(u)),star(u)) ),
inference(spr,[status(thm),theory(equality)],[11062,3298]),
[iquote('0:SpR:11062.1,3298.0')] ).
cnf(18425,plain,
leq(star(star(u)),star(u)),
inference(mrr,[status(thm)],[18391,516]),
[iquote('0:MRR:18391.0,516.0')] ).
cnf(18428,plain,
( ~ leq(one,u)
| leq(u,star(u)) ),
inference(mrr,[status(thm)],[18380,516]),
[iquote('0:MRR:18380.1,516.0')] ).
cnf(18504,plain,
( ~ leq(one,u)
| ~ leq(star(u),u)
| equal(star(u),u) ),
inference(res,[status(thm),theory(equality)],[18428,88]),
[iquote('0:Res:18428.1,88.0')] ).
cnf(18537,plain,
( ~ leq(star(u),u)
| equal(star(u),u) ),
inference(mrr,[status(thm)],[18504,9246]),
[iquote('0:MRR:18504.0,9246.1')] ).
cnf(18550,plain,
equal(star(star(u)),star(u)),
inference(res,[status(thm),theory(equality)],[18425,18537]),
[iquote('0:Res:18425.0,18537.0')] ).
cnf(18561,plain,
$false,
inference(unc,[status(thm)],[18550,7]),
[iquote('0:UnC:18550.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KLE039+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 12:57:26 EDT 2022
% 0.13/0.35 % CPUTime :
% 3.65/3.82
% 3.65/3.82 SPASS V 3.9
% 3.65/3.82 SPASS beiseite: Proof found.
% 3.65/3.82 % SZS status Theorem
% 3.65/3.82 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.65/3.82 SPASS derived 14047 clauses, backtracked 0 clauses, performed 0 splits and kept 2730 clauses.
% 3.65/3.82 SPASS allocated 97599 KBytes.
% 3.65/3.82 SPASS spent 0:00:03.36 on the problem.
% 3.65/3.82 0:00:00.04 for the input.
% 3.65/3.82 0:00:00.03 for the FLOTTER CNF translation.
% 3.65/3.82 0:00:00.10 for inferences.
% 3.65/3.82 0:00:00.00 for the backtracking.
% 3.65/3.82 0:00:03.16 for the reduction.
% 3.65/3.82
% 3.65/3.82
% 3.65/3.82 Here is a proof with depth 10, length 56 :
% 3.65/3.82 % SZS output start Refutation
% See solution above
% 3.65/3.82 Formulae used in the proof : additive_idempotence multiplicative_right_identity multiplicative_left_identity goals additive_commutativity order star_unfold_right star_unfold_left additive_associativity right_distributivity left_distributivity star_induction_left
% 3.65/3.82
%------------------------------------------------------------------------------