TSTP Solution File: KLE039+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE039+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 8.40s 8.61s
% Output : Refutation 8.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of clauses : 52 ( 27 unt; 0 nHn; 52 RR)
% Number of literals : 79 ( 0 equ; 30 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(addition(u,u),u),
file('KLE039+2.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE039+2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE039+2.p',unknown),
[] ).
cnf(7,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE039+2.p',unknown),
[] ).
cnf(8,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE039+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE039+2.p',unknown),
[] ).
cnf(10,axiom,
leq(addition(one,multiplication(u,star(u))),star(u)),
file('KLE039+2.p',unknown),
[] ).
cnf(11,axiom,
leq(addition(one,multiplication(star(u),u)),star(u)),
file('KLE039+2.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE039+2.p',unknown),
[] ).
cnf(14,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE039+2.p',unknown),
[] ).
cnf(15,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE039+2.p',unknown),
[] ).
cnf(16,axiom,
( ~ leq(star(skc3),star(star(skc3)))
| ~ leq(star(star(skc2)),star(skc2)) ),
file('KLE039+2.p',unknown),
[] ).
cnf(17,axiom,
( ~ leq(addition(multiplication(u,v),w),v)
| leq(multiplication(star(u),w),v) ),
file('KLE039+2.p',unknown),
[] ).
cnf(51,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[8,7]),
[iquote('0:SpR:8.1,7.0')] ).
cnf(59,plain,
( ~ equal(u,u)
| leq(u,u) ),
inference(spl,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpL:2.0,9.0')] ).
cnf(64,plain,
leq(u,u),
inference(obv,[status(thm),theory(equality)],[59]),
[iquote('0:Obv:59.0')] ).
cnf(110,plain,
( ~ leq(addition(u,v),w)
| equal(addition(u,addition(v,w)),w) ),
inference(spr,[status(thm),theory(equality)],[12,8]),
[iquote('0:SpR:12.0,8.1')] ).
cnf(116,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[2,12]),
[iquote('0:SpR:2.0,12.0')] ).
cnf(118,plain,
equal(addition(addition(u,v),w),addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[7,12]),
[iquote('0:SpR:7.0,12.0')] ).
cnf(126,plain,
equal(addition(u,addition(v,w)),addition(v,addition(u,w))),
inference(rew,[status(thm),theory(equality)],[12,118]),
[iquote('0:Rew:12.0,118.0')] ).
cnf(144,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[116,9]),
[iquote('0:SpL:116.0,9.0')] ).
cnf(148,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[144]),
[iquote('0:Obv:144.0')] ).
cnf(154,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[7,148]),
[iquote('0:SpR:7.0,148.0')] ).
cnf(168,plain,
leq(u,addition(v,addition(w,u))),
inference(spr,[status(thm),theory(equality)],[12,154]),
[iquote('0:SpR:12.0,154.0')] ).
cnf(172,plain,
leq(u,addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[7,168]),
[iquote('0:SpR:7.0,168.0')] ).
cnf(182,plain,
( ~ leq(addition(u,v),w)
| leq(v,w) ),
inference(spr,[status(thm),theory(equality)],[51,168]),
[iquote('0:SpR:51.1,168.0')] ).
cnf(195,plain,
( ~ leq(u,v)
| equal(addition(multiplication(u,w),multiplication(v,w)),multiplication(v,w)) ),
inference(spr,[status(thm),theory(equality)],[8,15]),
[iquote('0:SpR:8.1,15.0')] ).
cnf(224,plain,
( ~ leq(addition(u,v),w)
| leq(u,w) ),
inference(spr,[status(thm),theory(equality)],[51,172]),
[iquote('0:SpR:51.1,172.0')] ).
cnf(335,plain,
( ~ leq(u,v)
| equal(addition(multiplication(w,u),multiplication(w,v)),multiplication(w,v)) ),
inference(spr,[status(thm),theory(equality)],[8,14]),
[iquote('0:SpR:8.1,14.0')] ).
cnf(417,plain,
leq(multiplication(u,star(u)),star(u)),
inference(res,[status(thm),theory(equality)],[10,182]),
[iquote('0:Res:10.0,182.0')] ).
cnf(447,plain,
( ~ leq(multiplication(u,v),w)
| ~ leq(w,v)
| leq(multiplication(star(u),w),v) ),
inference(spl,[status(thm),theory(equality)],[8,17]),
[iquote('0:SpL:8.1,17.0')] ).
cnf(495,plain,
leq(one,star(u)),
inference(res,[status(thm),theory(equality)],[11,224]),
[iquote('0:Res:11.0,224.0')] ).
cnf(1700,plain,
( ~ leq(addition(u,v),w)
| equal(addition(u,w),w) ),
inference(spr,[status(thm),theory(equality)],[110,116]),
[iquote('0:SpR:110.1,116.0')] ).
cnf(1712,plain,
( ~ leq(addition(u,v),w)
| equal(addition(v,addition(u,w)),w) ),
inference(spr,[status(thm),theory(equality)],[110,126]),
[iquote('0:SpR:110.1,126.0')] ).
cnf(1790,plain,
( ~ leq(addition(u,v),w)
| equal(addition(v,w),w) ),
inference(rew,[status(thm),theory(equality)],[1700,1712]),
[iquote('0:Rew:1700.1,1712.1')] ).
cnf(2992,plain,
( ~ leq(one,u)
| equal(addition(v,multiplication(u,v)),multiplication(u,v)) ),
inference(spr,[status(thm),theory(equality)],[4,195]),
[iquote('0:SpR:4.0,195.1')] ).
cnf(3153,plain,
( ~ leq(one,u)
| equal(addition(v,multiplication(v,u)),multiplication(v,u)) ),
inference(spr,[status(thm),theory(equality)],[3,335]),
[iquote('0:SpR:3.0,335.1')] ).
cnf(3279,plain,
( ~ leq(star(u),star(u))
| leq(multiplication(star(u),star(u)),star(u)) ),
inference(res,[status(thm),theory(equality)],[417,447]),
[iquote('0:Res:417.0,447.0')] ).
cnf(3297,plain,
leq(multiplication(star(u),star(u)),star(u)),
inference(mrr,[status(thm)],[3279,64]),
[iquote('0:MRR:3279.0,64.0')] ).
cnf(3328,plain,
( ~ leq(star(u),star(u))
| leq(multiplication(star(star(u)),star(u)),star(u)) ),
inference(res,[status(thm),theory(equality)],[3297,447]),
[iquote('0:Res:3297.0,447.0')] ).
cnf(3342,plain,
leq(multiplication(star(star(u)),star(u)),star(u)),
inference(mrr,[status(thm)],[3328,64]),
[iquote('0:MRR:3328.0,64.0')] ).
cnf(9206,plain,
equal(addition(multiplication(star(u),u),star(u)),star(u)),
inference(res,[status(thm),theory(equality)],[11,1790]),
[iquote('0:Res:11.0,1790.0')] ).
cnf(9232,plain,
equal(addition(star(u),multiplication(star(u),u)),star(u)),
inference(rew,[status(thm),theory(equality)],[7,9206]),
[iquote('0:Rew:7.0,9206.0')] ).
cnf(10214,plain,
( ~ leq(one,u)
| leq(v,multiplication(u,v)) ),
inference(spr,[status(thm),theory(equality)],[2992,148]),
[iquote('0:SpR:2992.1,148.0')] ).
cnf(11328,plain,
( ~ leq(one,u)
| equal(multiplication(star(u),u),star(u)) ),
inference(spr,[status(thm),theory(equality)],[9232,3153]),
[iquote('0:SpR:9232.0,3153.1')] ).
cnf(24795,plain,
( ~ leq(one,u)
| ~ leq(one,star(u))
| leq(u,star(u)) ),
inference(spr,[status(thm),theory(equality)],[11328,10214]),
[iquote('0:SpR:11328.1,10214.1')] ).
cnf(24806,plain,
( ~ leq(one,star(u))
| leq(star(star(u)),star(u)) ),
inference(spr,[status(thm),theory(equality)],[11328,3342]),
[iquote('0:SpR:11328.1,3342.0')] ).
cnf(24841,plain,
leq(star(star(u)),star(u)),
inference(mrr,[status(thm)],[24806,495]),
[iquote('0:MRR:24806.0,495.0')] ).
cnf(24842,plain,
~ leq(star(skc3),star(star(skc3))),
inference(mrr,[status(thm)],[16,24841]),
[iquote('0:MRR:16.1,24841.0')] ).
cnf(24850,plain,
( ~ leq(one,u)
| leq(u,star(u)) ),
inference(mrr,[status(thm)],[24795,495]),
[iquote('0:MRR:24795.1,495.0')] ).
cnf(24948,plain,
~ leq(one,star(skc3)),
inference(res,[status(thm),theory(equality)],[24850,24842]),
[iquote('0:Res:24850.1,24842.0')] ).
cnf(24980,plain,
$false,
inference(mrr,[status(thm)],[24948,495]),
[iquote('0:MRR:24948.0,495.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE039+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n017.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 08:50:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 8.40/8.61
% 8.40/8.61 SPASS V 3.9
% 8.40/8.61 SPASS beiseite: Proof found.
% 8.40/8.61 % SZS status Theorem
% 8.40/8.61 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.40/8.61 SPASS derived 18049 clauses, backtracked 0 clauses, performed 0 splits and kept 4020 clauses.
% 8.40/8.61 SPASS allocated 102687 KBytes.
% 8.40/8.61 SPASS spent 0:00:08.08 on the problem.
% 8.40/8.61 0:00:00.04 for the input.
% 8.40/8.61 0:00:00.03 for the FLOTTER CNF translation.
% 8.40/8.61 0:00:00.13 for inferences.
% 8.40/8.61 0:00:00.00 for the backtracking.
% 8.40/8.61 0:00:07.84 for the reduction.
% 8.40/8.61
% 8.40/8.61
% 8.40/8.61 Here is a proof with depth 9, length 52 :
% 8.40/8.61 % SZS output start Refutation
% See solution above
% 8.40/8.61 Formulae used in the proof : additive_idempotence multiplicative_right_identity multiplicative_left_identity additive_commutativity order star_unfold_right star_unfold_left additive_associativity right_distributivity left_distributivity goals star_induction_left
% 8.40/8.61
%------------------------------------------------------------------------------