TPTP Problem File: GRP028-4.p
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%--------------------------------------------------------------------------
% File : GRP028-4 : TPTP v9.0.0. Released v2.6.0.
% Domain : Group Theory (Semigroups)
% Problem : In semigroups, left and right solutions => right id exists
% Version : [CL73] axioms.
% English : If there are left and right solutions, then there is a right
% identity element.
% Refs : [Cha70] Chang (1970), The Unit Proof and the Input Proof in Th
% : [CL73] Chang & Lee (1973), Symbolic Logic and Mechanical Theo
% Source : [CL73]
% Names : Example 1 [CL73]
% Status : Unsatisfiable
% Rating : 0.00 v5.4.0, 0.06 v5.3.0, 0.10 v5.2.0, 0.00 v2.6.0
% Syntax : Number of clauses : 5 ( 3 unt; 0 nHn; 3 RR)
% Number of literals : 11 ( 0 equ; 7 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 1 ( 1 usr; 0 prp; 3-3 aty)
% Number of functors : 3 ( 3 usr; 0 con; 1-2 aty)
% Number of variables : 17 ( 0 sgn)
% SPC : CNF_UNS_RFO_NEQ_HRN
% Comments :
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cnf(associativity1,axiom,
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ) ).
cnf(associativity2,axiom,
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) ) ).
cnf(left_soln,hypothesis,
product(left_solution(X,Y),X,Y) ).
cnf(right_soln,hypothesis,
product(X,right_solution(X,Y),Y) ).
%----There is an element for which no X is identity
cnf(prove_there_is_a_right_identity,negated_conjecture,
~ product(not_identity(X),X,not_identity(X)) ).
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