## TSTP Solution File: KLE089+1 by SPASS---3.9

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE089+1 : TPTP v6.4.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n011.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 14:21:31 EDT 2017

% Result   : Theorem 0.06s
% Output   : Refutation 0.06s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   11 (  11 unt;   0 nHn;  11 RR)
%            Number of literals    :   11 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

%------------------------------------------------------------------------------
cnf(1,axiom,
file('KLE089+1.p',unknown),
[] ).

cnf(7,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE089+1.p',unknown),
[] ).

cnf(11,axiom,
~ equal(multiplication(domain__dfg(skc2),skc3),zero),
file('KLE089+1.p',unknown),
[] ).

cnf(12,axiom,
file('KLE089+1.p',unknown),
[] ).

cnf(13,axiom,
file('KLE089+1.p',unknown),
[] ).

cnf(21,axiom,
file('KLE089+1.p',unknown),
[] ).

cnf(80,plain,
inference(spr,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpR:12.0,1.0')] ).

cnf(338,plain,
inference(spr,[status(thm),theory(equality)],[13,21]),
[iquote('0:SpR:13.0,21.0')] ).

cnf(4281,plain,
inference(spr,[status(thm),theory(equality)],[7,338]),
[iquote('0:SpR:7.0,338.0')] ).

cnf(4310,plain,
equal(multiplication(domain__dfg(skc2),skc3),zero),
inference(rew,[status(thm),theory(equality)],[80,4281,12]),
[iquote('0:Rew:80.0,4281.0,12.0,4281.0')] ).

cnf(4311,plain,
\$false,
inference(mrr,[status(thm)],[4310,11]),
[iquote('0:MRR:4310.0,11.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : KLE089+1 : TPTP v6.4.0. Released v4.0.0.
% 0.00/0.04  % Command  : run_spass %d %s
% 0.03/0.23  % Computer : n011.star.cs.uiowa.edu
% 0.03/0.23  % Model    : x86_64 x86_64
% 0.03/0.23  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23  % Memory   : 32218.625MB
% 0.03/0.23  % OS       : Linux 3.10.0-514.6.1.el7.x86_64
% 0.03/0.23  % CPULimit : 300
% 0.03/0.23  % DateTime : Thu Jul 13 17:24:22 CDT 2017
% 0.03/0.23  % CPUTime  :
% 0.06/0.58
% 0.06/0.58  SPASS V 3.9
% 0.06/0.58  SPASS beiseite: Proof found.
% 0.06/0.58  % SZS status Theorem
% 0.06/0.58  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.58  SPASS derived 3202 clauses, backtracked 0 clauses, performed 0 splits and kept 794 clauses.
% 0.06/0.58  SPASS allocated 88480 KBytes.
% 0.06/0.58  SPASS spent	0:00:00.32 on the problem.
% 0.06/0.58  		0:00:00.02 for the input.
% 0.06/0.58  		0:00:00.02 for the FLOTTER CNF translation.
% 0.06/0.58  		0:00:00.02 for inferences.
% 0.06/0.58  		0:00:00.00 for the backtracking.
% 0.06/0.58  		0:00:00.25 for the reduction.
% 0.06/0.58
% 0.06/0.58
% 0.06/0.58  Here is a proof with depth 2, length 11 :
% 0.06/0.58  % SZS output start Refutation
% See solution above
% 0.06/0.58  % SZS output end Refutation
% 0.06/0.58  Formulae used in the proof : additive_identity domain1 goals additive_commutativity left_distributivity
% 0.06/0.58
%------------------------------------------------------------------------------
```