TSTP Solution File: KLE040+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE040+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 2.00s 2.22s
% Output : Refutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of clauses : 33 ( 19 unt; 0 nHn; 33 RR)
% Number of literals : 48 ( 0 equ; 18 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('KLE040+2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE040+2.p',unknown),
[] ).
cnf(7,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE040+2.p',unknown),
[] ).
cnf(8,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE040+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE040+2.p',unknown),
[] ).
cnf(10,axiom,
leq(addition(one,multiplication(u,star(u))),star(u)),
file('KLE040+2.p',unknown),
[] ).
cnf(11,axiom,
leq(addition(one,multiplication(star(u),u)),star(u)),
file('KLE040+2.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE040+2.p',unknown),
[] ).
cnf(15,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE040+2.p',unknown),
[] ).
cnf(16,axiom,
( ~ leq(addition(multiplication(u,v),w),v)
| leq(multiplication(star(u),w),v) ),
file('KLE040+2.p',unknown),
[] ).
cnf(18,axiom,
( ~ leq(star(skc3),multiplication(star(skc3),star(skc3)))
| ~ leq(multiplication(star(skc2),star(skc2)),star(skc2)) ),
file('KLE040+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(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(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(382,plain,
( ~ leq(multiplication(u,v),w)
| ~ leq(w,v)
| leq(multiplication(star(u),w),v) ),
inference(spl,[status(thm),theory(equality)],[8,16]),
[iquote('0:SpL:8.1,16.0')] ).
cnf(441,plain,
leq(multiplication(u,star(u)),star(u)),
inference(res,[status(thm),theory(equality)],[10,182]),
[iquote('0:Res:10.0,182.0')] ).
cnf(520,plain,
leq(one,star(u)),
inference(res,[status(thm),theory(equality)],[11,224]),
[iquote('0:Res:11.0,224.0')] ).
cnf(3277,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(3739,plain,
( ~ leq(star(u),star(u))
| leq(multiplication(star(u),star(u)),star(u)) ),
inference(res,[status(thm),theory(equality)],[441,382]),
[iquote('0:Res:441.0,382.0')] ).
cnf(3757,plain,
leq(multiplication(star(u),star(u)),star(u)),
inference(mrr,[status(thm)],[3739,64]),
[iquote('0:MRR:3739.0,64.0')] ).
cnf(3758,plain,
~ leq(star(skc3),multiplication(star(skc3),star(skc3))),
inference(mrr,[status(thm)],[18,3757]),
[iquote('0:MRR:18.1,3757.0')] ).
cnf(11952,plain,
( ~ leq(one,u)
| leq(v,multiplication(u,v)) ),
inference(spr,[status(thm),theory(equality)],[3277,148]),
[iquote('0:SpR:3277.1,148.0')] ).
cnf(12631,plain,
~ leq(one,star(skc3)),
inference(res,[status(thm),theory(equality)],[11952,3758]),
[iquote('0:Res:11952.1,3758.0')] ).
cnf(12634,plain,
$false,
inference(mrr,[status(thm)],[12631,520]),
[iquote('0:MRR:12631.0,520.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE040+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 09:26:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.00/2.22
% 2.00/2.22 SPASS V 3.9
% 2.00/2.22 SPASS beiseite: Proof found.
% 2.00/2.22 % SZS status Theorem
% 2.00/2.22 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.00/2.22 SPASS derived 8974 clauses, backtracked 0 clauses, performed 0 splits and kept 1918 clauses.
% 2.00/2.22 SPASS allocated 94011 KBytes.
% 2.00/2.22 SPASS spent 0:00:01.82 on the problem.
% 2.00/2.22 0:00:00.03 for the input.
% 2.00/2.22 0:00:00.03 for the FLOTTER CNF translation.
% 2.00/2.22 0:00:00.06 for inferences.
% 2.00/2.22 0:00:00.00 for the backtracking.
% 2.00/2.22 0:00:01.67 for the reduction.
% 2.00/2.22
% 2.00/2.22
% 2.00/2.22 Here is a proof with depth 7, length 33 :
% 2.00/2.22 % SZS output start Refutation
% See solution above
% 2.00/2.22 Formulae used in the proof : additive_idempotence multiplicative_left_identity additive_commutativity order star_unfold_right star_unfold_left additive_associativity left_distributivity star_induction_left goals
% 2.00/2.22
%------------------------------------------------------------------------------