## TSTP Solution File: KLE011+1 by SPASS---3.9

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE011+1 : TPTP v6.4.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32218.625MB
% OS       : Linux 3.10.0-514.6.1.el7.x86_64
% CPULimit : 300s
% DateTime : Fri Jul 14 14:21:21 EDT 2017

% Result   : Theorem 0.06s
% Output   : Refutation 0.06s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   15
% Syntax   : Number of clauses     :   48 (  24 unt;   0 nHn;  48 RR)
%            Number of literals    :   82 (   0 equ;  44 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

%------------------------------------------------------------------------------
cnf(1,axiom,
test__dfg(skc3),
file('KLE011+1.p',unknown),
[] ).

cnf(2,axiom,
test__dfg(skc2),
file('KLE011+1.p',unknown),
[] ).

cnf(4,axiom,
file('KLE011+1.p',unknown),
[] ).

cnf(5,axiom,
equal(multiplication(u,one),u),
file('KLE011+1.p',unknown),
[] ).

cnf(6,axiom,
equal(multiplication(one,u),u),
file('KLE011+1.p',unknown),
[] ).

cnf(11,axiom,
file('KLE011+1.p',unknown),
[] ).

cnf(15,axiom,
( ~ complement(u,v)
| equal(multiplication(v,u),zero) ),
file('KLE011+1.p',unknown),
[] ).

cnf(16,axiom,
( ~ complement(u,v)
| equal(multiplication(u,v),zero) ),
file('KLE011+1.p',unknown),
[] ).

cnf(17,axiom,
( ~ complement(u,v)
file('KLE011+1.p',unknown),
[] ).

cnf(18,axiom,
file('KLE011+1.p',unknown),
[] ).

cnf(20,axiom,
( ~ test__dfg(u)
| ~ equal(c(u),v)
| complement(u,v) ),
file('KLE011+1.p',unknown),
[] ).

cnf(22,axiom,
file('KLE011+1.p',unknown),
[] ).

cnf(23,axiom,
file('KLE011+1.p',unknown),
[] ).

cnf(24,axiom,
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
file('KLE011+1.p',unknown),
[] ).

cnf(25,axiom,
file('KLE011+1.p',unknown),
[] ).

cnf(26,plain,
inference(rew,[status(thm),theory(equality)],[18,25,23]),
[iquote('0:Rew:18.0,25.0,18.0,25.0,18.0,25.0,18.0,25.0,23.0,25.0,23.0,25.0')] ).

cnf(27,plain,
( ~ equal(c(skc2),u)
| complement(skc2,u) ),
inference(res,[status(thm),theory(equality)],[2,20]),
[iquote('0:Res:2.0,20.0')] ).

cnf(30,plain,
( ~ equal(c(skc3),u)
| complement(skc3,u) ),
inference(res,[status(thm),theory(equality)],[1,20]),
[iquote('0:Res:1.0,20.0')] ).

cnf(59,plain,
( ~ complement(u,v)
inference(spr,[status(thm),theory(equality)],[17,11]),
[iquote('0:SpR:17.1,11.0')] ).

cnf(81,plain,
complement(skc3,c(skc3)),
inference(eqr,[status(thm),theory(equality)],[30]),
[iquote('0:EqR:30.0')] ).

cnf(94,plain,
complement(skc2,c(skc2)),
inference(eqr,[status(thm),theory(equality)],[27]),
[iquote('0:EqR:27.0')] ).

cnf(186,plain,
inference(spr,[status(thm),theory(equality)],[18,11]),
[iquote('0:SpR:18.0,11.0')] ).

cnf(195,plain,
inference(spr,[status(thm),theory(equality)],[4,18]),
[iquote('0:SpR:4.0,18.0')] ).

cnf(198,plain,
inference(spr,[status(thm),theory(equality)],[11,18]),
[iquote('0:SpR:11.0,18.0')] ).

cnf(207,plain,
inference(rew,[status(thm),theory(equality)],[18,198]),
[iquote('0:Rew:18.0,198.0')] ).

cnf(209,plain,
inference(rew,[status(thm),theory(equality)],[207,26]),
[iquote('0:Rew:207.0,26.0')] ).

cnf(279,plain,
( ~ complement(u,v)
inference(spr,[status(thm),theory(equality)],[17,23]),
[iquote('0:SpR:17.1,23.0')] ).

cnf(291,plain,
( ~ complement(u,v)
inference(rew,[status(thm),theory(equality)],[6,279]),
[iquote('0:Rew:6.0,279.1')] ).

cnf(309,plain,
( ~ complement(u,v)
inference(spr,[status(thm),theory(equality)],[17,22]),
[iquote('0:SpR:17.1,22.0')] ).

cnf(321,plain,
( ~ complement(u,v)
inference(rew,[status(thm),theory(equality)],[5,309]),
[iquote('0:Rew:5.0,309.1')] ).

cnf(335,plain,
( ~ complement(u,v)
| ~ equal(one,one)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
inference(spl,[status(thm),theory(equality)],[59,24]),
[iquote('0:SpL:59.1,24.0')] ).

cnf(349,plain,
( ~ complement(u,v)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[335]),
[iquote('0:Obv:335.1')] ).

cnf(350,plain,
( ~ complement(u,v)
| ~ equal(zero,zero)
| ~ equal(zero,zero)
| complement(v,u) ),
inference(rew,[status(thm),theory(equality)],[16,349,15]),
[iquote('0:Rew:16.1,349.2,15.1,349.1')] ).

cnf(351,plain,
( ~ complement(u,v)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[350]),
[iquote('0:Obv:350.2')] ).

cnf(568,plain,
complement(c(skc2),skc2),
inference(res,[status(thm),theory(equality)],[94,351]),
[iquote('0:Res:94.0,351.0')] ).

cnf(790,plain,
inference(spr,[status(thm),theory(equality)],[207,11]),
[iquote('0:SpR:207.0,11.0')] ).

cnf(878,plain,
inference(rew,[status(thm),theory(equality)],[18,790]),
[iquote('0:Rew:18.0,790.0')] ).

cnf(2063,plain,
( ~ complement(u,v)
inference(spr,[status(thm),theory(equality)],[291,207]),
[iquote('0:SpR:291.1,207.0')] ).

cnf(2285,plain,
( ~ complement(u,v)
inference(spr,[status(thm),theory(equality)],[321,195]),
[iquote('0:SpR:321.1,195.0')] ).

cnf(2334,plain,
( ~ complement(c(skc2),skc2)
inference(spl,[status(thm),theory(equality)],[321,209]),
[iquote('0:SpL:321.1,209.0')] ).

cnf(2335,plain,
( ~ complement(u,v)
inference(rew,[status(thm),theory(equality)],[11,2285]),
[iquote('0:Rew:11.0,2285.1')] ).

cnf(2368,plain,
( ~ complement(c(skc2),skc2)
inference(rew,[status(thm),theory(equality)],[207,2334,186]),
[iquote('0:Rew:207.0,2334.1,186.0,2334.1')] ).

cnf(2369,plain,
( ~ complement(c(skc2),skc2)
inference(rew,[status(thm),theory(equality)],[2335,2368,878,2063]),
[iquote('0:Rew:2335.1,2368.1,878.0,2368.1,2063.1,2368.1')] ).

cnf(2370,plain,
( ~ complement(c(skc2),skc2)
inference(rew,[status(thm),theory(equality)],[11,2369]),
[iquote('0:Rew:11.0,2369.1')] ).

cnf(2371,plain,
inference(mrr,[status(thm)],[2370,568]),
[iquote('0:MRR:2370.0,568.0')] ).

cnf(2380,plain,
( ~ complement(skc3,c(skc3))
| ~ equal(one,one) ),
inference(spl,[status(thm),theory(equality)],[59,2371]),
[iquote('0:SpL:59.1,2371.0')] ).

cnf(2384,plain,
~ complement(skc3,c(skc3)),
inference(obv,[status(thm),theory(equality)],[2380]),
[iquote('0:Obv:2380.1')] ).

cnf(2385,plain,
\$false,
inference(mrr,[status(thm)],[2384,81]),
[iquote('0:MRR:2384.0,81.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : KLE011+1 : TPTP v6.4.0. Released v4.0.0.
% 0.00/0.04  % Command  : run_spass %d %s
% 0.02/0.23  % Computer : n028.star.cs.uiowa.edu
% 0.02/0.23  % Model    : x86_64 x86_64
% 0.02/0.23  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23  % Memory   : 32218.625MB
% 0.02/0.23  % OS       : Linux 3.10.0-514.6.1.el7.x86_64
% 0.02/0.23  % CPULimit : 300
% 0.02/0.24  % DateTime : Thu Jul 13 17:11:51 CDT 2017
% 0.02/0.24  % CPUTime  :
% 0.06/0.50
% 0.06/0.50  SPASS V 3.9
% 0.06/0.50  SPASS beiseite: Proof found.
% 0.06/0.50  % SZS status Theorem
% 0.06/0.50  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.50  SPASS derived 1841 clauses, backtracked 0 clauses, performed 0 splits and kept 704 clauses.
% 0.06/0.50  SPASS allocated 99396 KBytes.
% 0.06/0.50  SPASS spent	0:00:00.25 on the problem.
% 0.06/0.50  		0:00:00.02 for the input.
% 0.06/0.50  		0:00:00.02 for the FLOTTER CNF translation.
% 0.06/0.50  		0:00:00.01 for inferences.
% 0.06/0.50  		0:00:00.00 for the backtracking.
% 0.06/0.50  		0:00:00.17 for the reduction.
% 0.06/0.50
% 0.06/0.50
% 0.06/0.50  Here is a proof with depth 3, length 48 :
% 0.06/0.50  % SZS output start Refutation
% See solution above
% 0.06/0.50  % SZS output end Refutation
% 0.06/0.50  Formulae used in the proof : goals additive_idempotence multiplicative_right_identity multiplicative_left_identity additive_commutativity test_2 additive_associativity test_3 right_distributivity left_distributivity
% 0.06/0.50
%------------------------------------------------------------------------------
```