TPTP Problem File: SET113+1.p
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% File : SET113+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% Domain : Set Theory
% Problem : Uniqueness of 1st and 2nd when X is not an ordered pair of sets
% Version : [Qua92] axioms : Reduced & Augmented > Complete.
% English :
% Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% Source : [Qua92]
% Names :
% Status : Theorem
% Rating : 1.00 v5.4.0
% Syntax : Number of formulae : 44 ( 16 unt; 0 def)
% Number of atoms : 107 ( 24 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 68 ( 5 ~; 4 |; 31 &)
% ( 19 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 0 prp; 1-2 aty)
% Number of functors : 26 ( 26 usr; 5 con; 0-3 aty)
% Number of variables : 91 ( 84 !; 7 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
% Bugfixed : v5.4.0 - Bugfixes to SET005+0 axiom file.
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%----Include set theory axioms
include('Axioms/SET005+0.ax').
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%----OP8: Uniqueness of 1st and 2nd when X is not an ordered pair of sets
%----All four theorems combined.
fof(unique_1st_and_2nd_in_pair_of_non_sets1,conjecture,
! [U,V,X] :
( ( ? [Y,Z] :
( member(Y,universal_class)
& member(Z,universal_class)
& X = ordered_pair(Y,Z) )
& X = U
& V = X )
| ( first(X) = U
& second(X) = V ) ) ).
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