TPTP Problem File: HAL005+1.p
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%--------------------------------------------------------------------------
% File : HAL005+1 : TPTP v9.0.0. Released v2.6.0.
% Domain : Homological Algebra
% Problem : Lemma for the short Five Lemma, Part 2
% Version : [TPTP] axioms.
% English :
% Refs : [Wei94] Weibel (1994), An Introduction to Homological Algebra
% Source : [TPTP]
% Names :
% Status : CounterSatisfiable
% Rating : 0.00 v8.1.0, 0.25 v7.5.0, 0.60 v7.4.0, 0.00 v7.3.0, 0.33 v7.0.0, 0.00 v6.4.0, 0.33 v6.2.0, 0.64 v6.1.0, 0.45 v6.0.0, 0.54 v5.5.0, 0.50 v5.4.0, 0.57 v5.3.0, 0.71 v5.2.0, 0.67 v5.0.0, 0.57 v4.1.0, 0.80 v4.0.0, 0.75 v3.7.0, 0.33 v3.5.0, 0.67 v3.4.0, 0.33 v3.2.0, 0.67 v3.1.0, 1.00 v2.6.0
% Syntax : Number of formulae : 32 ( 17 unt; 0 def)
% Number of atoms : 96 ( 22 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 64 ( 0 ~; 0 |; 39 &)
% ( 2 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 0 prp; 1-4 aty)
% Number of functors : 17 ( 17 usr; 14 con; 0-3 aty)
% Number of variables : 76 ( 67 !; 9 ?)
% SPC : FOF_CSA_RFO_SEQ
% Comments :
%--------------------------------------------------------------------------
%----Include Standard homological algebra axioms
include('Axioms/HAL001+0.ax').
%--------------------------------------------------------------------------
fof(alpha_morphism,axiom,
morphism(alpha,a,b) ).
fof(beta_morphism,axiom,
morphism(beta,b,c) ).
fof(gamma_morphism,axiom,
morphism(gamma,d,e) ).
fof(delta_morphism,axiom,
morphism(delta,e,r) ).
fof(f_morphism,axiom,
morphism(f,a,d) ).
fof(g_morphism,axiom,
morphism(g,b,e) ).
fof(h_morphism,axiom,
morphism(h,c,r) ).
fof(alpha_injection,axiom,
injection(alpha) ).
fof(gamma_injection,axiom,
injection(gamma) ).
fof(beta_surjection,axiom,
surjection(beta) ).
fof(delta_surjection,axiom,
surjection(delta) ).
fof(alpha_beta_exact,axiom,
exact(alpha,beta) ).
fof(gamma_delta_exact,axiom,
exact(gammma,delta) ).
fof(alpha_g_f_gamma_commute,axiom,
commute(alpha,g,f,gamma) ).
fof(beta_h_g_delta_commute,axiom,
commute(beta,h,g,delta) ).
fof(f_surjection,hypothesis,
surjection(f) ).
fof(h_surjection,hypothesis,
surjection(h) ).
fof(lemma3,axiom,
! [E] :
( element(E,e)
=> ? [R,B1] :
( element(R,r)
& apply(delta,E) = R
& element(B1,b)
& apply(h,apply(beta,B1)) = R
& apply(delta,apply(g,B1)) = R ) ) ).
fof(lemma8,conjecture,
! [E] :
( element(E,e)
=> ? [B1,E1,A] :
( element(B1,b)
& element(E1,e)
& subtract(e,apply(g,B1),E) = E1
& element(A,a)
& apply(gamma,apply(f,A)) = E1
& apply(g,apply(alpha,A)) = E1 ) ) ).
%--------------------------------------------------------------------------