TSTP Solution File: KLE041+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE041+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 02:28:13 EDT 2022
% Result : Theorem 71.14s 71.33s
% Output : Refutation 71.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of clauses : 46 ( 31 unt; 0 nHn; 46 RR)
% Number of literals : 61 ( 0 equ; 16 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
leq(skc2,skc3),
file('KLE041+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE041+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE041+1.p',unknown),
[] ).
cnf(8,axiom,
~ leq(star(skc2),star(skc3)),
file('KLE041+1.p',unknown),
[] ).
cnf(9,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE041+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE041+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE041+1.p',unknown),
[] ).
cnf(12,axiom,
leq(addition(one,multiplication(u,star(u))),star(u)),
file('KLE041+1.p',unknown),
[] ).
cnf(13,axiom,
leq(addition(one,multiplication(star(u),u)),star(u)),
file('KLE041+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE041+1.p',unknown),
[] ).
cnf(17,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE041+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ leq(addition(multiplication(u,v),w),v)
| leq(multiplication(star(u),w),v) ),
file('KLE041+1.p',unknown),
[] ).
cnf(20,plain,
equal(addition(skc2,skc3),skc3),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(56,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[10,9]),
[iquote('0:SpR:10.1,9.0')] ).
cnf(107,plain,
( ~ leq(addition(u,v),w)
| equal(addition(u,addition(v,w)),w) ),
inference(spr,[status(thm),theory(equality)],[14,10]),
[iquote('0:SpR:14.0,10.1')] ).
cnf(114,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(116,plain,
equal(addition(addition(u,v),w),addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[9,14]),
[iquote('0:SpR:9.0,14.0')] ).
cnf(123,plain,
equal(addition(u,addition(v,w)),addition(v,addition(u,w))),
inference(rew,[status(thm),theory(equality)],[14,116]),
[iquote('0:Rew:14.0,116.0')] ).
cnf(150,plain,
equal(addition(multiplication(skc2,u),multiplication(skc3,u)),multiplication(skc3,u)),
inference(spr,[status(thm),theory(equality)],[20,17]),
[iquote('0:SpR:20.0,17.0')] ).
cnf(295,plain,
( ~ leq(addition(u,multiplication(v,w)),w)
| leq(multiplication(star(v),u),w) ),
inference(spl,[status(thm),theory(equality)],[9,18]),
[iquote('0:SpL:9.0,18.0')] ).
cnf(536,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[114,11]),
[iquote('0:SpL:114.0,11.0')] ).
cnf(544,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[536]),
[iquote('0:Obv:536.0')] ).
cnf(562,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[9,544]),
[iquote('0:SpR:9.0,544.0')] ).
cnf(569,plain,
leq(addition(u,v),addition(u,addition(v,w))),
inference(spr,[status(thm),theory(equality)],[14,544]),
[iquote('0:SpR:14.0,544.0')] ).
cnf(588,plain,
leq(u,addition(v,addition(w,u))),
inference(spr,[status(thm),theory(equality)],[14,562]),
[iquote('0:SpR:14.0,562.0')] ).
cnf(601,plain,
( ~ leq(u,v)
| leq(u,addition(w,v)) ),
inference(spr,[status(thm),theory(equality)],[56,588]),
[iquote('0:SpR:56.1,588.0')] ).
cnf(1299,plain,
( ~ leq(addition(u,v),w)
| equal(addition(u,addition(w,v)),w) ),
inference(spr,[status(thm),theory(equality)],[123,56]),
[iquote('0:SpR:123.0,56.1')] ).
cnf(1998,plain,
( ~ leq(u,v)
| leq(u,addition(v,w)) ),
inference(spr,[status(thm),theory(equality)],[9,601]),
[iquote('0:SpR:9.0,601.1')] ).
cnf(2137,plain,
( ~ leq(addition(u,v),w)
| equal(addition(u,w),w) ),
inference(spr,[status(thm),theory(equality)],[107,114]),
[iquote('0:SpR:107.1,114.0')] ).
cnf(2146,plain,
( ~ leq(addition(u,v),w)
| equal(addition(v,addition(u,w)),w) ),
inference(spr,[status(thm),theory(equality)],[107,123]),
[iquote('0:SpR:107.1,123.0')] ).
cnf(2246,plain,
( ~ leq(addition(u,v),w)
| equal(addition(v,w),w) ),
inference(rew,[status(thm),theory(equality)],[2137,2146]),
[iquote('0:Rew:2137.1,2146.1')] ).
cnf(7160,plain,
leq(addition(u,multiplication(skc2,v)),addition(u,multiplication(skc3,v))),
inference(spr,[status(thm),theory(equality)],[150,569]),
[iquote('0:SpR:150.0,569.0')] ).
cnf(10514,plain,
equal(addition(one,star(u)),star(u)),
inference(res,[status(thm),theory(equality)],[13,2137]),
[iquote('0:Res:13.0,2137.0')] ).
cnf(10527,plain,
( ~ leq(addition(u,v),w)
| equal(addition(u,addition(w,x)),addition(w,x)) ),
inference(res,[status(thm),theory(equality)],[1998,2137]),
[iquote('0:Res:1998.1,2137.0')] ).
cnf(10576,plain,
( ~ leq(addition(u,v),w)
| equal(addition(w,v),w) ),
inference(rew,[status(thm),theory(equality)],[10527,1299]),
[iquote('0:Rew:10527.1,1299.1')] ).
cnf(10622,plain,
leq(addition(u,one),addition(u,star(v))),
inference(spr,[status(thm),theory(equality)],[10514,569]),
[iquote('0:SpR:10514.0,569.0')] ).
cnf(10785,plain,
equal(addition(multiplication(u,star(u)),star(u)),star(u)),
inference(res,[status(thm),theory(equality)],[12,2246]),
[iquote('0:Res:12.0,2246.0')] ).
cnf(10829,plain,
equal(addition(star(u),multiplication(u,star(u))),star(u)),
inference(rew,[status(thm),theory(equality)],[9,10785]),
[iquote('0:Rew:9.0,10785.0')] ).
cnf(11048,plain,
leq(addition(u,one),addition(star(v),u)),
inference(spr,[status(thm),theory(equality)],[9,10622]),
[iquote('0:SpR:9.0,10622.0')] ).
cnf(79525,plain,
leq(addition(star(skc3),multiplication(skc2,star(skc3))),star(skc3)),
inference(spr,[status(thm),theory(equality)],[10829,7160]),
[iquote('0:SpR:10829.0,7160.0')] ).
cnf(79658,plain,
equal(addition(star(skc3),multiplication(skc2,star(skc3))),star(skc3)),
inference(res,[status(thm),theory(equality)],[79525,10576]),
[iquote('0:Res:79525.0,10576.0')] ).
cnf(79735,plain,
leq(addition(multiplication(skc2,star(skc3)),one),star(skc3)),
inference(spr,[status(thm),theory(equality)],[79658,11048]),
[iquote('0:SpR:79658.0,11048.0')] ).
cnf(79906,plain,
leq(addition(one,multiplication(skc2,star(skc3))),star(skc3)),
inference(rew,[status(thm),theory(equality)],[9,79735]),
[iquote('0:Rew:9.0,79735.0')] ).
cnf(80019,plain,
leq(multiplication(star(skc2),one),star(skc3)),
inference(res,[status(thm),theory(equality)],[79906,295]),
[iquote('0:Res:79906.0,295.0')] ).
cnf(80025,plain,
leq(star(skc2),star(skc3)),
inference(rew,[status(thm),theory(equality)],[4,80019]),
[iquote('0:Rew:4.0,80019.0')] ).
cnf(80026,plain,
$false,
inference(mrr,[status(thm)],[80025,8]),
[iquote('0:MRR:80025.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE041+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 14:10:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 71.14/71.33
% 71.14/71.33 SPASS V 3.9
% 71.14/71.33 SPASS beiseite: Proof found.
% 71.14/71.33 % SZS status Theorem
% 71.14/71.33 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 71.14/71.33 SPASS derived 58859 clauses, backtracked 0 clauses, performed 0 splits and kept 14091 clauses.
% 71.14/71.33 SPASS allocated 140915 KBytes.
% 71.14/71.33 SPASS spent 0:01:09.78 on the problem.
% 71.14/71.33 0:00:00.03 for the input.
% 71.14/71.33 0:00:00.03 for the FLOTTER CNF translation.
% 71.14/71.33 0:00:00.47 for inferences.
% 71.14/71.33 0:00:00.00 for the backtracking.
% 71.14/71.33 0:01:09.08 for the reduction.
% 71.14/71.33
% 71.14/71.33
% 71.14/71.33 Here is a proof with depth 8, length 46 :
% 71.14/71.33 % SZS output start Refutation
% See solution above
% 71.14/71.33 Formulae used in the proof : goals additive_idempotence multiplicative_right_identity additive_commutativity order star_unfold_right star_unfold_left additive_associativity left_distributivity star_induction_left
% 71.14/71.33
%------------------------------------------------------------------------------