## TSTP Solution File: KLE089+1 by Muscadet---4.5

View Problem - Process Solution

```%------------------------------------------------------------------------------
% Problem  : KLE089+1 : TPTP v6.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw

% Computer : n177.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-573.1.1.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Oct  8 14:00:34 EDT 2015

% Result   : Theorem 0.02s
% Output   : Proof 0.02s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : KLE089+1 : TPTP v6.2.0. Released v4.0.0.
% 0.00/0.02  % Command  : muscadet %s
% 0.01/1.06  % Computer : n177.star.cs.uiowa.edu
% 0.01/1.06  % Model    : x86_64 x86_64
% 0.01/1.06  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.01/1.06  % Memory   : 32286.75MB
% 0.01/1.06  % OS       : Linux 2.6.32-573.1.1.el6.x86_64
% 0.01/1.06  % CPULimit : 300
% 0.01/1.06  % DateTime : Tue Oct  6 22:02:56 CDT 2015
% 0.01/1.06  % CPUTime  :
% 0.02/1.23
% 0.02/1.23
% 0.02/1.23  SZS status Theorem for theBenchmark.p
% 0.02/1.23
% 0.02/1.23  SZS output start Proof for theBenchmark.p
% 0.02/1.23
% 0.02/1.23  * * * * * * * * * * * * * * * * * * * * * * * *
% 0.02/1.23  in the following, N is the number of a (sub)theorem
% 0.02/1.23         E is the current step
% 0.02/1.23           or the step when a hypothesis or conclusion has been added or modified
% 0.02/1.23  hyp(N,H,E) means that H is an hypothesis of (sub)theorem N
% 0.02/1.23  concl(N,C,E) means that C is the conclusion of (sub)theorem N
% 0.02/1.23  obj_ct(N,C) means that C is a created object or a given constant
% 0.02/1.23  addhyp(N,H,E) means add H as a new hypothesis for N
% 0.02/1.23  newconcl(N,C,E) means that the new conclusion of N is C
% 0.02/1.23             (C replaces the precedent conclusion)
% 0.02/1.23  a subtheorem N-i or N+i is a subtheorem of the (sub)theorem N
% 0.02/1.23     N is proved if all N-i have been proved (&-node)
% 0.02/1.23               or if one N+i have been proved (|-node)
% 0.02/1.23  the initial theorem is numbered 0
% 0.02/1.23
% 0.02/1.23  * * * theorem to be proved
% 0.02/1.23  ![A, B]: (addition(domain(A), antidomain(B))=antidomain(B)=>multiplication(domain(A), B)=zero)
% 0.02/1.23
% 0.02/1.23  * * * proof :
% 0.02/1.23
% 0.02/1.23  * * * * * * theoreme 0 * * * * * *
% 0.02/1.23  *** newconcl(0, ![A, B]: (addition(domain(A), antidomain(B))=antidomain(B)=>multiplication(domain(A), B)=zero), 1)
% 0.02/1.23  *** explanation : initial theorem
% 0.02/1.23  ------------------------------------------------------- action ini
% 0.02/1.23  create object(s) z2 z1
% 0.02/1.23  *** newconcl(0, addition(domain(z1), antidomain(z2))=antidomain(z2)=>multiplication(domain(z1), z2)=zero, 2)
% 0.02/1.23  *** because concl((0, ![A, B]: (addition(domain(A), antidomain(B))=antidomain(B)=>multiplication(domain(A), B)=zero)), 1)
% 0.02/1.23  *** explanation : the universal variable(s) of the conclusion is(are) instantiated
% 0.02/1.23  ------------------------------------------------------- rule !
% 0.02/1.23  *** newconcl(0, seul(domain(z1)::A, seul(antidomain(z2)::B, seul(addition(A, B)::C, antidomain(z2)::C)))=>seul(domain(z1)::D, multiplication(D, z2)::zero), 3)
% 0.02/1.23  *** because concl(0, addition(domain(z1), antidomain(z2))=antidomain(z2)=>multiplication(domain(z1), z2)=zero, 2)
% 0.02/1.23  *** explanation : elimination of the functional symbols of the conclusion
% 0.02/1.23  for example, p(f(X)) is replaced by only(f(X)::Y, p(Y))
% 0.02/1.23  ------------------------------------------------------- elifun
% 0.02/1.23  create object z3
% 0.02/1.23  *** addhyp(0, domain(z1)::z3, 4)
% 0.02/1.23
% 0.02/1.23  create object z4
% 0.02/1.23  *** addhyp(0, antidomain(z2)::z4, 4)
% 0.02/1.23
% 0.02/1.23  *** addhyp(0, antidomain(z2)::z4, 4)
% 0.02/1.23  *** newconcl(0, seul(domain(z1)::A, multiplication(A, z2)::zero), 4)
% 0.02/1.23  *** because concl(0, seul(domain(z1)::A, seul(antidomain(z2)::B, seul(addition(A, B)::C, antidomain(z2)::C)))=>seul(domain(z1)::D, multiplication(D, z2)::zero), 3)
% 0.02/1.23  *** explanation : to prove H=>C, assume H and prove C
% 0.02/1.23  ------------------------------------------------------- rule =>
% 0.02/1.23  *** addhyp(0, z4=z5, 5)
% 0.02/1.23  *** because hyp(0, antidomain(z2)::z4, 4), hyp(0, antidomain(z2)::z5, 4), 4
% 0.02/1.23  *** explanation : z4 and z5 have the same definition
% 0.02/1.23  *** because hyp(0, z4=z5, 5), hyp(0, addition(z3, z4)::z5, 4)
% 0.02/1.23  *** explanation : z5 is replaced by z4 in the hypotheses
% 0.02/1.23  ------------------------------------------------------- treatequal_hyp
% 0.02/1.23  *** newconcl(0, multiplication(z3, z2)::zero, 7)
% 0.02/1.23  *** because concl(0, seul(domain(z1)::A, multiplication(A, z2)::zero), 4), hyp(0, domain(z1)::z3, 4)
% 0.02/1.23  *** explanation : _ is replaced by z3 in multiplication(_, z2)::zero
% 0.02/1.23  ------------------------------------------------------- rule concl_only
% 0.02/1.23  *** newconcl(0, seul(multiplication(z3, z2)::A, A=zero), 8)
% 0.02/1.23  *** because concl(0, multiplication(z3, z2)::zero, 7)
% 0.02/1.23  *** explanation :  FX::Y is rewriten only(FX::Z, Z=Y)
% 0.02/1.23  ------------------------------------------------------- rule concl2pts
% 0.02/1.23  *** addhyp(0, multiplication(z3, z2)::z6, 9), newconcl(0, z6=zero, 9)
% 0.02/1.23  *** because concl(0, seul(multiplication(z3, z2)::A, A=zero), 8)
% 0.02/1.23  *** explanation : creation of object z6 and of its definition
% 0.02/1.23  ------------------------------------------------------- rule concl_only
% 0.02/1.23  *** because obj_ct(0, z6)
% 0.02/1.23  *** explanation : rule if obj_ct(A, B)then addhyp(A, addition(B, zero)::B, _)
% 0.02/1.23  built from the axiom axiom:additive_identity
% 0.02/1.23  *** addhyp(0, multiplication(z4, z2)::zero, 63)
% 0.02/1.23  *** because hyp(0, antidomain(z2)::z4, 4), obj_ct(0, z2)
% 0.02/1.23  *** explanation : rule if (hyp(A, antidomain(B)::C, _), obj_ct(A, B))then addhyp(A, multiplication(C, B)::zero, _)
% 0.02/1.23  built from the axiom axiom:domain1
% 0.02/1.23  ------------------------------------------------------- rule axiom:domain1_1
% 0.02/1.23  *** because hyp(0, addition(z3, z4)::z4, 6), hyp(0, multiplication(z4, z2)::zero, 63), hyp(0, multiplication(z3, z2)::z6, 9), hyp(0, multiplication(z4, z2)::zero, 63), obj_ct(0, z3), obj_ct(0, z4), obj_ct(0, z2)
% 0.02/1.23  *** explanation : rule if (hyp(A, addition(C, E)::B, _), hyp(A, multiplication(B, D)::H, _), hyp(A, multiplication(C, D)::F, _), hyp(A, multiplication(E, D)::G, _), obj_ct(A, C), obj_ct(A, E), obj_ct(A, D))then addhyp(A, addition(F, G)::H, _)
% 0.02/1.23  built from the axiom axiom:left_distributivity
% 0.02/1.23  ------------------------------------------------------- rule axiom:left_distributivity_1
% 0.02/1.23  *** addhyp(0, z6=zero, 65)
% 0.02/1.23  *** because hyp(0, addition(z6, zero)::z6, 21), hyp(0, addition(z6, zero)::zero, 64), 64
% 0.02/1.23  *** explanation : z6 and zero have the same definition